ABSTRACT
Title of dissertation: ESSAYS ON PRODUCT INTRODUCTION
Xuezhen Tao
Doctor of Philosophy, 2018
Dissertation directed by: Professor Andrew Sweeting
Department of Economics
This dissertation contributes to the study of product introduction from two
aspects. Chapter 1 and 2 study firms’ strategic decisions in product release fre-
quencies as well as their dynamic pricing and innovation decisions in the flagship
smartphone market. Chapter 3 studies consumers’ multi-version consumption in
response to periodic new product releases in the video game industry.
In Chapter 1, I extend the dynamic innovation framework developed by Ericson
and Pakes [1995] by incorporating firms’ choices of their product release timing. In
this new framework, firms first commit to their product release frequencies, then
based on their committed schedules, I solve for their pricing and innovation decisions
upon each product release. The welfare analysis in the counterfactual analysis shows
that when the market shift from the duopoly to a monopoly, social welfare improves
as higher innovation dominates higher prices and slower releases in welfare impact.
In Chapter 2, I adopt the framework developed in Chapter 1, and further
extend the discussion to provide managerial implications on firms’ optimal prod-
uct release strategies in two dimensions: staggering in product release timing, and
maintaining regular release schedules. Based on the simulated market outcome,
firms should stagger their product releases with others and maintain the regular
form of their release schedules.
In Chapter 3, I study consumers’ responses to firms’ new product releases in
the video game industries. Video game players are observed to continue playing
their old games even after their new purchases, which contrasts with the single-
product consumption assumption in the existing durable good literature. This pa-
per develops a new framework where video game players allocate their playing time
within their game portfolios based on a latent variable, “game preference.” The
game preference is constructed to be flexible as it captures both contemporaneous
heterogeneities across game versions and game modes, and also intertemporal het-
erogeneities across individuals like past gaming activities. We estimate the model
parameters based on the data provided by Wharton Consumer Analytic Initiatives
and report how our model fits the data pattern in three dimensions: game purchase
decisions, game play decisions and game duration.
ESSAYS ON PRODUCT INTRODUCTION
by
Xuezhen Tao
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2018
Advisory Committee:
Professor Andrew Sweeting, Chair/Advisor
Professor Ginger Jin
Professor Daniel Vincent
Professor Jie Zhang
Professor Bo Bobby Zhou
©c Copyright by
Xuezhen Tao
2018

Dedication
To my wife, Weijia, and my parents.
ii
Acknowledgments
Here, in the stage of graduating, I consider myself extremely lucky. I once
hesitated and got frustrated for so many times, but still manage to present to the
public what I have accomplished in these years. These contributions might be trivial
and may need further development before it would have impacts on the real economy,
but at least this is a gigantic milestone for me that I would cherish forever. I owe
my gratitude to all the people who have offered help in the process of this thesis;
thank you so much for making this thesis possible.
First and foremost, I would like to thank my main advisor, Professor Andrew
Sweeting. It is really hard to enumerate all the support he has provided in the past
three years. Whenever I have encountered a certain problem, Andrew will always be
there to give suggestions and insights. He also helped revise my job market paper
for so many times, and I will always keep those drafts full of his written suggestions.
I would also like to thank my advisors, Professor Ginger Jin and Professor
Daniel Vincent. Ginger is so patient when discussing the stent data project, and I
managed to learn a lot about empirical studies from her. Dan could always provide
straightforward explanation and intuition on seemingly complicated matters, which
helps me a lot to avoid unnecessary trials. Thanks are due to Professor Bobby Zhou
and Professor Jie Zhang for agreeing to serve on my thesis committee. I have also
learned a lot on marketing research from the talk with them.
I owe my deepest thanks to my family - my parents who unconditionally sup-
port my studies, and have always stood by me. For Weijia, thank you so much for
iii
joining my life during my PhD study. You are always my “co-author.”
Thank you all!
iv
Table of Contents
Dedication ii
Acknowledgements iii
List of Tables vii
List of Figures viii
1 Overview 1
2 Market Competition and Product Introduction: A Study of the Flagship
Smartphone Industry 5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 State space . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 Consumer’s problem . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.3 Firm’s problem . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.4 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.5 Bounding the state space . . . . . . . . . . . . . . . . . . . . . 29
2.3 Data and industry background . . . . . . . . . . . . . . . . . . . . . . 30
2.4 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4.1 Demand estimation . . . . . . . . . . . . . . . . . . . . . . . . 36
2.4.2 Supply estimation . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.5 Estimation result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.5.1 Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.5.2 Empirical results . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.6 Counterfactual: effects of different release schedules . . . . . . . . . . 46
2.6.1 Release schedules in the duopoly market . . . . . . . . . . . . 47
2.6.2 Release schedules in the monopoly market . . . . . . . . . . . 52
2.7 Appendix: Algorithms for solving the model . . . . . . . . . . . . . . 55
v
3 Managerial Implications for Durable Goods Release Schedule 57
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Staggering product releases . . . . . . . . . . . . . . . . . . . . . . . 59
3.3 Release schedule switching . . . . . . . . . . . . . . . . . . . . . . . . 63
3.3.1 Model setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.3.2 The value of commitment . . . . . . . . . . . . . . . . . . . . 70
3.3.3 The cost of switching . . . . . . . . . . . . . . . . . . . . . . . 73
3.4 Appendix: Commitment vs. no-commitment in product releases . . . 74
4 A Tale of Old and New: Multi-Version Consumption in the Video Game
Industry 81
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.2 Data and empirical summaries . . . . . . . . . . . . . . . . . . . . . . 84
4.2.1 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2.2 Multiproduct consumption . . . . . . . . . . . . . . . . . . . . 87
4.2.3 Persistent gaming preferences . . . . . . . . . . . . . . . . . . 90
4.2.4 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.3.1 Utility from game play . . . . . . . . . . . . . . . . . . . . . . 96
4.3.2 Game purchase decision . . . . . . . . . . . . . . . . . . . . . 98
4.4 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.4.1 Likelihood function of game play . . . . . . . . . . . . . . . . 100
4.4.2 Likelihood function of game purchase . . . . . . . . . . . . . . 102
4.5 Estimation result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.5.1 Parameter estimates . . . . . . . . . . . . . . . . . . . . . . . 104
4.5.2 Model fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.6 Counterfactual analyasis . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.8 Appendix: Supplemental summary statistics . . . . . . . . . . . . . . 115
Bibliography 118
vi
List of Tables
2.1 Possible quality increment . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 Announcement dates of smartphones expanding quality frontier from
Apple and Samsung . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.4 List of parameters to be estimated . . . . . . . . . . . . . . . . . . . 36
2.5 Parameter Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.6 Empirical and Simulated Moments . . . . . . . . . . . . . . . . . . . 43
2.7 Simulated policy function: Symmetric duopoly . . . . . . . . . . . . . 48
2.8 Simulated policy function: Monopoly and symmetric duopoly . . . . 53
3.1 Simulated policy function: R1 = R2 = 12, ∆R = 0, 3, 6 . . . . . . . . . 63
3.2 Model specifications with or without committed product releases . . . 78
4.1 Summary statistics: by players . . . . . . . . . . . . . . . . . . . . . . 87
4.3 Summaries on PB player count . . . . . . . . . . . . . . . . . . . . . 89
4.4 Summaries on PB percentage across initial and current games . . . . 89
4.5 Regression of players’ future purchase probabilities on current playing
time and PB behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.6 Average total duration across players (seconds) . . . . . . . . . . . . 92
4.7 Regression on game duration and game play dummy over past dura-
tion in the same mode . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.8 List of parameters to be estimated . . . . . . . . . . . . . . . . . . . 101
4.9 Parameter estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.10 Imputed and actual game session durations (in seconds) . . . . . . . . 109
4.11 Imputed probabilities of game play between play and no-play obser-
vations in players’ most recent version . . . . . . . . . . . . . . . . . 110
4.12 Imputed purchase probabilities between buyers and non-buyers . . . . 110
4.13 Comparison of game duration with and without the single-game re-
striction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.14 Comparison of game duration with and without game preferences . . 113
4.15 Summary statistics: by game sessions . . . . . . . . . . . . . . . . . . 116
4.17 Imputed and actual game duration by game mode and version . . . . 117
vii
List of Figures
2.1 Smartphone quality frontier for top five manufacture in the US . . . . 31
2.2 Firms’ prices, investments and profits over quality differences and
consumers’ average holding quality . . . . . . . . . . . . . . . . . . . 44
2.3 Apple and Samsung’s market share within each 12-month window . . 45
2.4 Apple and Samsung’s quality path . . . . . . . . . . . . . . . . . . . . 45
2.5 Firm 1’s market share in each 12-month period with different release
schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.6 Firm 1’s market share over time . . . . . . . . . . . . . . . . . . . . . 54
3.1 Optimal prices over quality differences in different staggering release
schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.2 Graphic illustration of ∆R = 0, 3, 6, R1 = R2 = 12 . . . . . . . . . . . 62
3.3 Partial commitment: example . . . . . . . . . . . . . . . . . . . . . . 65
3.4 Deviation decisions by new product quality and consumers’ holdings . 71
3.5 Firm’s payoff and average price across new product quality and con-
sumers’ holdings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.6 Deviation decisions by new product quality and consumers’ holdings . 75
3.7 The monopolist’s value and prices across new product quality for
R = 3 and R = 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.8 Average price and market share over product qualities: with or with-
out commitment of release . . . . . . . . . . . . . . . . . . . . . . . . 79
3.9 Consumers’ demand within each 12-month for R = 1, 2, 3 . . . . . . . 79
4.1 Game activation over time . . . . . . . . . . . . . . . . . . . . . . . . 88
4.2 Correspondence between imputed and actual game duration . . . . . 107
viii
Chapter 1: Overview
New product introductions are prevalent across various industries, and fre-
quently observed in our daily life: Apple’s new iPhone models with better graphics
and more features released in every autumn, Intel’s faster and more energy-efficient
CPU models released based on its “tick-tock” schedule, sports video games’ new ver-
sions released periodically in every game season, new car models with new designs
released at the end of each year, etc. It is natural to attribute these product intro-
duction scenarios to firms’ investment on product introduction, which generates the
potential new product features and better product components to be incorporated
into the new products. In this thesis, I highlight an equally important factor during
this process, firms’ product release strategy, and illustrate how firms utilize both
strategies to schedule their new product introductions.
I first became interested in the product introduction pattern when I started to
follow Apple’s new phone releases. In every autumn when it was close to the release
confeerence, Apple fans talked about what the new iPhone models look like, and
what upgrades would be incorporated in the new model. After the release, people
then shift their topic, get either excited or disappointed at the new phones, and start
another cycle of forecasting phones in the next year. While consumers may only
1
focus on each specific iPhone model and comment on its specifications like “Why
does it come with only 1GB RAM while Android flagships are already equipped
with 3GB RAM,” what really attracts me and motivates the first two chapters
in this thesis is Apple’s long term plan of new product releases, where it has to
guarantee enough quality improvement between consecutive releases to motivate
the upgrade purchases while not making consumers concerned about being obsolete
when they make the purchase. After all, when a firm designs new products while
taking into account what it would release later, everything becomes complicated
and challenging.
Just take an easy example and think about how a new iPhone is “designed in
California”: engineers in Apple come up with ideas about how the new smartphone
looks like, then adopt its hardware components, e.g. CPU, RAM, GPU, battery,
from the suppliers. While Apple could become determined to introduce the best
phone ever and adopt the best of every component, it might risk losing current
sales because of the higher price tags due to the higher cost, and also the future
sales as the current buyers will have little incentive to buy if future products are
not significantly better than this model. A better solution would be to spread out
the potential improvement over several product generations and keep a steady pace
of product improvement. and, if necessary, even alter the pace of product releases.
Note that these adjustments are in addition to firms’ long term innovation decisions:
firms can choose their optimal investment decisions in improving product qualities in
the long run, but conditional on their investment level, they still have the flexibility
of materializing these improvement in one product or across several generations.
2
The first two chapters propose a new framework which allows firms to ex-
plicitly choose the format of their release schedules. In this framework, firms first
simultaneously select their release frequencies, then they play a dynamic innovation
and pricing game conditional on the pre-committed release dates. This framework
facilitates the discussion of how different release schedules could impact the market
outcome, including both social welfare and firms’ profits. For marketing practices,
this framework can also be utilized to shed light on how firms should arrange their
product release schedules to maximize their long-term profits in the durable good
market.
One assumption imposed in this framework is that each consumer only uses
at most one unit of smartphone at any given time. This assumption is plausible
for smartphones where consumers gain little value from their second units, it is
hard to argue that consumers always shift their total product usage towards the
new products after purchase. In the third chapter, Andrew Sweeting and I use a
dataset which documents video game players’ activities in a major sports video game
franchise, and find two interesting patterns.
First, players utilize multiple game versions in their portfolios. Around 13%
to 20%, ranging across game versions, of players continue to play their old games
after buying the new game versions, which we term as “port-back.”
Second, players exhibit persistent gaming experiences towards certain game
modes over time. For example, a player may spent consistently more time in the
career mode than average, which cannot be explained by the game mode specific
preference.
3
To accommodate these two patterns, we construct a framework where play-
ers allocate their playing time across different games modes and game versions in
their portfolios, and make purchase decisions in regards to new versions periodically
released in the market. With this framework, we find that players’ playing time
across different game versions are weakly substituted: when players are restricted
to only play the newest game version in their portfolio, their playing time in the new
game only increase by 0.3%. In contrast, we also find strong correlation in players
game preferences across periods: when players preferences are only determined by
common utility factors like version fixed effect, mode fixed effect, time fixed effect
and player random effect, their playing time in the new game will fall by 13.9%, and
in the old game by 6.9%.
4
Chapter 2: Market Competition and Product Introduction: A Study
of the Flagship Smartphone Industry
2.1 Introduction
Successful firms in durable consumer technology industries (e.g., smartphones,
tablets, personal computers) are typically oligopolists who periodically release new
products that contain a number of incremental improvements. These firms have
to trade-off how frequently to release new products with how many innovations
they can incorporate in each release. However, this trade-off is absent from the
recent literature on innovation that has followed the tradition of Ericson and Pakes
[1995] (EP hereafter), because in these models firms simply choose how much to
invest in a stochastic innovation process and new innovations are assumed to be
incorporated into products as soon as they are realized. The objective of this paper
is to incorporate the distinction between release frequencies and quality changes
into a dynamic innovation model that can be used to examine both optimal firm
strategies and classic welfare questions from the literature on innovation.
There are at least three a priori reasons for including product releases explic-
itly into the model. First, in many consumer technology industries product releases
5
are observed to be very regular. For example, in the smartphone industry, Apple
releases new products around September each year, while Samsung has made two
releases per year, around March and around September. We also observe regular
product updates in the automobile industry [Blonigen et al., 2017], and in both
of these consumer-focused industries the pattern likely reflects the fact that new
releases can be made using incremental improvements in many components, and
do not require a single drastic innovation as in the hard drive [Igami, 2017] and
upstream CPU industries [Goettler and Gordon, 2011, GG hereafter]. In EP-style
models, however, realized innovations tend to be irregular, because innovation suc-
cess is stochastic even if a firm exerts steady effort over time
Second, the willingness to pay of forward-looking consumers for leading edge
durable products is likely to depend on when they expect new versions to be released.
Therefore if forward-looking consumers are to be included in the model as allowed
by GG, it is natural to also include an explicit model of the release decisions of
firms.
Third, it is plausible that some counterfactual environment changes will cause
release frequencies and the average magnitude of incremental improvements to change
in different directions whereas an EP-style framework would force them to change in
only one direction. I specifically find this to be the case when I change the market
structure from duopoly to monopoly, as a monopolist is predicted to release prod-
ucts less frequently but to increase the overall innovation rate, so that total welfare
increases.
The structure of my empirical model is that firms first choose, and fully commit
6
to, the frequency with which they release new products, and then, conditional on
these frequencies, they play a dynamic game, with a Markov Perfect Equilibrium,
where they choose the prices of new releases and how much to invest to increase the
quality of each release. Consumers are forward-looking and make optimal choices
about when to replace their current holdings based on the products that are currently
available and their expectations of future prices and releases.
The model is estimated using data on flagship models sold by the leading
smartphone manufacturers, Apple and Samsung. The smartphone industry is a
consumer-oriented technology industry with regular release cycles and some uncer-
tainties about how innovative each release will be. It therefore fits the assumptions
of my model quite well. I allow for phones sold by other manufacturers to be present
in the market, but do not model these manufacturers in a strategic way, in order to
limit the computational burden. I develop a two-stage estimator that exploits the
fact that under my assumptions, consumer choice sets will be known to be fixed for
several periods. The supply side is estimated using a nested fixed point procedure
where, following GG, I use backwards induction in order to avoid problems that
may arise from a multiplicity of equilibria. Simulated and actual moments are very
close, indicating that this quite restricted parameterization is able to fit the data.
Given the parameter estimates, I use the model to examine the welfare im-
plications of market concentration, and to provide suggestions on firms’ optimal
product release schedules. When I change the market structure from a hypothetical
symmetric and single-product duopoly to a monopoly, price goes up by 30%, the
innovation rate goes up by 7.4%, and product releases become less frequent from
7
once every 6 months to once every 12 months. Consumer surplus and social welfare
both increase as the monopolist’s higher innovation is only partially offset by the
higher prices and slower releases.
My model is simplified in several aspects, which facilitates the computation
but introduces several limitations as well. First, I adopt a single-product firm setup
where I interpret product quality as reflecting the average quality of the flagship
smartphones sold by each firm. In doing so I ignore important portfolio aspects of
firm’s problem. Second, I only include Apple and Samsung as strategic players, and
represent all other manufacturers as a composite and non-strategic firm “Other”.
While firms like HTC and LG also introduce popular flagship smartphones, their
quality frontiers fall behind the two major players and I assume they have very
limited market impact in the flagship market. Third, when I estimate the model I
assume that firms fully commit to their regular release schedules and cannot change
them afterwards. While I do not see changes in schedules, consumers may believe
that changes are possible and adjust their behaviors as a result. I examine this
assumption in the counterfactual by comparing outcome to a model with partial
commitment and show that commitment is valuable.
It has been discussed for decades whether, in general, market competition
increases innovation. Schumpeter [1942] proposed a negative relationship between
market competition and firms’ innovation, where Arrow [1962] argued that com-
petition might increase innovation, as a monopolist would not want to replace its
own profits. The empirical literature has found evidence of an inverted U-shaped
relationship between competition and innovation across industries [Aghion et al.,
8
2005].
For the durable good markets, Carlton and Gertner [1989] show that com-
petition with consumers’ existing holdings incentivizes the monopolist to innovate
more and results in higher social surplus; Waldman [1993, 1996] further extends
this notion of competition with consumers’ holdings into planned obsolescence and
concludes that the monopolist over-invests to reduce the value of consumers’ cur-
rent holdings and increases consumers’ future upgrade purchases. Gowrisankaran
and Rysman [2012] provide a framework to track consumer demand in the durable
good market with a rapid price decline and fast quality improvement. These papers
highlight the importance of accounting for consumers’ current holdings when study-
ing durable good firms’ product innovation decisions, and this paper extends their
setup by allowing firms to control the pace of new product releases, which indirectly
affects the evolution of consumer holdings.
This paper also contributes to the literature of dynamic oligopoly competi-
tion. Pakes and McGuire [1994] and EP established the basis for the oligopoly
dynamic investment literature. This framework has been widely adapted and ap-
plied to various industries and problems, including mergers [Gowrisankaran, 1999,
Gowrisankaran and Holmes, 2004], research joint ventures [Song, 2011], and invest-
ment with product differentiation [Narajabad and Watson, 2011].1 Eizenberg [2014],
Nosko [2010], and Fan and Yang [2016] study firms’ product positioning decisions
in a static setting, and Sweeting [2013] in a dynamic setup. Papers studying smart-
1Pakes and McGuire [2001], Ferris et al. [2012], Doraszelski and Pakes [2007], Borkovsky et al.
[2010, 2012], and Farias et al. [2012] propose various algorithms and methods to solve this type of
dynamic problems.
9
phone manufacturers focus on bargaining between smartphone manufacturers and
wireless carriers [Sinkinson, 2014, Luo, 2016], vertical integration of upstream hard-
ware makers and smartphone manufacturers [Yang, 2016], and smartphone manu-
facturers’ product portfolio choice [Fan and Yang, 2016, Wang, 2017].
This paper develops a dynamic oligopoly model in the durable good context,
and it is closely related to GG. GG also uses a dynamic demand and dynamic
supply framework to study firms’ competition in the CPU market. They show
that a more concentrated market structure leads to higher innovation and higher
price, and consumer surplus is lower as the loss of higher prices dominates the gain
from higher innovation. This paper extends their framework by allowing firms to
separately control their product releases aside from the innovation process.
The rest of the paper is organized as follows. Section 2 describes the model
setup. Section 3 provides details on data. Section 4 describes estimation strategies
and Section 5 provides the results. Section 6 presents counterfactual results on
product release frequencies.
2.2 Model
I present a dynamic model of a differentiated-product oligopoly selling durable
goods. Although this model is designed to describe the smartphone industry, it could
be applied to other industries where durable goods with regular release schedules are
sold, like the automobile industry where manufacturers carry out minor or major
improvements in their new products every year [Blonigen et al., 2017].
10
In this model, in every period each consumer observes all firms’ current prod-
uct offerings and either buys a new smartphone and scraps her current smartphone
(“purchasing”), or continues to use her current smartphone for another period
(“waiting”).2 Consumers’ values of purchasing and waiting, which govern their
purchase decisions, are affected by their expectations of firms’ product qualities,
prices, and future release schedules. For example, if future products are expected to
have higher qualities and lower prices, or if a better product will be available soon,
consumers prefer to wait rather than immediately buy new phones.
Firms choose and commit to their product release frequencies simultaneously
at the beginning of the model, which determines their product release schedules in all
future periods. Given these pre-committed schedules, firms play a dynamic oligopoly
game where they choose prices and invest to improve their product qualities when
they are scheduled to release new products, and continue with their previous product
offerings in other periods.
2.2.1 State space
Time is discrete with infinite horizon t = 1, 2, , . . ., and each period represents
one month in both estimation and the counterfactual analysis. A finite number of
firms are indexed by j = 1, 2, . . . , J , and an infinite number of consumers are indexed
by i. Both firms and consumers are infinitely present with no entry or exit. In the
model, there are two active firms (Apple and Samsung) making strategic choices of
2According to comScore reports, smartphone penetration in the US mobile market increased
from 60% in July 2013 to 79% in January 2016. This high penetration rate motivates my assump-
tion that every consumer uses smartphone when not buying.
11
their release schedules, innovations, and product prices, and a third firm, “Other,”
included to capture competition from other firms in the flagship smartphone market,
with its product characteristics evolving over time in a deterministic form.3 I only
include firm “Other” in the model when estimating the parameters and remove it
in the counterfactual analysis.
Firms choose their release schedules, in terms of number of periods between
their consecutive releases, simultaneously before their further product decisions.4
To alleviate the computational burden, I restrict firms’ possible choices of interval
length, Rj, to factors of 12 months, e.g. 3, 6, 12, so firms’ release schedules take the
form of Z releases every year where Z is some positive integer. For example, Rj = 6
indicates that firm j releases a new product in every 6 months, or equivalently, twice
every year. In order to uniquely characterize firms’ release schedules given their
choices of release frequencies, I further assume that all firms release new products
simultaneously in at least one period, so starting from that period, both forward
and backward, all firms’ future release schedules are fully determined.5 Next I will
discuss how each state variable in consumer’s and firm’s problem is defined, and
how these variables evolve over time.
3In July 2013, the first month observed in my data, 92.2% of smartphone subscribers were using
iPhones or Android phones, and this percentage increased over time. So firm “Other” essentially
captures all other firms selling Android smartphones, such as HTC and LG. More details on firm
Other will be provided when setting up firm’s problem.
4This setup implicitly assumes that every firm’s new products are released regularly and re-
peatedly. This assumption is made in accordance with the observed release patterns in data where
both Apple and Samsung release new phones near September, while Samsung also release new
phones in March.
5One possibility ruled out by this assumption is that, two firms choose to both release once
every year, but their release periods are six months apart from each other. This is considered in
the counterfactual analysis where firms are allowed to stagger their releases from those of their
rivals.
12
State of release schedule rt
In period t, each firm has an indicator, rjt = 1, 2, . . . , Rj, which measures
the number of periods left until its next scheduled product release. For example,
rjt = 1 means that at time t, firm j will release a new product in the next period.
The market level release state is defined by collecting all firm level indicators as
rt = (r1t, r2t, . . . , rJt). Given firm j’s commitment of release interval Rj, rjt evolves
in a deterministic way as follows:
 rj,t−1 − 1, if rj,t−1 > 1rjt =  .Rj, if rj,t−1 = 1
That is, rjt will decrease by one in each period until it reaches one, after which it is
then set back to Rj and firm j’s new phone is released. Firms are denoted as “active”
in periods in which they are scheduled to release new products (i.e. rjt = Rj), and
“inactive” in other periods.
Quality vector qt
I adopt the single-product firm setup where each firm sells only one product at
any time t with quality qjt and price pjt, which can be interpreted as average quality
and average price for the multi-product firms observed in data. With this setup,
I ignore the portfolio management decisions and only capture the upward quality
trend resulting from firms introducing new products and discontinuing the old ones.
The market level quality and price vectors at time t collect all firms’ product
13
characteristics as qt = (q1t, q2t, . . . , qJt), pt = (p1t, p2t, . . . , pJt), respectively. If
firm j releases a new product at time t, then qjt and pjt are set as its quality
and price; otherwise, firm j sells the same product as in the previous period (i.e.
q 6jt = qj,t−1, pjt = pj,t−1).
Product quality is discrete with nq levels of constant increment of δ, defined as
qjt ∈ {q, q+δ, . . . , q̄ , q+(nq−1)δ}. When firms release new products, they choose
an investment amount which dictates the probability of the higher quality increment.
Holding all other states as fixed, higher investment increases the probability of the
higher quality increment. More details are provided when I describe how I solve
firms’ optimal investment decisions.
In this model, firms’ product qualities are non-decreasing over time and will
exceed the upper bound after several product releases if not bounded. To maintain
this upward quality trend brought by new product introductions as well as restrict
quality values on the preset quality grids, I define the quality state space in a way
such that it is bounded, as in GG. More details are provided after I have defined
consumer’s and firm’s value functions are constructed.
Distribution of consumers’ holdings ∆t
Consumers are atomistic in the sense that each consumer believes her individ-
ual purchase decision has no effect on firms’ price and quality choices. To measure
competition from consumers’ current holdings in each firm’s problem, I follow GG
6Note that I assume prices cannot be adjusted when firms do not release new products so they
are informative when predicting sales in the future. This setup also assumes no quality depreciation
for the new products on sale.
14
and assume that firms keep track of the distribution of consumers’ holdings ∆, which
is constructed as follows. Denote the proportion of consumers using firm j’s phones
with quality qk , q+ (k− 1)δ at time t as ∆j∑kt. Summing up these proportions over
all manufacturers and quality levels gives jj,k ∆kt = 1. The market level distri-
bution variable is defined by collecting proportion values of all three firms (Apple,
Samsung and Other) and all nq quality levels as ∆t = {∆jkt}j,k.
In this model, ∆t evolves based on consumers’ purchase decisions. Intuitively
speaking, if firm j’s current product is not of quality qk, then ∆
j
k,t+1 only includes
consumers in ∆jkt choosing to wait; otherwise, ∆
j
k,t+1 also includes consumers not in
∆jkt but buying phones from firm j at time t. To formally express this evolution,
denote the probability of buying quality qk′ product from firm j
′ when using quality
′
qk product from firm j as Pr
j→j
k→k′ , where the arrow denotes the direction of change
due to consumers’ purchases. Then the imputed consumer distribution, ∆̃jk,t+1 is
calculated according to:
  ∑  j ′∆kt 1− Prj→j k→k′ , if qjt =6 qk
j j
′,qk′=qj′∆̃ tk,t+1 = ∑ ∑ . (2.1) ∆j′ j′→j j j→j′k′,tPrk′→k −∆kt Prk→k′ , if qjt = qk
j′,k′ j′,qk′=qj′t
In this expression, the two sub-cases correspond to when firm j does and does not
sell a product with quality qk, which determines if there is an inflow of consumers
into ∆jk,t+1. Note that the outflow of consumers only sums up over the qualities
of products that the other firms sell at time t instead of all quality levels. This is
15
because consumers are assumed never to exit the market, and the only way to leave
∆jk is to buy a new phone (other than firm j’s phone if its quality is qk).
The distribution variable ∆ is of high dimensions so it is necessary to use a
coarser approximation.7 To alleviate the computational burden while still including
∆ in the state space, I assume that ∆ can take values from 20 preset candidates
by first calculating imputed distribution ∆̃ as in (2.1), and then reallocating it
to its nearest candidate in terms of the average holding quality, to get the new
distribution ∆ in the new state. This reallocation proc∑eeds as follows: for each ∆
candidate, calculate its average holding quality as q∆ = k,j qk∆
j
k; next, the closest
∆ candidate to ∆̃ is determined by:
∣∣∣∣∣ ∣∣∣∣∣∣ ∑ ∣− j ∣∣∣∣∣
∣
∆t+1 = min q∆ ∆̃k,t+1qk ∣∣ . (2.2)∆
j,k
Equation (2.1), (2.2) jointly define the evolution of ∆ based on consumers’ purchases.
This assumption of using average holding quality to approximate ∆ evolution creates
bias in both mean quality and other moments like variances, skewness, etc. To
reduce the bias in mean quality, my 20 ∆ candidates are generated such that their
mean qualities are widely spread to cover extreme distributions, and also condense
around observed mean qualities so even minor changes in mean qualities are reflected
by moving across different ∆ candidates; for other biases like moments of second or
even higher orders, I assume that these biases do not affect firms’ profits significantly
when biases in mean quality levels are not large.
7Suppose each consumer proportion value ∆jkt is discrete and takes 5 values, then with only 5
quality levels and 3 firms, there will be in total 55×3 ≈ 3× 1010 possible values for ∆t.
16
Individual holding characteristics Iit
The individual holding characteristics Iit has two dimensions: its manufacturer
Jit and quality qit, which jointly determine consumers’ utilities of retaining their
current holdings. Iit stays the same if consumer i does not buy a new smartphone,
and this implicitly assumes no quality depreciation over usage; if she buys a new
phone, Jit and qit are set as the manufacturer and the quality of her new phone.
State space for consumers and firms
In each period, firms observe the state of the release schedule rt, market level
quality vectors qt, and distribution of consumers’ holdings ∆; consumers observe all
state variables that manufacturers observe as well as their own holdings.
2.2.2 Consumer’s problem
Each consumer uses one smartphone at any time. In each period, each con-
sumer attains utility from her smartphone based on its quality, manufacturer fixed
effect, other unobserved utility shock and any disutility of monetary payment for
the new phone purchase. If consumer i buys a new smartphone from firm j with
quality qjt, her utility of using this new smartphone for the current period is given
by 8
uijt(Iit) = αqqjt − αppjt + ξjt + εijt , Uijt + εijt, (2.3)
8I tried to allow for consumer types with different brand preferences but it did not help fit the
demand.
17
where αq, αp measure her marginal utilities over the quality and the price, respec-
tively. ξjt indicates the brand preference for firm j, and εijt captures idiosyncratic
variations, which is independently and identically distributed across consumers,
products and time as type I extreme values. If consumer i keeps using her current
phone (“waiting”), her utility is determined by the quality and the manufacturer of
her current holding as
ui0t(Iit) = αqqit + ξit + εi0t , Ui0t + εi0t, (2.4)
where qit represents the quality of consumer i’s most recent purchase at time t.
ξit is the brand preference of her current phone, which is time varying because
of changes in her individual holding characteristics. Given the assumption that
consumers’ outside options are using smartphones as well, it is this relative quality
difference between consumers’ current holdings and new smartphones that motivates
consumers’ repeated purchases and firms’ new phone introductions over time.
Each consumer makes her purchase decisions by maximizing her expected dis-
counted utility of different purchase options and the outside option. Omitting the
time and the consumer subscript, using the prime sign to indicate values in the
next period, and using j = 0 to denote the no-purchase option, a consumer’s choice
specific value for product j is
∑∫
vj(q,∆, I, r, ε) = u +β V (q′,∆′ij , I ′ ′j, r , ε′)f(ε′)dε′×h ′c(q |q,∆′, r, ε)g∆′(∆,q, r, ε),
q′
(2.5)
18
where hc is the consumer’s belief about future product qualities, g∆′ gives ∆
′ after
consumers’ purchases in the current period, and f is the density function of ε. I ′
includes the j subscript to capture the information from consumer purchase. The
value of ∆′ is defined at the start of the next period, and so reflects consumers’
purchases in the current period. That is why the evolution of ∆ only depends on
the state in the current period (∆,q, r), while the transition of q′ depends on ∆′. As
is discussed above, ∆′ is calculated by reallocating the imputed value to its nearest
∆ candidate, which always gives a unique value instead of a probability distribution
over multiple values, so I use a degenerate function g∆′(∆,q, r, ε) for ∆
′ evolution.
The consumer’s value function is defined by the value of her optimal choice,
including the no-purchase option, as
V (q,∆, I, r, ε) = max vj(q,∆, I, r, ε). (2.6)
j∈{0,...,J}
Assuming that ε is distributed as type I extreme value, integrating over ε
yields
 ∑ [ ∑ ]
V̄ (q,∆, I, r) = log exp Uj + β V̄ (q′,∆′, I ′, r′)hc(q′|q,∆′, r)g∆′(∆,q, r)  ,
j∈{0,...,J} q′
(2.7)
from which the choice-specific value function takes the form
∑
v̄j(q,∆, I, r) = Uj + β V̄ (q′,∆′, I ′, r′)hc(q′|q,∆′, r)g∆′(∆,q, r), (2.8)
q′
19
which differs from vj(q,∆, I, r, ε) only in the integration of ε. Using this choice-
specific value functions, consumer’s individual choice probability in state (q,∆, r, I)
is
∑ exp(v̄j(q,∆, I, r))sj|I(q,∆, r) = . (2.9)
k∈{0,...,J} exp(v̄k(q,∆, I, r))
Finally, aggregating individual choice probabilities of buying from each firm
across all types of consumer holdings, the market share of product j is calculated as
∑
sj(q,∆, r) = s
j
j|I=(j,q (q,∆, r)∆ . (2.10)k) k
k
2.2.3 Firm’s problem
In each period, active firms invest to improve qualities of their new products,
where higher investment increases the probability of the greater quality improve-
ments. Once the investment outcome is realized, active firms simultaneously choose
new prices which are fixed until the next release, and new products are available for
consumers to buy.
I adopt the single-product firm setup in this model because of the huge compu-
tational burden to allow for multiproduct firms. Accounting for multiple products
would be important for questions related to product portfolios, like product line
pricing problems and quality alignment problems [Eizenberg, 2014, Nosko, 2010,
Fan and Yang, 2016]. This paper studies firms’ competition over the release fre-
quency with a focus on the upward trend of product qualities and product portfolio
management decisions are ignored.
20
I now present how I solve a firm’s problem using backward induction within
each period, by first solving for optimal prices given their investment outcomes, and
then solve for firms’ optimal investment decisions.
Optimal pricing
Given firms’ choices of prices, the period profit function for firm j, excluding
investment cost, is
πj(p,q,∆, r) = Msj(p,q,∆, r)[pj −mcj] (2.11)
where M is the fixed market size, sj(·) is the market share for firm j, p is the
vector of J prices and mcj is the constant marginal cost for firm j’s phones. Price is
included in the market share function just to explicitly denote firms’ price choices.
In this model, firms cannot adjust their product offerings, including both prices
and qualities, until releasing new products, so firm j should take into account all
of the profit in the next Rj periods when choosing new prices and investments.
Suppose firm j becomes active in period t0, then given its choice of product price
and quality, pj and qj for the newly released product, the sum of its discounted
profits until its next release takes the form
Πj,t0(pj, qj,q−j,t0 ,∆t0 , rt0) = ∣ R∑j−1 ∣∣E βtMπj,t0+t({pj} ∪ p−j,t0+t, {qj} ∪ q− ∣j,t0+t,∆t0+t, rt0+t)∣∣ pj, qj,q− j,t0 ,∆t0 , rt0 ,t=0
(2.12)
21
where
E [πj,t0+t({pj} ∪ p−∑j,t0+t, {qj} ∪ q−j,t0+t,∆t0+t, rt0+t)|pj, qj,q−j,t0 ,∆t0 , rt0 ]
= πj,t0+t({pj} ∪ p−j,t0+t, {qj} ∪ q−j,t0+t,∆t0+t, rt0+t) (2.13)
q−j,t0+t
×hf (q−j,t0+t|qt0 ,∆t0 , rt0)Eg∆t +t(∆t0 ,qt0 ,pt0)j 0
In this expression, hf is firm j’s belief about its competitors’ future qualities,j
and Eg gives expected ∆ with randomness coming from the evolution of all other
state variables between t0 and t0 +Rj. {pj}∪p−j,t0+t and {qj}∪q−j,t0+t are market
level price and quality vectors, respectively, at time t, with firm j’s price and quality
explicitly specified as unchanged. In periods when no other firms are active, hf isj
degenerate and the quality will be the same as in the previous period. In other
periods when at least one other firm is active, hf is firm j’s belief of those activej
firms’ policies. All future expectations are conditional on state variables in period
t0, which is when firm j chooses optimal investment and prices.
With a slight abuse of notation, use a prime sign to denote variables when
firm j becomes active again (e.g. at t = t0 + Rj). After the investment outcome is
realized, firm j maximizes its expected discounted profits by choosing the optimal
prices, which solves the problem
( )
W̃j(qj,q−j,∆, r) = max Πj(pj, qj,q−j,∆, r)+β
RjE Wj(qj,q′ ′−j,∆ , r′)|pj, qj,q−j,∆ .
pj
(2.14)
22
Optimal investment
In the smartphone industry, downstream manufacturers’ quality improvement
comes from adopting better components (like CPU, RAM and display technology)
and improving the manufacturing process (like optimizing hardware compatibility).
Potential quality improvement for new products accumulate over time, and more
frequent releases will result in less cumulative upstream innovations available for
each new product. To fit this pattern, I normalize the innovation outcomes for the
smartphone manufacturers based on their release frequencies. The intuition is that
firms with rare releases can increase the quality by a higher amount in each release,
while firms with frequent releases are constrained for minor quality improvements.
The ultimate goal is to guarantee the same range of possible quality increments in
each 12 months regardless of these manufacturers’ chosen release frequencies.
To be specific, each firm’s possible quality increment is defined as follows: if
R 2R
Rj ≥ 6, its quality qj can be increased to either q jj + δ or qj + j δ; if Rj < 6, then6 6
its quality qj can be either unchanged, or increased to qj + δ. In this way, firms with
frequencies Rj ≥ 3 will have the same upper bound of quality increment per year
4δ, so in the long run, no firms will be at a systematic disadvantage from choosing
a particular schedule. More details can be found in Table 2.1.
For example, if firm A and firm B chooses RA = 12, RB = 6, then possible
qualities for their new products, given current quality level qA and q
′
B, are qA =
q + 2δ or q + 4δ, q′A A B = qB + δ or qB + 2δ. In this way, in every 12 months, both
firm A and B can increase their qualities by up to 4δ and down to 2δ so both firms
23
Table 2.1: Possible quality increment
Per release Per 12 months
R τ ′ τ ′′ Upper bound Lower bound
3 0 δ 0 4δ
6 δ 2δ 2δ 4δ
12 2δ 4δ 2δ 4δ
have the same range of possible quality outcomes. To facilitate future expressions,
denote firm j’s higher and lower possible quality increment in each release as τ ′′j and
τ ′j, respectively.
It is also worth noting that my choice of τ ′, the quality increment when the in-
novation fails, is not zero for R = 6, 12. When the innovation outcomes are realized,
firms have to wait until their next releases to adjust their product qualities again,
which puts firms with less frequent releases at disadvantage. This “guaranteed”
quality increment reduces the potential loss as from failed innovation outcome, and
maintain the quality competition in the long run.9 A possible concern arising from
this setup is that, this guaranteed quality improvement is equivalent to guaranteed
product release, which may affect players’ expectation and the equilibrium outcome.
I tested my model framework by setting τ ′ to zero, and find that this has very lit-
tle impact on players’ strategies, as all players in the model are risk neutral and
they only care about expected quality increments. More details can be found in the
appendix in Chapter 2.
I also adjust investment cost in each product release. Firms invest for quality
increments every time they are scheduled to release new products, and this model
9Even with some success guaranteed, this model predicts that firms always invest.
24
should guarantee that firms with similar expected quality increment per year need
similar investment regardless of their release frequencies. To incorporate this prop-
erty, I adjust firms’ investment costs based on their Rj such that firm j’s true cost
R
of investment x is jj x
10
j. For example, suppose RA = 12, RB = 6, and both3
firms invest x0 in each release, then both firms pay the same investment cost per 12
months: x 12A = x0 = 4x0, x
6
3 B
= x0 · 2 = 4x3 0.
Denote the scale of quality improvement for firm j’s product as τ = q′j j − qj,
which takes the value of τ ′j or τ
′′
j . Given firm j’s investment xj, the probability of
higher quality outcome is formulated as
( ′′ )| aj(q)xχj τj = τj x = , (2.15)1 + aj(q)x
where
{ ( )}
max q− qj
aj(q) = a0,j max 1, a1,j , max q , max{qj}.11 (2.16)
δ j
a1,j > 0 introduces an “innovation spillover effect” by increasing the invest-
ment efficiency, aj(q) for lagging firms such that, holding investment and all other
state variables fixed, higher quality outcomes are more likely for the lagging firms
than the leader firms. This mechanism makes it easier for the lagging firm to catch
up with the leader firm.
Next, given the value function W̃j(qj,q−j,∆, r), which already incorporates
10 RThe denominator 3 is included only to simplify the result. For Rj = 3, 6, 12,
j
3 = 1, 2, 4.
11This functional form is formuated in EP and adopted by GG.
25
the optimal price choices, firm j chooses optimal investment by solving the following
problem,
Wj(qj,q−j,∆, r) = max W̃j(qj + τ
′
j,q−j,∆, r)χ(τj = τ
′
j|xj)
xj
, (2.17)
Rj
+W̃j(qj + τ
′′,q ,∆, r)χ(τ = τ ′′j −j j j |xj)− xj3
which takes weighted average between two investment outcome, q + τ ′ and q + τ ′′j j j j ,
and deducted the adjusted innovation cost. Equation (2.14) and (2.17) jointly define
firms’ value functions.
Firms’ choices of Rj at the beginning of the model is determined by their
expected value for all the future periods. For each of firm’s states s = (q,p,∆, r),
denote the probability of its occurrence in a∑sufficiently long duration as ps, then
firm j’s value given choice of (R ,R ) is W (s)p .12j −j s j s Given payoffs of each
combination of R, all firms simultaneously choose their optimal Rj, which completes
setup for firm’s problem.
Firm “Other”
Besides Apple and Samsung, I also include a third firm “Other” in the model
during estimation to capture competition from all other flagship smartphone man-
ufacturers, like HTC, Lenovo and LG. In general these firms’ quality frontier ex-
pansion paces are slower, and they sell their smartphones at cheaper prices. When
solving consumers’ problem, I assume that firm Other’s product quality qOt and pOt
12I assume a random steady state starting point to calculate this value.
26
are completely determined by Apple and Samsung’s product characteristics in the
following way:
qOt = min{qAt, qSt} − δ, pOt = .45 ∗ (pAt + pSt).
With this setup, qOt is always slightly lower than Apple and Samsung’s product
qualities, but it will increase over time with Apple and Samsung’s release of better
products. In accordance to this relative quality, I set pOt to be .9 times average price
of Apple and Samsung’s product prices. Consumers also know this determination
rule of {qOt, pOt}, so they only form expectations over future Apple and Samsung
product characteristics.
2.2.4 Equilibrium
Firms choose their optimal release frequency {Rj}j by solving for Nash equilib-
rium, where their payoffs are expected values given different combinations of {Rj}j
and all firms’ optimal price and investment choices conditional on the corresponding
release frequencies. I assume that such a pure strategy Nash equilibrium exists.
Conditional on the choices of {Rj}j, I adopt the symmetric pure-strategy
Markov-Perfect Nash equilibrium (MPNE) to solve for firms’ product choices and
consumers’ purchase decisions. This MPNE specifies that (1) firms’ and consumers’
equilibrium strategies depend only on current state, which consists of all payoff-
relevant variables; (2) consumers have rational expectations about firms’ policy
functions, which determine future qualities and prices, and the evolution of the
27
ownership distribution; and (3) each firm has rational expectations about its com-
petitors’ prices and investment and about the evolution of the consumer holding
distribution.
Formally speaking, an MPNE for this model, given the choice of {Rj}j is the
set
{V ∗, h∗c , g∗, {W ∗ ∗ ∗ ∗ ∗ Jc j , xj , pj , hf , g }j fj j=1},
which includes consumers’ equilibrium value V ∗, consumers’ beliefs about future
product quality and ownership distribution h∗c and g
∗
c , firms’ equilibrium value func-
tions W ∗j , their optimal policy functions of investment and prices x
∗, p∗j j , firms’ beliefs
about future qualities and the transition of consumer holding distribution h∗f , g
∗
f .j j
The expectation over future qualities is rational in that the expected distribution
matches the distribution resulting from consumers and firms behaving according to
their optimal policy functions.
One difficulty in estimating dynamic discrete games and conducting the coun-
terfactual analysis is the multiplicity of equilibrium in product choice and purchase
decisions, and release frequency choices. The literature has addressed this issue in
numerous ways, among which one choice is to use backward induction and derive
players’ values starting from given future values. When solving the model, I start
from a future period where I assume both consumers’ and firms’ values are only
determined by their payoffs in that period, and then using backward induction to
solve for their optimal policy functions holding fixed their actions in the next pe-
riod. For choices of release intervals, it is easy to check for the existence of multiple
28
equilibria in the normal form.
2.2.5 Bounding the state space
Firms’ product qualities increase in every product release so that, over time,
they can increase without bound. To numerically solve the model, I transform the
state space to finite size by redefining all qualities as relative qualities to a pre-
set quality boundary q̄. The capability to implement this quality transformation
without changing the dynamic game itself comes from the following proposition.
Proposition 1 (Goettler and Gordon (2011)) Shifting down qualities of the two
firm, q and q̃, by δ has no effect on firms’ payoffs and lowers consumers’ payoffs in
each state by αqδ− , the discounted value of the reduced utility in each period. More1 β
formally,
firms:
Wj(qj − δ,q−j − δ,∆, r) = Wj(qj,q−j,∆, r)
consumers:
V (q− αqδδ,∆, I = (q̃ − δ, J̃), r) + = V (q− δ,∆, I = (q̃, J̃), r)
1− β
The proof for this proposition rests on the following properties of the model:
(1) quality enters linearly in the utility function, so adding a constant to the util-
ity of each alternative, including new purchase and outside option, has no effect
on consumers’ choices within a logit demand system; (2) firms’ innovation only af-
29
fects probabilities of different quality increments, and cost of innovation, as well
as marginal cost per unit, is independent of quality levels; (3) ∆ tracks consumer
holding quality relative to the quality frontier so it is unaffected by a shift for all
quality levels. In practice, when a firm’s product quality is at the highest level, q̄,
and it invests to improve it by τ , I will then use this proposition and shift all quality
entries by τ .
2.3 Data and industry background
Smartphones were first introduced in 1999, and became widespread in the late
2000s.13 One distinction between the smartphone and its predecessor, the feature
phone, is that smartphone is capable of handling more complicated tasks, like play-
ing games, GPS navigation, taking photos, etc. To meet the hardware requirement
for performing these functions , smartphone manufacturers incorporate new and
better hardware components into their new smartphone models, resulting in rapid
improvement in smartphone qualities.
Figure 2.1 depicts this quality increasing trend from 2008 to 2016 by plotting
the quality frontier for the five largest manufacturer in the US market, Apple, Sam-
sung, LG, Motorola and HTC, where quality is measured using the benchmark score
collected from http://www.iphonebenchmark.net/ and http://www.androidbenchmark.net/.
These websites measure the smartphone performance on CPU, 2D and 3D graphics,
memory and disk, then combine these statistics to report an aggregate benchmark
score for each smartphone model, which I assume represents a smartphone’s overall
13https://en.wikipedia.org/wiki/Smartphone
30
performance. According to the figure, within the Android makers, which include
all firms except Apple, Samsung is leading the Android quality frontier and the
other three firms are mostly followers.14 We can also see that Apple’s own quality
frontier interacts with the Android frontier, which indicates active quality competi-
tion. Based on these two observations, I model the US flagship smartphone market
as Apple competes with Samsung in quality improvement, with all other firms as
followers and represented by a non-strategic firm “Other”.
Figure 2.1: Smartphone quality frontier for top five manufacture in the US
Apple HTC LG
8000
6000
4000
2000
0
an an an n n
8J J
a a
0 10 12
J J
14 6
J
20 20 20 20 20
1
Motorola Samsung
8000
6000
4000
2000
0
n n n n n n n n n n
8J
a Ja Ja Ja Ja Ja Ja Ja Ja Ja
00 1
0
0 1
2 14 16 08 10 12 14 16
2 2 20 20 20 20 20 20 20 20
Time
Firm frontier Android frontier
Note: Vertical axis represents quality, represented by benchmark scores, and horizontal axis
represents time. Quality frontier is defined as the highest quality among all smartphones all
manufacturers sold in each period.
A second observation from Figure 2.1 is that, product release schedules are
14Some of the smartphones from Samsung and HTC use the Windows Phone system, but market
shares of these smartphones are relatively small. By 2013 January, about 90% smartphones
being used adopted iOS and Android systems, so I only consider smartphones using these
two operating systems. Data source: http://www.comscore.com/Insights/Press-Releases/
2013/3/comScore-Reports-January-2013-U.S.-Smartphone-Subscriber-Market-Share?cs_
edgescape_cc=US.
31
very regular for both Apple and Samsung. Table 2.2 reports release dates of Apple
and Samsung’s flagship smartphone models. Samsung typically releases twice every
year: Galaxy S series in late February/March and Galaxy Note series in every late
August/September, while Apple only releases once every year in September after
2012. This regular release schedule can not be explained by the standard innovation
model, where investment outcomes are random and new products are automatically
released with successful outcomes. Instead it seems more plausible that firms commit
to a regular release schedule, and random outcomes only affect product qualities
and prices, not product release arrangements. Based on this release pattern, I
approximate release schedules by assuming that Samsung releases twice every year
in September and March, and Apple releases once every year in September.
To measure consumers’ responses to each smartphone release, I collected weekly
user percentages of major smartphone models from Fiksu.com from July 2013 to
January 2016. Fiksu publishes statistics from its two user trackers, iOS trackers
and Android trackers, each of which publishes weekly user percentages of smart-
phone models within that operating system.15 To calculate user percentages of each
smartphone model among all users, not just users from the same operating system,
I collected monthly subscriber percentages of iOS and Android smartphones in the
US for the same period from comScore reports, and aggregated weekly Fiksu data
to monthly data by only keeping data in the first week of each month.
15One caveat of this data source is that, users tracked in these services are from both US
and Europe, so I have to assume that user percentage of major smartphone models within their
corresponding operating system are similar between US and Europe market. Note that there is
no requirement for iOS and Android user percentage, which are quite different between US and
Europe.
32
Table 2.2: Announcement dates of smartphones expanding quality frontier from
Apple and Samsung
Release date
Galaxy Note October 29, 2011
Galaxy S3 May 3, 2012
Galaxy Note 2 September 26, 2012
Galaxy S4 March 14, 2013
Galaxy Note 3 September 25, 2013
Samsung Galaxy S5 February 24, 2014
Galaxy Note 4 September 3, 2014
Galaxy S6 Edge March 1, 2015
Galaxy Note 5 August 21, 2015
Galaxy S7 February 21, 2016
Galaxy Note 7 August 19, 2016
iPhone 4s October 4, 2011
iPhone 5 September 12, 2012
Apple iPhone 5s September 20, 2013
iPhone 6 September 9, 2014
iPhone 6s Plus September 9, 2015
iPhone 7 September 7, 2016
Note: In case where multiple smartphones are re-
leased simultaneously, only the model with the high-
est benchmark score is listed. Data were collected
from Wikipedia.
Smartphone sales prices are collected from archived manufacturer webpages.
I use full retail prices, instead of contract prices for two reasons. First, since 2013,
carriers started “unbundling” by encouraging consumers to buy new smartphones at
full price and enjoy discounts on their monthly service fees.16 Given these discounts,
the actual cost of acquiring a new smartphone, with or without the subsidized price,
has been close to the full retail price. Second, I am only modeling manufacturers’
16For example, AT&T offers a $25 discount per line for a family account if consumers buy
phones at full price, and this discount will be removed if a consumer chooses to buy smartphones
at the contract price. Overall expenditure between these two methods over two years are close,
but the contract price locks consumers in by disallowing them to buy other smartphones during
that two-year period.
33
pricing decisions, and in the smartphone market, this price is represented by the
full retail price.17 All prices are adjusted to the 2013 price level. My modeling
assumption of constant prices within each product cycle comes from the fact that
manufacturers hardly adjust their retail prices unless new phones are released, and
I do not have data of discounting in the retail channels.
Smartphone benchmark scores are collected from Passmark Rating. I assume
that the benchmark score of each smartphone model represents the quality of that
model and it is time invariant. In case a certain smartphone model has multiple
submodels, I select the submodel with the highest benchmark to represent the qual-
ity of that model.18 Table 2.3 reports the means and standard deviations of prices
and qualities for Apple and Smasung smartphones.
Table 2.3: Summary statistics
Mean Std. Dev.
Apple Price ($) 558.7 40.8
Quality (Passmark Score) 4152.1 1205.4
Samsung Price ($) 629.6 31.7
Quality (Passmark Score) 4973.5 1238.6
Finally, I also collected Apple and Samsung Electronics’ R&D expenditure
and total revenues from their quarterly SEC filings. I only collected these two firms’
17This choice of retail price as marginal revenue per unit is only an approximation in the firm’s
problem. In reality, both Apple and Samsung sell their smartphones through wireless carriers and
retailers, where they sell their smartphones to these vendors at discounted prices and earn less
mark-ups then selling directly on their websites. So my estimated marginal cost will be higher
than the actual manufacturing cost. But this retail price is accurate in estimating consumers’
preferences as it is close to consumers’ actual payments regardless of their purchase methods (pay
in full, special financing where consumers split the full retail price in 12 or 24 months or subsidized
price where consumers pay less for the smartphone, but have to pay more for their monthly bills).
18For example, there are 25 sub models for Samsung Galaxy S6 smartphone, and these sub
models differ slightly in hardware components like network devices. Benchmark scores among these
submodels are very similar, so I choose the top performance model to represent the quality of that
phone. Source: https://www.handsetdetection.com/properties/devices/Samsung/Galaxy%20S6.
34
overall R&D expeditures and revenues, as their smartphone-specific investments are
not publicly available. But given that smartphone sales are the largest revenue
sources for both firms, and flagship models require much more investment than the
nonflagship model, I assume that these collected numbers are informative on firms’
actual investments in their flagship models.19 These data are used to construct
moments for ratio of investment over total revenue.
2.4 Estimation
In this section, I provide details on how I estimate my model parameters using
my collected data. One data constraint to studying firms’ product introduction
decisions is that firms are inactive for most of the time, and there are not many
observations for firms’ choices of new product qualities and prices. In the total
31 months of data I collected, Apple and Samsung only released for three and six
times, respectively. To alleviate this constraint, I conduct my demand and supply
estimation separately: first, I utilize user number variations on smartphone model
level and estimate demand parameters, then given demand estimates and aggregated
firm-level data, I use simulated method of moments (SMM) to estimate the supply
parameters. The complete list of parameters to be estimated is as follows:
19In 2016, roughly 60% of Apple’s revenue came from iPhone sales in 2016, and
in 2016Q1, Samsung’s mobile decision generates 63% of Samsung Electronics’ total rev-
enue. Source: http://www.businessinsider.com/apple-iphone-sales-as-percentage-of-total-revenue-
chart-2017-1, http://www.eweek.com/mobile/samsung-smartphone-sales-help-hike-q1-2016-profit-
revenue
35
Table 2.4: List of parameters to be estimated
αq Quality coefficient
Demand estimation αp Price coefficient
ξA, ξS Apple, Samsung fixed effects
λA, λS Marginal cost
Supply estimation a0,A, a0,S Investment efficiency
a1,A, a1,S Spillover effect
2.4.1 Demand estimation
Given the release schedule that Apple introduces new phones in every Septem-
ber, and Samsung in every March and September, their flagship offerings do not
change for several months, which provides an opportunity to separate variations in
consumers’ expectations due to product changes and time changes.20
For example, suppose there are two periods, t = 1, 2, and each firm’s product
quality has not changed in these two periods. Denote consumer’s choice specific value
function for product j (use j = 0 for current holding) at time t as vjt(q, r,∆, I).
Then in the second period, consumer’s inclusive value before purchase is
( ∑ )
Vt=2(q, r,∆, I) = log exp(vj,t=2(q, r,∆, I = (qj,t=2, j)) (2.18)
j∈Jt=2
At t = 1, consumer’s choice specific value for product j is
vj,t=1 = uj + βVt=2(q, r,∆, I = (qj,t=1, j)) (2.19)
20In this subsection, I will denote smartphone model, instead of firms, as j. This notation only
applies when describing demand estimation.
36
which governs consumers’ purchase decisions at t = 1. Note that there is no un-
certainty in this expression: q is not changed in the next period, r and ∆ evolve
deterministically, and I is solely determined by consumer’s individual purchases. So
if all choice specific values at t = 2 are available, consumers’ demand at both t = 1
and t = 2 can be derived in a deterministic way.
My demand estimation proceeds in three steps. First, I truncate my observed
periods into non-overlapping and consecutive intervals such that new product re-
leases only occur in the last period of each interval. Next, I calculate consumers’
choice-specific value functions in the last period of each interval. Finally, values
for all other periods within the same interval are calculated through backward in-
duction. Approximation only exists in the second step, where consumers’ value
functions in the last period of each interval are approximated by assuming con-
tinuous usage of their current phone in that period for a fixed amount of periods.
Conditional on these values in the last period of each interval, values imputed for
the previous periods are rational. This is because there are no uncertainties between
consecutive periods (except the last period) within the same interval as both firms’
product offerings have not changed. With the assumption that consumers’ values
in the last period of each interval is correctly calculated, all their purchase decisions
are rational.
To be specific, each interval is denoted as I = 1, 2, . . . , nI , and the first and
last period in interval I are tI , t̄I , respectively. Choice specific values of buying
(using if j = 0) product j at time tt̄ is assumed to be 24 months of discountedI
37
utilities, that is, ∑23
Vj,t̄ = −αppj,t̄ × 1{j 6= 0}+ βtuI I j,t̄I
t=0
where β is the value discount factor per period, and uj denotes utility flow of using
smartphone j for one period.
Given these choice-specific values, consumers’ inclusive value at t̄I , which mea-
sures consumers’ value before their idiosyncratic shocks are realized and purchases
are made and after new products are released, is, (omitting other state variables for
simplicity)
∑ 
Vt̄ (I) = log exp(Vj,t̄ ) + exp(V0,t̄ (I))I I I
j∈Jt̄I
Then in periods tI , tI + 1, . . . , t̄I − 1, consumers correctly anticipate firms’
choices of prices and qualities in t̄I , and their value functions in period t are solved
using backward induction as
vj,t(I) = uj,t − αppj,t + βVt+1(I = (qjt, j)), V0,t(I) = u0,t + βVt+1(I)) (2.20)
and inclusive value is
(∑ )
Vt(I) = log exp(Vj,t(I)) + exp(V0,t(I)) (2.21)
j∈Jt
Given these choice specific values and inclusive values, in period t, demand for
product j among consumers with holding characteristic I is
38
exp(vj,t(I))
sj|I = (2.22)
exp(Vt(I))
Then the imputed user number for product j at time t+1, denoted as ñj,t+1 is
calculated as consumers who newly purchased phone j (if it is on sale) minus those
who previously were using phone j but purchased another phone at t.
∑ ∑
ñj,t+1 = sj|I=(q ′ n ′ − s ′ n (2.23)j′ ,j ) j ,t j |I=(qj ,j) jt
j′ j′
Note that I use actual instead of imputed phone users in period t, just to
avoid bias to accumulate over time. Finally, demand parameters are estimated by
minimizing distances between this imputed and actual user numbers in periods when
no phones are released.
min ||ñ(θD)− n|| (2.24)
θD
2.4.2 Supply estimation
Given demand estimates, I use simulated method of moments estimator that
minimizes the distances between a set of conditional moments and their simulated
counterparts from the model. To apply the model developed in the previous section,
first I convert Apple and Samsung into single-product firms. For each firm in each
month, I collect its flagship smartphone models on sale and take their average quality
and average price as the firm’s product quality and price in that month, respectively.
39
For each candidate value of supply parameter estiamtes θS, I solve the model
given RA = 12, RS = 6, and simulate S times for T periods each, starting at the
industry state in the first month of my data, (q, r,∆). The SMM estimator θ̂S is
θ̂S = arg min[mS,T (θ)−m ′T ] AT [mS,T (θ)−mT ] (2.25)
θ∈Θ
where mT and mS,T (θ) are observed and simulated moments, and AT is a positive
definite weighting matrix. My weighting matrix is attained directly from the stan-
dard deviations of moments in actual data. In the data I observe that in all of
three Apple releases, Apple’s product quality increased by approximately .14, and
Samsung’s product quality increment ranges from .02 to .1. So I set the quality step
size δ such that 4δ = .14, and the lowest quality level q as Apple’s quality in July
2013. In addition I choose quality levels nδ = 13 so Apple and Samsung’s simulated
qualities within the observation period will not be bounded.
My choice of moments to be matched captures firms’ competitions in new
product qualities and prices, given their committed product release schedules. My
moment vector consists of the following 12 moments:
• Average price across all periods for each firm.
• Percentage of R&D investment over total revenue.
• Average ratio of pj over qj′ where j, j′ = A, S.
• Average ratio of each firm’s own quality over industry quality frontier, i.e. the
higher of Apple and Samsung’s product qualities.
40
• Average ratio of product quality over mean holding qualities.
Identification
The demand parameters are identified by variations in different phones’ user
numbers and their corresponding characteristics. αq and αp affect user shifts among
phone models with different qualities and prices, and manufacturer fixed effect ξA, ξS
are identified by relative changes in total user base among Apple, Samsung and other
manufacturers.
The supply parameters are identified through variations in simulated moments.
Firms’ marginal cost parameters λA, λS are identified by average prices, where higher
marginal costs will increase firms’ prices. Spillover effect parameters a1,A, a1,S are
mainly identified by the ratio of each firm’s own product quality over industry quality
frontier, which measures to what extent each firm keeps up with its competitors in
quality advancement. Larger spillover parameters will improve firms’ investment
efficiencies when firms lag behind, and more likely to catch up with the industry
frontier, and therefore increase this ratio. Finally, investment efficiency parameters
a0,A, a0,S are identified from the ratio of investment over revenue, where higher
investment efficiency will lead to less investment and smaller ratio values. Other
moments, including ratio of prices over qualities, and new product qualities over
consumer holding qualities are also sensitive to variation in these parameters and
add to their identifications.
41
2.5 Estimation result
2.5.1 Estimates
I use the SMD estimator in (2.24) and (2.25) to estimate demand and sup-
ply parameters, respectively. Model setup parameters for supply estimations are
fixed as follows: product prices and qualities are normalized by 1/100 and 1/1000
respectively.
Table 2.5: Parameter Estimates
Estimates Std. Err.
αq Quality coef 10.3560 0.4007
αp Price coef 12.3640 3.7034Demand Parameters
ξA Apple FE 1.6794 0.1527
ξS Samsung FE 0.2996 0.1789
λA 0.3938 0.0005Marginal cost
λS 0.5466 0.0180
a
Supply Parameters 0,A
10.0942 0.4711
Investment efficiency
a0,S 19.3900 0.4400
a1,A 9.8869 0.8300Spillover effect
a1,S 9.8136 0.6214
Parameter estimates are reported in Table 4.9, and model’s fit in Table 2.6.
Implied price elasticity by demand estimates varies from 6 to 9, and for supply
estimation, the model fits the 12 moments reasonably well, despite having only 6
parameters. All demand parameters are statistically significant (except Samsung
fixed effect) given the relatively small standard errors. Dividing the estimated qual-
ity coefficient by the price coefficient implies that consumers are willing to spend
120 dollars for a 1000 units increase in benchmark scores (remember that price and
42
Table 2.6: Empirical and Simulated Moments
Fitted Value Avg moment value in actual data Std. dev. in actual data
Average price
Apple 0.5156 0.5587 0.0408
Samsung 0.6296 0.6165 0.0317
Ratio of investment over revenue
Apple 0.0062 0.0361 0.0073
Samsung 0.0723 0.0722 0.0025
Ratio of price over quality
pA/qA 1.3371 1.4597 0.4699
pA/qS 1.0502 1.1767 0.2284
pS/qS 1.2759 1.3177 0.3428
pS/qA 1.6296 1.6413 0.6226
Ratio of own quality over frontier
qA/q̄ 0.8035 0.8290 0.1180
qS/q̄ 1.0000 0.9975 0.0139
Ratio of new product quality over consumer holding quality
qA/qi 1.1757 1.2101 0.1600
qS/qi 1.4666 1.4652 0.1369
qualities are normalized by 1/100 and 1/1000, respectively). Relative brand val-
ues for Apple and Samsung with respect to other brands, calculated by dividing
their brand fixed effects by price coefficients, are 13 dollars and 2.42 dollars, re-
spectively. Investment efficiency and spillover estimates imply strong incentives in
quality catch-up.
2.5.2 Empirical results
Figure 2.2 presents firms’ prices, investments and profits for both Apple and
Samsung across states. The three rows correspond to prices, probabilities of higher
quality increment and market shares for each firm. The two columns correspond
to firms’ quality difference, in terms of qA − qS, and the average qualities of con-
43
Figure 2.2: Firms’ prices, investments and profits over quality differences and con-
sumers’ average holding quality
1000
800
500 600
400
0 5 10 15 20
0
-5000 0 5000
1 1
0.5 0.5
0 0
-5000 0 5000 0 5 10 15 20
1 1
Apple
0.5 0.5 Samsung
0 0
-5000 0 5000 0 5 10 15 20
q -q Consumer average holding quality
A S
Note: First column corresponds to firms’ quality difference, in terms of
qA − qS. Second column corresponds to consumers’ average holding qual-
ity where larger number indicates higher quality. Three rows represent
firms’ prices, probabilities of higher quality increment and market share. In
all the graphs, solid line denotes Apple, and dashed line denotes Sam-
sung. Mean values are calculated with equal weights given to all states.
sumers’ holdings, where larger numbers indicate higher quality of consumers’ hold-
ings. When a firm’s product quality is higher than its competitors, it increases its
price and earns higher market share.
Another important feature of this model is that, consumers are forward looking
and their purchase decisions will be affected by the number of periods until the next
product release. Figure 2.3 depicts average market share for Apple and Samsung
in each 12-month window, plotted separately for the highest and lowest levels of
consumer holding quality. These two subfigures correspond to Apple and Samsung’s
44
Price
Market share Pr(τ')
Figure 2.3: Apple and Samsung’s market share within each 12-month window
Apple
0.8
0.6
0.4
0.2 Lowest holding quality
Highest holding quality
0
0 2 4 6 8 10 12
Samsung
0.3
Lowest holding quality
0.2 Highest holding quality
0.1
0
0 2 4 6 8 10 12
Time
Figure 2.4: Apple and Samsung’s quality path
Apple
8000
Simulated
6000 Actual
4000
2000
0
0 5 10 15 20 25 30 35
Samsung
7000
Simulated
6000 Actual
5000
4000
3000
0 5 10 15 20 25 30 35
Time
market shares in terms of units sold within each 12-month window, where the first
month is set as each September. In general, both firms’ market shares decline as new
45
Samsung quality Apple quality Market share Market share
product release is approaching (T = 7 for Samsung only, and T = 13 for both Apple
and Samsung). At T = 6 both Apple and Samsung’s market shares decline, but
given its (slightly) higher brand preference, Apple’s market share is less affected,
and Samsung’s market share is restored to a higher level with its newly released
product. When T is close to 12, consumers will mostly stop buying and waiting for
new product to release.
Finally, to see how my model fits the data, Figure 2.4 reports the actual and
average simulated qualities for both Apple and Samsung starting from the industry
state in the first observed month for 31 months. My model fits Apple’s quality path
much better than Samsung, mostly because of its almost constant quality increment
in each product release. For Samsung, my model fits the average quality increment,
but there is a long lasting gap just because of quality discretization.21
2.6 Counterfactual: effects of different release schedules
In this section, I try to understand the effects of different release schedules,
in particular the trade-off between “more-but-minor” and “less-but-major”. First,
under a symmetric duopoly market setup, I show how firms’ optimal policies (i.e. in-
novation and prices) change when firms choose different release frequencies, which il-
lustrates the importance of considering product release frequencies separately. Next,
with the same analysis but in a monopoly market, I discuss a monopolist’s optimal
product release strategy. By further comparing this monopoly market outcome with
21For example, when at T = 5, which corresponds to 2013 November, Samsung’s quality is 3678
which is located between 3550 and 3900 on the quality grid, and therefore cannot be perfectly
fitted.
46
the duopoly case, I provide analysis on overall welfare impact of market concentra-
tion and decompose the source of this impact into changes in prices, innovation and
release frequencies.
2.6.1 Release schedules in the duopoly market
I adopt a symmetric duopoly market structure which is modified from the
previous model as follows: there are two firms, denoted as j = 1, 2. The composite
firm “Other” is removed; both firms’ marginal costs, investment efficiency, and
spillover effects are set as Apple’s parameter estimates; consumers’ brand preferences
are set as zero for any firm.22 With this market setup, I can ignore other firm-specific
characteristics that could potentially affect the market outcome, and evaluate the
pure effect of different release schedules.
One challenge to evaluate consumer surplus in this framework is that, con-
sumers benefit from accumulated quality increment in the past, but these increments
are removed when I shift all quality entries downward to bound the state space. To
address this issue, I store the accumulated quality improvement along with each
simulation, and use this accumulation, rather than the quality value in the state
space, to calculate consumer welfare. To make the results comparable, I simulate
the model for 1,000 periods in all counterfactual experiments, so higher consumer
surplus only comes from higher innovation and/or lower prices.
22Conditional on the symmetric duopoly structure, this zero brand preference is a normalization
rather than an assumption. This is because brand preference enters consumer’s utility of both new
purchase and current holding, and increasing these preferences by the same amount will not affect
consumers’ purchase decisions due to the logit demand form. So as long as these two firms have
the same brand preference (because of symmetry) and consumer’s brand preference comes from
her past purchase, I can set both brand preferences to zero without loss of generality.
47
At the beginning of the model, each firm chooses its release interval Rj from
{3, 6, 12} simultaneously to maximize their sales. Given this symmetric setup, firm
1’s policy functions in {R1, R2} = {R,R′} are the same with firm 2’s policy functions
in {R1, R2} = {R′, R}, so without loss of generality, I only report summary statistics
for R1 ≥ R2, i.e. firm 1 has equally or less frequent releases than firm 2. Table 2.7
reports summaries of these two firms’ policies.
Table 2.7: Simulated policy function: Symmetric duopoly
Price Firm 1 Firm 2
R2 12 6 3 12 6 3
12 $ 548.36 $ 569.05 $ 608.80 $ 547.13 $ 590.26 $ 583.35
R1 6 $ 572.20 $ 617.61 $ 571.29 $ 607.92
3 $ 552.67 $ 555.64
Prob of higher quality increment Firm 1 Firm 2
R2 12 6 3 12 6 3
12 0.940 0.977 0.981 0.938 0.869 0.863
R1 6 0.912 0.966 0.911 0.808
3 0.708 0.721
Firms’ profit per period Firm 1 Firm 2
R2 12 6 3 12 6 3
12 0.078 0.100 0.132 0.077 0.104 0.091
R1 6 0.085 0.123 0.085 0.120
3 0.063 0.065
Consumer Surplus Social Surplus
R2 12 6 3 12 6 3
12 3.797 4.563 4.906 3.952 4.766 5.129
R1 6 3.866 4.572 4.035 4.815
3 4.030 4.157
Note: All numbers are average value of simulated market outcomes. Differences in
two firms’ diagonal elements come from simulation errors.
From this table we can see that a firm charges higher prices when its competitor
releases new products more frequently. For example, as firm 2’s release frequency
speeds up from one release per year (R2 = 12) to four releases per year (R2 = 3), firm
48
1’s prices increase. One possible explanation for this pattern is that, per the model
setup, any firm with less frequent product releases has higher quality advancement
in each release, and this “temporary” quality boost, as compared to its competitor
with frequent but smaller quality advancement, establishes quality advantage and
enables it to charge higher prices. For the firm with more frequent releases, however,
it does not necessarily charge higher prices. For R2 = 12 or 3, firm 1’s prices increase
as R1 decreases from 12 to 3, but for R2 = 6, firm 1’s prices peak when R1 = 6.
Firms’ investment levels are represented by their probabilities of the higher
quality increment. Note that the investment outcomes are normalized conditional
on each firm’s release schedules, where possible quality improvements are smaller
in frequent release schedules and larger in less frequent release schedules, namely
”more-but-minor” and ”less-but-major”. Conditional on these normalized invest-
ment outcomes, we can see that when the competitor’s release becomes more fre-
quent, a firm invests more and improves its probability of the minor quality in-
crement. This pattern suggests that release frequencies and innovations are com-
plimentary in firms’ dynamic competition conditional on the normalized quality
increments: when a firm cannot match its competitor’s more frequent releases, it
invests more for higher quality increment in each release; if instead this firm chooses
to speed up its release frequency as well, it will spend less on its innovation.
With all these results combined, we can see how firms choose their release
schedules and product characteristics: firms balance between innovation and release
frequencies where high innovation is adopted in compensation for low release fre-
quency and vice versa; in response to its competitor’s more frequent releases, a firm
49
increases its innovation, but may or may not increase its release frequency; firms
with major product improvement charge higher prices.
Note that I have not identified a fixed cost associated with each product release
because I only observe market outcome when RA = 12, RS = 6, and any parameter
governing firms’ choices of release schedules cannot be identified. But it is interesting
to see that even where there is no fixed cost included, firms are still bounded from
choosing too frequent releases. For example, when R2 = 3, firm 1’s profit decreases
when R1 shifts from 12 to 3.
One reason for this finding is that more frequent releases do not necessarily
increase aggregate demand. To see this, I calculated firm 1’s market share within
each 12-month period, and it is averaged across all states for each combination of
(R1, R2). These average market shares are plotted in Figure 2.5.
Figure 2.5: Firm 1’s market share in each 12-month period with different release
schedules
R =12
2
0.4
0.3
R =12
0.2 1
R =6
1
0.1 R =3
1
0
0 2 4 6 8 10 12
Time
R =3
2
0.4
0.3
R =12
0.2 1
R =6
1
0.1 R =3
1
0
0 2 4 6 8 10 12
Time
50
Market share Market share
These two subfigures in Figure 2.5 correspond to R2 = 12 and R2 = 3, and in
each graph, three lines correspond to firm 1’s three choices of release frequencies:
R1 = 3, 6, 12. When both firms choose R = 12, market share slowly declines over
time as time approaches for the next product release (at t = 1, which is after t = 12);
if firm 1 chooses to release additionally at T = 7, i.e. change R1 to 6, then there
is an additional decline in its market share near T = 6 just as consumers expect
new release in the next period. Finally with more frequent releases, firm 1’s market
share decreases right before every product release, with a general declining trend in
each 12-month period for R2 = 12.
From this figure we can also see the sales decline before each new product
release, which can possibly offset sales boost brought by the additionally released
products and decrease the aggregate sales. For example, when R2 = 12, aggregate
demand for firm 1 decreases when it speeds up its frequency from R1 = 12 to
R1 = 6, where most of sales decline comes from consumers’ purchase delay at t = 6
anticipating a new product to be released at t = 7. Another finding is that the
extent of consumers’ purchase delay is correlated with the number of firms releasing
new products in the near future. For example, when R1 = 6 and R2 shifts from 12 to
3, firm 2 starts to release at t = 7 as well along with firm 1. As a result, consumers’
demand at t = 6 becomes much lower as they expect new products introduced by
both firms instead of just firm 1.
In conclusion, aggregate demand does not always increase when firms release
products more frequently because consumers’ demand declines significantly when
they expect new products to be released soon and this decline can offset the sales
51
boost brought by the new products. It is this property that bounds firms from
choosing too frequent release schedules.
2.6.2 Release schedules in the monopoly market
When a durable good market becomes more concentrated, existing firms may
alter their policies, including price, innovation, and as newly considered in this
paper, product release schedules, and all of these changes will affect social surplus.
GG studies a possible market structure change where AMD is no longer present in
the CPU market, and finds that Intel will innovate more and charge higher prices;
total surplus is lower though as gains from higher innovation is dominated by loss in
consumer surplus due to higher prices. Their analysis fits R&D intensive industries
where firms concentrate on innovation and release new products when they are
available, but could lead to biased welfare estimates in downstream manufacturer
industries, like smartphone and many other consumer electronics, where firms can
alter their schedules of new product release in the new market structure.
To examine the welfare impact from market concentration with possible changes
of release schedules considered, I change the market structure to monopoly and com-
pare its outcome to the duopoly market. To make the results comparable, I set the
monopolist’s marginal cost and investment efficiency as Apple estimates and remove
the brand preference as well. I also chose the duopoly market where R1 = R2 to be
compared with the monopoly market such that the duopoly market can be seen as
dividing the monopolist firm into two symmetric firms while still preserving its prod-
52
uct release schedules. In this way, differences in market outcome between monopoly
market with RM = R
′ and duopoly market with R1 = R2 = R
′ only come from
changes in market structure. For each choice of monopolist’s release schedule from
R = 3, 6, 12, I solve the model, simulate the market for 1,000 periods, and repeat
the simulation process for 500 times. Results are summarized in Table 2.8.
Table 2.8: Simulated policy function: Monopoly and symmetric duopoly
Price Profit Prob of τ ′′ Consumer Surplus Social Welfare
12 $ 746.23 0.238 0.986 5.154 5.392
Monopoly R1 6 $ 729.64 0.189 0.989 5.194 5.383
3 $ 649.13 0.148 0.988 5.216 5.364
12 $ 548.36 0.078 0.940 3.797 3.875
Duopoly R1 = R2 6 $ 572.20 0.085 0.912 3.866 3.950
3 $ 552.67 0.063 0.708 4.030 4.092
Note: Profits reported are average per-period profits in all the simulated periods,
with market size set as one. Units for profits, consumer surplus and social welfare
are in dollars.
From Table 2.8 we can see that, when the market becomes more concentrated,
the monopolist charges higher prices but also invests more in quality improvement,
which is consistent with Schumpeter’s hypothesis and the findings in GG. But in
this model, consumer surplus is higher in the monopoly market than in the duopoly
market, which implies that gains from monopolist’s higher innovation rates are only
partly offset by loss from its higher price levels. Because of higher consumer surplus
and higher profit levels in monopoly market, social surplus is also higher in the more
concentrated market structure.
A second observation is that a monopolist prefers less frequent product re-
leases, as profit of choosing R = 12 is higher than that of R = 3, 6. This preference
towards less frequent release schedules is because the monopolist only needs to com-
53
pete with consumers’ holdings, and as more frequent releases actually result in less
aggregate sales (as is shown in Figure 2.6), the monopolist would slow down its pace.
The monopolist’s choice of higher innovation and less frequent releases also
highlights the importance of separately modeling firms’ choices of frequency and
size of innovation. In a model where new product releases are driven by successful
innovation outcome, we can only see firms with either higher innovation and implied
frequent product releases, or lower innovation and rare releases, which will lead to
biased estimates of social welfare.
Figure 2.6: Firm 1’s market share over time
0.5
R =12
0.45 1
R =6
1
0.4 R =31
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0 2 4 6 8 10 12
Time
A further examination of consumers’ demand over each 12-month window,
as presented in Figure 2.6, suggests that consumers will still hold off purchasing
products immediately before each new product releases. By comparing demand
between R1 = 12 and R1 = 6 we can also see that speeding up release frequency
will not increase total sales, which is consistent with the finding in the symmetric
54
Market share
duopoly market.
2.7 Appendix: Algorithms for solving the model
The algorithm I implement for solving the dynamic model takes as input the
model structure and parameter values, and returns firms’ policies and consumers’
choice probabilities. There are n∆ × n2q × (12/Rj) states in firm j’s problem (that
is how many possibilities for each type of consumer distribution with each possible
combination of new product qualities and each possible release state),23 and n∆ ×
n2q × 12× nC holding states in each consumer’s problem, which expands firms’ states
into full 12 months and also includes all possible values of consumers’ holdings
(nCbasic = nq × 3). For each firm, the algorithm returns its optimal price and
investment, and for each consumer, the algorithm returns her purchase probabilities
for the three possible choices (Apple, Samsung and “Other”).
My model is solved by iterating between updating firms’ and consumers’ val-
ues until convergence. The outer loop checks if firms’ and consumers’ values have
converged between two consecutive iterations, and inner loops update firms’ policies
and consumers’ purchase probabilities. Detailed algorithm to solve this dynamic
model is as follows.
23For example, if Samsung releases twice every year (RS = 6), then holding all other state
variables constant, releasing in the 1st and 7th month are in two different states.
55
Algorithm 1 Dynamic model algorithm
1: Set initial consumer’s value V and firm’s value W as zero for all states.
2: while max |V k − V k−1| ≥ 1e− 5 or max |W k −W k−1| ≥ 1e− 5 do
3: for each firm j chooses each value on the price grid do . Solve for each
firm’s optimal prices
. Calculate intermediate values given preset price values, then extrapolate.
4: Simulate forward for Rj periods.
5: For each possible evolution path, ca∑lculate its probability Prm, cumula-tive profits Πm and value of final state W k−1m .
6: Values of choosing current price is Pr (Π + βRjW k−1m m m m )
7: end for
8: Extrapolate and update firms’ optimal prices.
9: for each firm j do . Solve for optimal investment and value
10: Simulate forward for Rj periods with optimal prices.
11: Calculate values of different innovation outcomes, then solve for optimal
investment.
12: Given firms’ optimal investment and prices, update their values to {W kj }j.
13: end for
14: Given firms’ policies, update consumers’ values and purchase probabilities
to {V ki , P rkij}i,j
15: Given firms’ policies and consumers’ purchase probabilities, update transi-
tion rules for ∆.
16: end while
56
Chapter 3: Managerial Implications for Durable Goods Release Sched-
ule
3.1 Introduction
In this chapter, I adopt the model framework developed in Chapter 1, and
apply it in the general durable goods market to provide managerial implications
on product release schedule arrangement. As discussed in the previous chapter,
product release schedule in the model introduces several additional implications for
firms’ strategic choices.
First, release frequencies determine the pace of materializing up-to-date in-
novation outcomes, where firms can release products more frequently to improve
product qualities and outperform competitors for most of the time, but this fre-
quent releases also raise consumers’ awareness of new product releases in the near
future and increase their value of waiting rather than buying the current products.
Second, firms can alter their relative release timing with respect to others’
strategically, either capture the market with early releases, or postpone the releases
to incorporate the most recent innovation outcomes.
Third, firms can also alter their format of product release schedules, like speed-
57
ing up/slowing down the pace of their product introduction or even transform into
irregular release schedules, which can have long term effects because consumers’
expectations of future releases are also updated based on the new schedule.
The first implication has been discussed in Chapter 1 where the market out-
comes under duopoly and monopoly are compared. Firms choose their release fre-
quency by balancing between the gains of selling more products with frequent quality
updates and the loss of sales due to consumers’ frequent expectations of new releases.
When the market becomes more competitive, firms’ concern of frequent consumer
expectation is alleviated and the gains from additional releases become dominant.
As a result, firms introduce products more frequently with more firms present in
the market.
This chapter studies the second and third implications, or more specifically,
the market outcome when firms change their relative release timing or switch their
release frequency along the time. Based on the simulated results, I find that a
duopolist can benefit from staggering its releases relative to those of the other firm, as
firms can spend the additional time increasing its product qualities and outperform
other firms’ new products. This result also suggests no additional value for the
simultaneity in releases. I also show that it is valuable for a firm to be seen as
committed to a regular release schedule, as the possibility of switching schedules in
the future affects consumers’ current purchases and hurts firms’ values.
There is a branch of literature that studies firms’ product release decisions in
the presence of strategic consumers. Borkovsky [2017] studies innovators’ timing
decisions of their product releases in a non-durable good context and finds that
58
firms innovate and release more aggressively when products are vertically, rather
than horizontally, differentiated. Cohen et al. [1996] and Lobel et al. [2015] analyze
the trade-off between release frequency and quality improvement in the monopoly
market. Cohen et al. [1996] finds that more frequent releases are not necessarily
profitable if the existing product has a high margin and the new product has a large
market potential. Lobel et al. [2015] further compare the monopolist’s profit in two
scenarios, “varying schedule with fixed investment” and “varying investment with
fixed schedule”, concluding that the schedule commitment is valuable. My paper
generalizes their discussions with more flexible release schedules and an empirical
application in an oligopoly market. I show that the market structure affects firms’
product release scheduling as well. Casadesus-Masanell and Yoffie [2007] examine
the release decisions for complementary products and find that upstream suppliers
release aggressively while downstream manufacturers delay the adoption to profit
from the installed base. Paulson Gjerde et al. [2002], Balcer and Lippman [1984] and
Farzin et al. [1998] study firms’ technology adoption decisions given an exogenous
advance of the technological frontier in a limited dynamic framework.
3.2 Staggering product releases
In the model I make an assumption that all firms release simultaneously in
at least one period. While this assumption is helpful in sufficiently determining all
future release schedules given firms’ choices of release intervals {Rj}j, it also rules
out some examples of interest. For example, in a duopoly market where both firms
59
choose R = 12, this assumption only allows for the schedule where both firms release
new products simultaneously and repeatedly every 12 months. It is also possible,
however, that these two firms still release new products every 12 months, but their
releases are 6 months apart from each other (say, one in every January and the
other in every July); in this case, by setting its new product release apart from
its competitor, which I term as “staggering,” a duopolist firm can outperform its
competitor with better quality products for 6 months, at a cost of being dominated
by its competitor’s product for the other 6 months.
My analysis is based on the symmetric duopoly market as constructed in Sec-
tion 2.6.1, and I limit both firms’ release frequencies as R1 = R2 = 12. To capture
the relative timing of product releases, I define a new variable, “release difference
∆R”, which is the number of periods between two firms’ nearest product releases.
For example, suppose firm 1 releases at t, t+ 12, t+ 24, . . ., and ∆R = 1, then with-
out loss of generality, firm 2 is assumed to release at t− 1, t+ 11, t+ 23, . . ., which
means that firm 2 always releases products relatively earlier than, if not together
with firm 1. With R = 12 for both firms, ∆R takes value between 0 and 6,
1 where
∆R = 0 represents the simultaneous “conglomerate” release, and ∆R = 6 means
6-month-apart “dispersed” release.
Figure 3.1 shows how both firms’ average prices vary based on their relative
product qualities. A firm charges higher price when it sells higher quality products,
and its price will increase with this quality advancement. We can also see that when
these two firms’ product releases are less concentrated (∆R increases from 0 to 6),
1∆R = 7 for example, is equivalent to ∆R = 5 and switching two firms’ moving order.
60
Figure 3.1: Optimal prices over quality differences in different staggering release
schedules
1000
=0
R
800 =3R
=6
R
600
400
-5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000
1000
=0
R
800 =3R
=6
R
600
400
-5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000
q -q
2 1
both firms charge higher prices which indicates softened market competition.
Note that these two firms are symmetric when ∆R = 0 or 6, and their corre-
sponding price curves are also symmetric in Figure 3.1. For ∆R = 3, firm 2 releases
new products 3 months ahead of firm 1. By comparing firms’ price curves when ∆R
increases from 0 to 6, we can find that firm 2’s prices are monotonically increasing
while firm 1’s prices peak at ∆R = 3. This pattern implies that when firm 2 shifts
away from firm 1’s product releases and introduces products earlier, both firms ben-
efit from softened market competition and firm 1 can extract more surplus from its
innovation at ∆R = 3. This is a result of the number of periods that each firm’s
product dominates the market, which is shown in Figure 3.2.
Figure 3.2 illustrates how release timing affects firms’ market dominance.
Firms have equal market dominance when ∆R = 0 or 6: when ∆R = 0, both firms
61
Firm 2 price Firm 1 price
Figure 3.2: Graphic illustration of ∆R = 0, 3, 6, R1 = R2 = 12
Firm 1 & 2 Firm 1 & 2 Firm 1 & 2
∆R = 0 : Time
t=1 t=13 t=25
Firm 2 Firm 1 Firm 2 Firm 1 Firm 2
∆R = 3 : Time
t=1 t=4 t=13 t=16 t=25
Firm 2 dominates Firm 1 dominates Firm 2 dominates Firm 1 dominates
Firm 2 Firm 1 Firm 2 Firm 1 Firm 2
∆R = 6 : Time
t=1 t=7 t=13 t=19 t=25
Firm 2 dominates Firm 1 dominates Firm 2 dominates Firm 1 dominates
release simultaneously across all times and no firm has any advantage/disadvantage
in release timing; when ∆R = 6, each firm “dominates” the market by 6 months
with its new products just released, and then becomes “dominated” by another 6
months with its competitor’s even newer products. Firms’ symmetric positions in
these two cases guarantee that their optimal policies and value functions are also
symmetric, which leads to the same shape of price curves as in Figure 3.1. When
∆R = 3, firm 2 releases new products and dominates the market for only 3 months,
and then becomes dominated by firm 1 for 9 months, which gives firm 1 higher mar-
ket power to extract surplus from its quality advancement and explains why firm
1’s prices are the highest when ∆R = 3. To better understand the welfare implica-
tion of these three release schedules, Table 3.1 reports summary statistics of both
firms’ policies, including price, profit and probability of higher quality increment,
and welfare impacts.
Consistent with the graph, both firms’ policies are the same when ∆R = 0
62
Table 3.1: Simulated policy function: R1 = R2 = 12, ∆R = 0, 3, 6
Price Profit Pr(τ ′′) Consumer surplus Social Welfare
Firm 1 $ 548.36 0.0780 0.9399
∆R = 0 3.7910 3.9461Firm 2 $ 547.13 0.0771 0.9382
Firm 1 $ 636.53 0.1240 0.9917
∆R = 3 3.6380 3.8469Firm 2 $ 560.81 0.0849 0.9928
Firm 1 $ 610.58 0.1086 0.9930
∆R = 6 3.6194 3.8350Firm 2 $ 616.26 0.1070 0.9930
and 6, and the differences in these statistics only come from simulation errors. Firm
1’s price and profit are the highest at ∆R = 3. The welfare estimates suggest
that consumers’ surplus and social welfare are the highest at ∆R = 0 where firms’
compete in simultaneous release schedules and charge lower prices.
Based on this result, we can see that firms should focus on their market domi-
nance and try to make their products among the best choices for longer periods. For
example, if no competitor firm will release new product in the next few months, and
a firm can either introduce a new product now with similar quality to its competi-
tors, or improve and release a better product in the next period, my result shows
that this firm should choose the latter option.
3.3 Release schedule switching
In the previous analysis, I adopt the model assumption that firms take full
commitment on their release schedules: once they have made their choices, they
have to release products accordingly throughout the dynamic innovation and pricing
game that follows. This assumption helps focus my discussion on firms’ dynamic
63
competition while treating firms’ release schedules as exogenous, and the results
provided using this framework can be interpreted as firms’ strategies in the long run
given their current release schedules.
Another way to approach the observed regular release schedule in the data
is to assume that firms keep introducing new products regularly to build up their
“reputations” of regular release schedules. In other words, firms are not bounded
by any pre-set release rules; they can release new products whenever they want, but
preferably they choose to maintain their regular release schedules. This alternative
model setup cannot be rejected by the data either, and it can also provide insights on
the regular form of firms’ release schedules: by comparing market outcomes between
the full commitment and the partial commitment model setup, I can evaluate both
the value of maintaining uncommitted release schedules, and the cost of switching
to alternative schedules. Based on the simulated market outcome, I find that firm’s
schedule commitment is valuable, and it is costly to switch schedules.
To implement this flexible choice of schedules and relax the full commitment
assumption, I modify the model framework by allowing firms to deviate from their
previously chosen schedules in the dynamic pricing and innovation game for at most
once, then be committed to their new schedules. The feasibility of this “deviate-
then-commit” setup, which I term as “partial commitment”, is still restrictive con-
sidering that firms could deviate regardless of their past histories, but it is flexible
enough to capture the two features of interest: the value of maintaining regular re-
lease schedules comes from the difference between full-commitment case and firms’
strategies before their deviations; the cost of switching can be evaluated from firms’
64
delaying deviations. Without much modification from the previous framework, this
new model setup is also computationally feasible.
This subsection proceeds as follows. First, the new model setup is described
in details to show how I modify the model to accommodate the partial commitment
setup; next, with the new model setup applied in the monopoly market, I evaluate
the value of maintaining the uncommitted release schedules by studying how the
monopolist keeps its favorite schedule without deviating to others; finally I evaluate
the cost of switching schedules by studying how the monopolist delays its deviation
to its favorite schedule.
3.3.1 Model setup
To accommodate firms’ flexibility in adjusting their release schedules, I adopt
partial commitment to release schedules where I allow for a firm to deviate from its
initial schedule at most once. For example, firm 1 first chooses to release once every
12 months, then after 2 years, switches to and commits to releasing once every 6
months, as is illustrated in Figure 3.3.
Figure 3.3: Partial commitment: example
Firm 1 chooses R1 = 12 Deviate to R1 = 6
Time
Product releases: t = 1 t = 13 t = 25 t = 31 t = 37 t = 43 t = 49
To be more specific, I adopt the monopoly model as in Section 2.6.2 where
the monopolist’s innovation efficiency and marginal cost are the same with Apple
parameter estimates, and consumers’ preferences over brand are removed (with only
65
quality and price preferences left).2 The model timing under this framework is as
follows:
1. At the very beginning, the monopolist chooses its temporary release frequency
R1 = R
T
1 . (T for temporary)
2. STAGE 1: Given R1, the monopolist becomes active if it is scheduled to
release new products and remains inactive otherwise.
• In each period, if the monopolist is active:
(a) If the monopolist has never deviated, it decides whether to deviate
and commit to a new release schedule R1 = R
C T
1 =6 R1 (C for com-
mitment) or not. After deviation, the game enters STAGE 2.
(b) The monopolist invests to improve the quality of its new product,
and conditional on the investment outcome, sets price for this new
product.
(c) Every consumer observes the updated product offering and decides
whether to buy it or keep using her current phone.
• If the monopolist is inactive:
(a) The monopolist’s product offering remains unchanged from the pre-
vious period.
(b) Every consumer observes the updated product offering and decides
whether to buy it or keep using her current phone.
2This monopoly setup is to remove market competition’s impact, and only focus on firms’
management over its product life cycles. I will evaluate how rival competitors’ strategies affect a
firm’s release schedules in future research.
66
It is worth noting that the monopolist is restricted to change its release sched-
ule when it is active rather than in every period. This restriction on the timing
of deviation helps simplify the monopolist’s strategy space and consumers’ beliefs,
and reduce the computational burden. Another assumption is that RC1 6= RT1 , which
indicates that the monopolist cannot commit to its current temporary release sched-
ule. This is to avoid the degenerate case where the monopolist commits to the new
schedule right at the beginning, which is equivalent to the full commitment prob-
lem. This forced schedule switching setup is also necessary to learn the importance
of commitment in two ways. First, if RT1 = 12, which is also the monopolist’s most
preferred release schedule in the full commitment case, how would the monopolist
maintain this preferred schedule without commitment? Second, if RT1 6= 12, then
the monopolist would want to switch to RC1 = 12, but is there any cost associated
with the schedule switching that delays the change?
I use backward induction to solve this partial commitment game. First, I
calculate the monopolist’s payoff after deviation (Stage 2) by solving the full com-
mitment game with the newly committed release schedules. Next, given the payoff
of deviating, the monopolist’s innovation and pricing decisions before the deviation
(Stage 1) are solved through iteration. Consumers’ beliefs about possible deviations
are also updated.
67
STAGE 2: After deviation
When the monopolist deviates and commits to an alternative release schedule,3
the whole game is the same as in the full commitment. Denote the industry state is
(q,∆, r) when the monopolist deviates, where q and ∆ represent the product quality
and consumer distribution, respectively, and r is the number of periods before the
monopolist’s next release. Based on the model timing, q represents the product
quality before the new product release in the current period, and r takes the value
of RC1 , the newly committed release frequency. Given the new release schedule R
C
1 , I
can solve the optimal pricing and innovation decisions as well as consumers’ purchase
decisions, and the monopolist’s payoff of deviation, represented by its value in the
corresponding industry state, can be written as WD(q,∆, r = RC1 ) (D for deviation).
STAGE 1: Before deviation – General
Before the deviation, the monopolist makes innovation and pricing decisions
as well, but during each product release, it also decides on whether to change its
product release schedules. To facilitate the expression, denote the monopolist’s
payoff after deciding not to deviate as WND(q,∆, r = RT1 ), where r takes value
of RT1 , the current temporary release schedule. Set d(q,∆, r = R
T
1 ) = 1 if the
monopolist deviates at state (q,∆, r = RT1 ), and zero otherwise, then
3Consistent with the previous model, release frequency R still takes value from {3, 6, 12}.
68
d(q,∆, r = RT1 ) = 1⇔ WND(q,∆, r = RT1 ) ≤ max WD(q,∆, r = RC1 ), (3.1)
RC=6 RT1 1
and the monopolist’s value before deviation decisions is defined as
( )
W (q,∆, r = RT1 ) = ︸ 1− d(q,∆, r = RT1 ︷)︷WND(q,∆, r = RT1 ︸) + d︸(q,∆, r = RT1 ) maxRC 6=︷R︷ WD(q,∆, r = RC1 ) .T1 1 ︸
Value of no deviation Value of deviation
(3.2)
WND(q,∆, r = RT1 ) is computed in two steps: first, compute consumers’ value
with their beliefs of future deviations included; second, given updated demand,
iterate and update WND until convergence.
STAGE 1: Before deviation – Consumer’s problem
Iteration on consumer’s value function is the same with the main model, except
in periods right before each product release. In these periods, consumers form ex-
pectations on the monopolist’s deviation decisions as well alongside with its pricing
and innovation decisions. Similar with the notation for the firms, denote consumer’s
value under deviation and no-deviation as V D(q,∆, r, I) and V ND(q,∆, r, I), and
their beliefs of the monopolist’s deviation decision as dc(q,∆, r = RT ),41 then their
4RT1 is consumers’ believed optimal deviation. For simplicity I use the same notation as the
monopolist’s choice.
69
value function before the monopolist’s deviation decision is calculated as
V (q,∆, r, I) = dc(q,∆, r = RT D1 )V (q,∆, r, I)+(1−dc(q,∆, r = RT1 ))V ND(q,∆, r, I),
(3.3)
which completes updating the iteration over consumers’ values.
STAGE 1: Before deviation – The monopolist’s problem
As is in the main model, I use backward induction by first solving the monop-
olist’s optimal investment decisions, and then its optimal pricing decisions. What is
different here is that the value function achieved with these two decisions only gives
WND(q,∆, r = RT1 ), i.e. the payoff without deviation, and the monopolist’s value
function used in future iterations, W (q,∆, r = RT1 ), needs an additional round of
calculation based on (3.2).
With iterations on updating consumers’ and the monopolist’s value functions,
as well as their policy functions, conditional on consumers’ beliefs of deviation are
rational, i.e. dc(q,∆, r = RT1 ) = d(q,∆, r = R
T
1 ), I can then solve for the equilibrium
of this STAGE 1 game.
3.3.2 The value of commitment
To study how the monopolist maintains reputation over its current release
schedule without making any commitment, I set the monopolist to choose R = 12
first, which is its most preferred release schedule in the full commitment case, and
only allow it to deviate/commit to R = 3 or R = 6 later. Intuitively, one might
70
expect that the monopolist should, on average, keep its R = 12 schedule and earn
more profits without any deviation, but based on the model outcome, I find that it
does deviate in some states, which is depicted in Figure 3.4.
Figure 3.4: Deviation decisions by new product quality and consumers’ holdings
6000
5500 Deviation
5000
4500
4000
3500 No Deviation
3000
2500
2000
2 4 6 8 10 12 14 16 18 20
Quality: Consumer holdings
From Figure 3.4 we can see that, when the new product quality is high, and
consumer holdings are of low quality, the monopolist would prefer to deviate from
R = 12.5 This is even more interesting when one considers how the market evolves:
the monopolist improves its product quality until it reaches q̄, then stays at q̄ with
decreasing consumers’ holding quality to enlarge the relative quality difference be-
tween new products and consumer holdings. Based on this evolution model, the de-
viation always happens after a sufficiently long period where qj = q̄ and consumer
holding qualities are pushed down by new releases, which contrasts the intuition
that the monopolist wants to maintain R = 12 schedule.
To see why this happens, in Figure 3.5, (a) and (b) present the monopolist’s
payoff in three cases: (1) deviation to one of the other two schedules (R = 3, 6),
5In this outcome, the monopolist only deviates to R = 6 if possible so I suppress the expression
of solving for optimal deviation schedules.
71
Quality: New Product
Figure 3.5: Firm’s payoff and average price across new product quality and con-
sumers’ holdings
(a) (b)
104 4×
5 ×105.5
Deviation Deviation
No deviation No deviation
4.5 5Full commitment Full commitment
4.5
4
4
3.5
3.5
3
3
2.5
2.5
2 2
1.5 1.5
0 5 10 15 20 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
Quality: Consumer holdings Quality: New Product
(c) (d)
750 950
Partial commitment Partial commitment
Full commitment, R=12 900 Full commitment, R=12
Full commitment, R=6 Full commitment, R=6
850
700
800
750
650 700
650
600
600
550
500
550 450
0 5 10 15 20 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
Quality: Consumer holdings Quality: New Product
72
Firm value W Firm value W
Firm value W Firm value W
(2) no deviation with current R = 12 schedule, and (3) full commitment model
without possibility of deviation. We can see that the monopolist’s incentive to
deviate (represented by the relative difference between (1) and (2)) is larger when
consumers are using lower quality products and new product qualities are high,
which is consistent with Figure 3.4. But we can also see that with possible deviations
in the future, the monopolist’s payoff becomes flatter: it is not so low in “bad
situations” like higher quality holding or low quality new product to sell, and not so
high in “good situations” either. In this sense, the ability to deviate in the future
serves as partial insurance. By further comparing (1), (2) with (3), the removal of
the commitment device still hurts the monopolist so it is no longer able to extract
that much surplus from its sales, which shows that the full commitment assumption
does provide the monopolist additional market power.
By further comparing the monopolist’s average prices, as is shown in (c) and
(d), we can see that the price before deviation lies between R = 12, its current release
schedule, and R = 6 its target deviation schedule. In other words, the monopolist
charges lower prices when it no longer has commitment power, to be closer to the
schedule it is likely to deviate to.
3.3.3 The cost of switching
An alternative aspect of the commitment decisions is whether there is any
cost associated with the deviation from a firm’s previously uncommitted release
schedules. To see this, I assume that the monopolist chooses R = 3 or 6 at first, and
73
can deviate to one of the other two release schedules later. Given that R = 12 is
the monopolist’s most preferred schedule, the monopolist should deviate it as early
as possible, and any deferral will be explained by costs of this schedule switching.
Figure 3.6 reported the monopolist’s deviation decisions for each combination
of new product qualities and consumers’ holdings.6 In these two cases, the monop-
olist’s deviation decisions are more randomized than R = 12, but we can still see
that the deviation occurs more frequently when the firm’s new product is of high
quality; for some low quality states, the monopolist would rather continue with its
current release schedule for the moment and postpone the deviation.
To better understand the occurrence of this “deviation delay,” Figure 3.7 plots
the monopolist’s payoff and prices over its new product qualities for R = 3 and
R = 6. In (a) and (b), the payoff of deviation and no-deviation intertwines which
leads to the irregular deviation decisions, but as the monopolist’s product is of
higher quality, deviation dominates in both cases. By comparing these payoffs with
their counterpart in full commitment, we can see that the possibility of deviation to
better release schedules significantly increases the firm’s payoffs. In (c) and (d), the
monopolist’s price choices are not much different from the full-commitment choices
under the same release schedule.
3.4 Appendix: Commitment vs. no-commitment in product releases
In the durable goods market, the manufacturer’s ability to commit to future
prices and quality improvement is influential on consumers’ demand. Without com-
6For both R = 3 and R = 6, the monopolist only deviates to R = 12 if possible.
74
Figure 3.6: Deviation decisions by new product quality and consumers’ holdings
(a) R = 3 (b) R = 6
6000 6000
5500 5500
5000 Deviation 5000 Deviation
4500 4500
4000 4000
3500 3500
3000 3000
No deviation No deviation
2500 2500
2000 2000
2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20
Quality: Consumer holdings Quality: Consumer holdings
Figure 3.7: The monopolist’s value and prices across new product quality for R = 3
and R = 6
(a) Firm’s value: R = 3 (b) Firm’s value: R = 6
104 104
5.5 5.5
No deviation No deviation
5 Deviation 5 Deviation
Full commitment, R=3 Full commitment, R=6
4.5
4.5
4
4
3.5
3.5
3
3
2.5
2.5
2
1.5 2
1 1.5
1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
Quality: New Products Quality: New Product
(c) Average price: R = 3 (d) Average price: R = 6
950 950
Partial commitment Partial commitment
900 Full commitment, R=12 900 Full commitment, R=12
Full commitment, R=3 Full commitment, R=6
850 850
800 800
750 750
700 700
650 650
600 600
550 550
500 500
450 450
1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
Quality: New Product Quality: New Product
75
Average price (USD) Firm value W Quality: New Product
Average price (USD) Firm value W Quality: New Product
mitment, durable goods firms have the incentive to charge lower prices or improve
product qualities to cater to the rest of the market after consumers with higher
willingness to pay have made the purchase. If consumers are rational and forward-
looking, they can expect firms’ such behavior and postpone their purchase, which
in turn hurts firms’ sales. This problem can be alleviated when firms have a com-
mitment device: firms can commit to their future prices and qualities which could
totally be different from their ex post optimal choices, but consumers’ beliefs in this
commitment can increase their demand and may increase firms’ total revenue as a
result.
This paper modifies the framework in Ericson and Pakes [1995] and Goettler
and Gordon [2011] by assuming that firms commit to their product release schedules
and release new products when they are scheduled to, rather than may or may not
release new products depending on the innovation outcome. This framework allows
me to study the role of product release frequency explicitly, but it also endows these
durable goods firms the ability to commit, which is a strong assumption considering
that there is hardly any firm making promises on how often it will release new
products in the future. Take Apple for example: new iPhone models are released
every year in September after iPhone 4S,7 so it is natural for people to believe that
new iPhone models will be released like this in the future as well. But Apple is not
bounded by this pattern; it can definitely skip one year, or release its new models
“irregularly” in August or November. Even though this irregular release is not highly
7Excluding iPhone SE which was released in March 2016, because it is not considered as a
flagship model.
76
likely, consumers can still expect it and adjust their purchase behavior accordingly,
e.g. someone bought an iPhone in August rather than waiting for another month
because she did not believe a new iPhone to be introduced in the next month. So it
remains a question whether this assumption of full commitment is too strong and
leads to biased welfare analysis.
In this section, I studies the role of firms’ commitment to their release schedules
in my model and examines its impact on the market outcome. To see this, I adopt
the monopoly model used in 2.6.2 and modify it as follows.
1. In this model, the monopolist’s new product release is represented by the
increase in relative quality of its product to consumers’ holdings. Therefore
to allow the monopolist not to release any new product even if it is scheduled
to, I set the lower possible quality increment (τ ′) as zero for “no-committed
release” cases.
2. To make the market outcome comparable when the monopolist chooses dif-
ferent release schedules, I adjust the higher possible quality increment (τ ′′) to
equalize the upper bounds of quality increment per year.
3. The control group, “committed release” is constructed by setting τ ′ to δ, so
the monopolist always release new products when it is scheduled to.
In total there are five cases to be considered: three no-commitment cases and
two commitment cases. Setup details are summarized in table 3.2.
Case 2 and 4, as well as case 3 and 5, are designed to compare firms’ policies
and market response when new product releases are committed or stochastic. In
77
Table 3.2: Model specifications with or without committed product releases
Possible quality increment Range of Q increase per year
R τ ′ τ ′′ Lower bound Upper bound
Case 1 1 0 δ 0 12δ
Case 2 No commit 2 0 2δ 0 12δ
Case 3 3 0 3δ 0 12δ
Case 4 2 δ 2δ 6δ 12δ
Commit
Case 5 3 δ 3δ 4δ 12δ
case 4 and 5, the monopolist is guaranteed to release a new product every time it
is scheduled to with at least δ increase in its product quality, while in case 2 and 3,
the monopolist’s product quality might be unchanged. Other model components,
including the upper bound of quality increment per year, and the distribution of
consumers’ holdings are not different, so discrepancies in the market outcome will
mostly result from firms’ commitment of new product releases.8
Figure 3.8 shows how the monopolist’s market share and price changes over
its product quality in both committed and non-committed case, where the top two
subfigures correspond to case 2 and 4, and the bottom two figures correspond to
case 3 and 5. From the graph, for both average price and average market share,
they are almost the same with or without commitment to product releases and
the minor discrepancy comes from changes in the monopolist’s innovation problem
as illustrated in footnote 8. This suggests that both consumers and firms are not
affected by firms’ commitment to product releases, what they care about is the
8 The other source of the possible discrepancy comes from the changes in the monopolist’s
innovation. By increasing τ ′, the lower possible quality increment from 0 to δ, the monopolist’s
gain by switching from τ ′ to τ ′′ decreases so it will invest less in quality improvement. This
changes in investment cost then affects firms’ value functions and price choices, and furthermore,
consumers’ demand. Based on the results, the impact from this mechanism is of limited scale.
78
Figure 3.8: Average price and market share over product qualities: with or without
commitment of release
R=2 R=2
0.6
No commit 700 No commit
0.4 Commit Commit
600
0.2 500
0 400
0 2000 4000 6000 0 2000 4000 6000
R=3 R=3
0.6
No commit 700 No commit
0.4 Commit Commit
600
0.2 500
0 400
0 2000 4000 6000 0 2000 4000 6000
Product quality Product quality
possibility of product releases. To see this, I plot the consumers’ demand within
each 12-month period in case 1 through 3 and it is presented in figure 3.9.
Figure 3.9: Consumers’ demand within each 12-month for R = 1, 2, 3
0.4
0.35
0.3
0.25
0.2
0.15
0.1
R=1
0.05 R=2
R=3
0
0 2 4 6 8 10 12
Time
Note that in case 1, new product releases are not committed; in each period
79
Market share Market share Market share
Price Price
firms may or may not release new products depending on the investment outcome,
which is the same setup as the innovation structure. Given this setup, the mo-
nopolist’s market share averaged across other state variables (product quality and
consumer distribution) is the same over time and results in a horizontal line.
When case 2 and 3 are added where new product releases are still not com-
mitted at any time, but for some periods new products are guaranteed not to be
introduced, consumers’ demand starts to fluctuate where they buy more right after
the new product is released, and hold up their purchase before each new release.
When the new product is potentially of higher quality (R = 3 as compared to R = 2
or 1), more consumers choose to wait.
This pattern suggests that if the new products differ from the current products
only in qualities, firms’ commitment of product release does not have any effect on
consumers’ and firms’ problem.9 Instead, it is the expectation of possible quality
increase in the future that induces consumers’ purchase delays. This is an interesting
result as it implies that in the innovation model where firms make investment and
may or may not increase its product quality in every period, consumers’ demand
are both boosted by the innovation outcome (if successful) and weakened by their
expectation of possible quality increase in the future at the same time. So it is
necessary to separate these two effects to better evaluate firms’ innovation strategies.
9If consumers’ value new products in other dimensions, like fashion or advertisement exposure,
this result will no longer hold.
80
Chapter 4: A Tale of Old and New: Multi-Version Consumption in
the Video Game Industry
(Co-authored with Andrew Sweeting)
4.1 Introduction
Empirical models of demand for durable goods typically assume that con-
sumers use and derive utility from the most recent version of the product that they
own. While this assumption is sensible for some products, like large appliances, it is
inaccurate for products which are almost costless to store and where older versions
may offer a different and not necessarily inferior user experiences. In this paper,
we establish the empirical evidence for multi-product consumption in a video game
franchise, where video game players may continue to play the old games after buying
the new versions, and provide a framework to analyze their optimal time allocation
decisions among their game portfolios.
There are various reasons that consumers may continue to use their old units
after buying the upgraded ones. For example, the old product may include certain
features that consumers value but removed in the new products, or the old and new
products may be complementary in usage. In our empirical setting, we assume that
81
players develop their product-specific preferences through usage, and their relatively
high preferences towards the old games, as compared to the new ones, incentivize the
continuing usage of the old games. This assumption is supported by two empirical
findings.
First, players spend relatively more time in “serially-featured modes,” like the
career mode, when they play the old game after new purchases. In these modes,
players develop their game progress through consecutive matches and their game
progress cannot be transferred to other game versions. These non-transferrable
game progresses result in individual specific preference towards the old game versions
relative to the new games.
Second, players more likely to play old games after new purchases are also less
likely to buy future game versions. Players make their purchase decisions based on
the additional value brought by the new game, so if they enjoy their old versions
and will spend much time on it regardless of their purchase decisions, they will not
value their new games much.
Based on these empirical evidence, we develop a framework where players al-
locate playing time within their game portfolios and across different game modes,
based on a latent variable, “game preference.” Players’ game preferences include
common components across individuals like game-specific and mode-specific prefer-
ences, and heterogeneous components as well including individual effects and each
player’s past gaming preferences in the same game mode. We show that incorporat-
ing individual heterogeneity is important to fit this detailed usage data and capture
the variations.
82
We estimate the model parameters using a proprietary dataset provided by
Wharton Consumer Analytic Initiative, which documents players’ play and purchase
activities in a major sports video game franchise from 2011 to 2016. In the data
we focus on three types of player strategies: game purchase decisions, choices of
game versions and modes to play, and game play duration. Given the parameter
estimates, we show how the model fits the data in these three dimensions.
Product development and updates are among the most important marketing
questions [Norton and Bass, 1987]. Past research on product innovation focus on
consumer purchase decisions [Mahajan et al., 1991, Rogers, 2010], where the de-
pendent variables are the timing and the rate of consumer adoption decisions rather
than consumers’ product usage patterns. As more detailed usage data is made avail-
able, recent studies show that post-purchase behavior is important to understand
consumers’ incentives of upgrade purchase and evaluate the impact on long-term
purchasing and usage patterns [Golder and Tellis, 2004]. This paper utilizes the
observed video game activities to impute their real-time game preferences and their
purchase intentions for the future game releases.
Consumers’ product usage patterns are determined by their endogenous prod-
uct preferences, and previous research focus on how consumer involvement with the
products and learning process motivate their continued product usage [Westbrook
and Oliver, 1991, Holt, 1995]. Albuquerque and Nevskaya [2012] and Nevskaya and
Albuquerque [2012] use data on players’ game activities in a multiplayer game and
evaluate players’ responses to introduction of new game contents. They find that
the success of game version updates depends on consumer heterogeneity, rate of
83
content consumption and social interaction. This paper further allows players to
allocate their playing time in multiple game versions in their portfolios, and develop
version-specific game preferences.
The rest of this paper is structured as follows. Section 2 describes the data and
provide empirical evidence on players’ multi-game consumption behavior. Section
3 sets up the model and Section 4 provides details about the estimation strategy,
with estimation result and model fit presented in Section 5. Section 6 presents the
counterfactual analysis, and Section 7 concludes the chapter.
4.2 Data and empirical summaries
This section describes the data format and the game franchise we study, and
also provide empirical support on key model setup, including players’ multi-product
consumption and persistent gaming preferences.
4.2.1 Data Description
Our data is provided by Wharton Consumer Analytic Initiative and it docu-
ments game players’ play activities in a major sports video game franchise.1 The
publisher of this game franchise releases a new game version every summer and
is named after the following year to distinguish from previous game versions. To
facilitate the expression without revealing the game identity, we rename the game
version named after year 201X as game GX. For example, game G5 was released
1To comply with the data usage agreement, we will not reveal the game title or the identity of
its publisher. All relevant information that could potentially reveal the entity is also anonymized
in this paper.
84
in 2014 summer with 2015 in its name.
Players in our data are randomly selected from the population as follows:
around 20,000 players are selected from those whose first observe game version is G2
or earlier version; for each game from G3 to G6, around 10,000 players are selected
from those who purchased the game as their first game versions in the franchise.
Once a player is selected, all his future game session activities until summer 2016
are included.2 Since we do not observe players’ actual date of purchases directly,
we take each player’s initial observed game play date for each game version as his
purchase date.
For each game session, we observe its date, game mode, game version and the
session duration. Given that the original game mode descriptions might reveal the
identity of the game, we combine similar game modes into major categories and
rename them in more general terms that still reflect the game mode features but
could apply for general sports video games as follows:
• “Career” mode: players act as athletes to improve their skills or act as a
manager to run a team. Players can save their current game progress and
resume later.
• “Instant Play” mode: players choose their teams and compete with the CPU
for a single match. Match results have no cumulative effects.
• “Ultimate Mode”: players trade cards of professionals with each other or buy
them from the system, and use them to form their teams. Their purchased
2Since we do not observe the total sales of each game version, in this paper we focus on players’
individual behavior rather than making inference on the aggregate level statistics like market share.
85
cards may be valid for a short time.
• “Occasional Play” mode: players initiate a match series like a championship
cup, which requires playing for several matches until winning the final or being
eliminated. Players play fewer games than in the career mode, and they can
save game progress and continue later.
Table 4.1 provides summaries on player count and average total duration across
players. Career mode, ultimate mode and occasional play mode are the three most
popular game modes in terms of game session count and session duration. Career
mode is consistently popular among all game versions in terms of game duration,
whereas the Ultimate Mode gains popularity starting from G5. The ultimate mode’s
significantly higher standard deviations suggests that game time in this mode is more
concentrated into a smaller group of players.
Figure 4.1 plots the number of new game activation in each month based
on the buyers’ initial game version observed in the data. When a new version is
released, there will be two peaks in purchases: right after the new game release,
and during the holiday seasons. If we further look into the composition of game
buyers, those who buy the new games are most likely the existing players who have
played previous game versions, while new comers who are new to the franchise are
more likely to buy the game during holidays. Based on this difference, we define
“pre-holiday” periods as dates after release and before November 15 each year, and
“holiday” periods as the rest of the annual cycle. The different types of buyers in
these two periods will be captured by their time-specific purchase costs.
86
Table 4.1: Summary statistics: by players
(a) Player count
Game Version
G2 G3 G4 G5 G6
Career 7,953 13,090 12,652 15,056 16,476
Instant Play 11,303 14,291 16,960 23,449 22,526
Game Mode Ultimate Mode 3,012 6,900 10,785 12,812 13,517
Occasional Play 7,633 13,754 9,852 11,157 16,849
(b) Average total duration across players (seconds)
Game Version
G2 G3 G4 G5 G6
Career 59869 86484 105212 105288 91754
Instant Play 13227 21172 24067 24358 17489
Game Mode Ultimate Mode 24006 45403 67618 136819 106507
Occasional Play 58616 61938 79388 80065 68273
(c) Standard deviation of total duration across players (seconds)
Game Version
G2 G3 G4 G5 G6
Career 157387 195829 198001 193502 153279
Instant Play 32888 49280 56784 63507 38868
Game Mode Ultimate Mode 70578 139855 215969 312891 228893
Occasional Play 167403 196234 206518 213324 146489
Notes: All players who have played at least one game session in any game are
included.
4.2.2 Multiproduct consumption
In the durable good literature, it is commonly assumed that consumers’ outside
options are completely represented by their more recent purchases. In the video
game industry, this would predict that a player should completely shift his playing
time to the new game version after purchase and discontinue his game play in the
old games. While this prediction is intuitive as the new game has better graphics
87
Figure 4.1: Game activation over time
10000
5000
0
2011Jan 2012Jan 2013Jan 2014Jan 2015Jan 2016Jan
Date
G2 G3 G4 G5 G6
performance, in data we observed that some players still play their old games after
buying the new game versions, which we term as “port-back.” The formal definition
of “port-back” is as follows.
Definition 1 (Porting Back in Video Game) Player A is defined as porting
back in game version x if
1. Game version x is player A’s most recent purchase in his game portfolio X.
2. There exists a version x′, where x′ =6 x, x ∈ X, such that player A played
version x′ after buying version x.
There are several implications from this definition. First, a player needs at
least two game versions to be eligible, as he needs an old game version to port back
88
Game activation count
to, and this requirement excludes players’ initial versions. Second, porting back
behavior is player-version specific, so it is possible that player A ported back in G4
but not in G5 because he stopped playing old games (including G4) after buying
G5. To facilitate the expression, we denote porting back players as PB players, and
non-porting back players as NPB players. Similarly we define game sessions when
players port back as PB sessions, and others as NPB sessions.
Table 4.3: Summaries on PB player count
Player count
PB %
NPB player PB player Total
G3 6,027 1,414 7,441 19.00%
G4 8,192 1,935 10,127 19.11%
Current game
G5 10,959 2,868 13,827 20.74%
G6 14,389 2,237 16,626 13.45%
Notes: “Current game” denotes players’ most recent game versions
in terms of purchase date. For each game version, define a player
to be PB player if he ported back to earlier versions when this
version is his current version. Discrepancy in the player count be-
tween this table and player purchase statistics comes from players
with no active game sessions observed.
Table 4.4: Summaries on PB percentage across initial and current games
Current game
G3 G4 G5 G6
G2 19.00% 17.75% 18.51% 11.49%
G3 21.44% 19.86% 12.30%
Initial game
G4 25.01% 16.27%
G5 14.64%
Notes: “Initial game” is defined as the first game a player
bought. For each combination of initial game and current
game, the number reported is the percentage of PB play-
ers among total players.
Table 4.3 provides summaries on the distribution of PB players across different
89
game versions. Approximately 13% to 20% of players ported back in our example,
which is a large base considering the popularity of this sports game franchise. But
we can also see that game G6 has a significantly lower portion of PB players than
other games, and this portion is unanimously lower regardless of their initial game
versions. Therefore it is necessary to incorporate game version specific fixed effect
when modeling players’ PB choices. Table 4.4 further disentangles the percentage
of PB players based on the current game version and players’ initial game version.
On average, less players would port back when their current versions are more
recent as compared to their initial versions, which could be potentially explained
as players buying multiple game versions are more likely those who appreciate the
game features brought by the new game versions.
4.2.3 Persistent gaming preferences
All game versions in the game franchise we study here are similar in design,
where game versions only differ in graphics, up-to-date sports information and cer-
tain game contents, so we assume that each player has correlated game preferences
over time and across different versions he has played. Given that players’ purchase
intentions are determined by the additional values of the new game, which is also
affected by players’ values of the old game in the portfolio, this assumption estab-
lishes correlations between players’ purchase activities and past playing activities as
well.
To validate this assumption, we regress players’ purchase probabilities and
90
playing hours for the next game over their current game session duration. Several
data patterns can be found in Table 4.5.
Table 4.5: Regression of players’ future purchase probabilities on current playing
time and PB behavior
If buy next Dur in next ver If buy next Dur in next ver
If PB -0.251∗∗∗ -1.965∗∗∗
(-5.75) (-9.60)
Log(duration) in current ver 0.0809∗∗∗ 0.494∗∗∗ 0.113∗∗∗ 0.667∗∗∗
(97.78) (109.66) (29.82) (42.01)
If PB × Log(duration) in current ver 0.0179∗∗∗ 0.160∗∗∗
(4.78) (9.44)
Duration in PB session -0.0263∗∗∗ -0.0210
(-8.00) (-1.65)
Current game FE Yes Yes Yes Yes
Initial game FE Yes Yes Yes Yes
Observations 79236 39870 6225 4049
R2 0.201 0.278 0.141 0.318
t statistics in parentheses
∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
First, for any game version, if a player ports back, he will play less in the next
new game version purchased. Players’ port-back behavior indicates their higher
preferences towards the old game relative to the new game, so this pattern can be
explained if these port-back players’ higher preferences towards the old games are
persistent over time.
Second, longer playing time is associated with higher purchase probabilities.
To incorporate this pattern, we associate both players’ playing time and purchase
intentions with their game preferences γ.
Third, longer playing time in PB sessions is linked to lower purchase probabil-
ities. In our model, PB players have higher game preferences towards the old game,
so the lower purchase intentions can be explained as lower additional value brought
91
by the new game relative to their current game portfolios.
Table 4.6 also describes the average duration each player spent across different
modes. The statistics are categorized between PB and NPB players, and for PB
players, the average duration in PB and NPB sessions. As is in the last column,
which reports the ratio of PB and NPB sessions for the PB players, we can see that
PB players spend more in Career Mode, as compared to others.
Table 4.6: Average total duration across players (seconds)
NPB Players PB Players
PB/NPB ratio
NPB Sessions PB sessions
Career 103458 76566 14699 0.19
Instant Play 21743 21455 2762 0.13
G3 Ultimate Team 24321 35921 1250 0.03
Occasional Play 75842 59326 4735 0.08
Career 100662 74728 12946 0.17
Instant Play 22471 28845 4034 0.14
G4 Ultimate Team 42454 82601 3265 0.04
Occasional Play 56481 49693 7222 0.15
Career 91797 71836 12550 0.17
Instant Play 26451 35541 5585 0.16
G5 Ultimate Team 82614 145385 5323 0.04
Occasional Play 48246 47471 5748 0.12
Career 77739 68949 8442 0.12
Instant Play 17254 23019 4336 0.19
G6 Ultimate Team 69001 125796 5769 0.05
Occasional Play 55924 76922 2778 0.04
Finally, to see how game durations within each player is correlated over time
and within each game mode, we run two regressions on game duration and a dummy
variable that equals one if the play plays the corresponding mode in a period over
past game activities, as in Table 4.7.
Both game duration and game play dummy are positively correlated with
92
Table 4.7: Regression on game duration and game play dummy over past duration
in the same mode
(1) (2)
Total duration If play (1=play, 0=no play)
Past duration 0.365∗∗∗ 0.00000336∗∗∗
(13.78) (15.30)
Instant Play × Past duration -0.397∗∗∗ 0.00000434∗∗∗
(-5.59) (7.39)
Ultimate × Past duration 0.0277 -0.00000142∗∗∗
(0.58) (-3.68)
Occasional Play × Past duration -0.158∗∗∗ -0.000000562
(-3.91) (-1.66)
Time FE Yes Yes
Player FE Yes Yes
Observations 2853 5815
R2 0.281 0.206
Notes: t statistics in parentheses. * p < .05, ** p < .01, *** p < .001. Obser-
vation unit is user-mode-period level. “Past dur” is each player’s duration in the
same mode in the previous period (zero if not played). In the first regression, only
observations with positive duration are included.
players’ past game duration in the career mode (the base level) and the ultimate
mode. For example if a play plays a lot in Career mode at t, he is also predicted to
play the Career mode at t+ 1 and spend more time on the mode as well. Duration
in Occasional mode is less predictive for future duration, and for Instant Play mode,
players’ game duration is almost uncorrelated (=.365-.397). Such differences across
different modes motivate our model setup that players’ preferences are correlated
over time, and such correlations are mode-specific.
In regards to predicting whether a player would play a mode, as reported in
the second column, the instant play mode is the most predictable among others as
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it has the highest correlation with past game duration activities. The relatively low
R2 may indicate, however, that game play dummies could be hard to fit.
4.2.4 Data processing
Data is processed into player-mode-version-period level observations. For each
group of players defined by their initial game versions played, we drop the top 10%
players in terms of their total playing time in their initial and subsequent versions.3
In each period, assume each player has 500 hours to allocate across different game
modes and the outside option.
There are two periods defined between each two consecutive releases: “pre-
holiday”, defined as between the release and November 15 each year, and “holiday”
for the rest of the annual cycle. After dropping the top 10% players, there are 53,076
players remaining in the sample. In estimation, we take a 2% random sample, which
includes 1087 players, to facilitate the computation while maintaining enough player
heterogeneity.
4.3 Model
In this section, we develop a model framework that incorporates both players’
game purchase decisions and game play activities. Players observe the newest game
version in each period, and decide whether to buy it to be included in their game
portfolios for all of the future periods; conditional on their updated game portfolios,
3The cumulative playing time thresholds are 2654.48 hours, 1275.68 hours, 1247.08 hours, 906.79
hours, 297.88 hours for players initially played in G2 through G6, respectively.
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they allocate their playing time across different game modes and game versions.
Denote player as i, game mode as m, game version as v and period as t. At
the beginning of period t, denote player i’s game portfolio as Vi,t−1. In each period,
the model proceeds as follows.
1. For all the games v ∈ Vi,t−1, players observe their realized preferences in period
t, {γimvt}m∈M,v∈V .i,t−1
2. If a player is eligible to purchase in period t (defined below), he receives a
signal of his preference towards the game modes in the new game version v̄t,
and decide whether to buy the new game (Vit , Vi,t−1 ∪ {v̄t}) or continue to
play his current game portfolio (Vit , Vi,t−1).
3. If the player buys the new game, his preference towards the new game is
realized as {γimvt}m∈M,v=v̄t .
4. Based on the realized game preferences, the player allocates his playing time.
A player is defined as “eligible to purchase in period t” if (1) he has not
purchased v̄t yet; (2) he has purchased an earlier version before period t. The first
requirement rules out repeated purchases of the same game version. The second
requirement rules out players potentially buying the new game as their first game
versions. As will be illustrated in the data section, we do not observe the market
size of all potential game buyers; therefore we only model players’ upgrade purchase
decisions when they already play the game franchise for at least one period.
In the rest of this section, we first present players’ utility function from playing
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the game conditional on their game portfolios and realized gaming preferences; then
given the utility specification, we solve for players’ game purchase decisions.
4.3.1 Utility from game play
We follow Crawford and Yurukoglu [2012] and assume that players’ maximize
their utilities by allocating their time across all the modes and versions they have
access to, in the form, 4
∑ ∑
max = γimvt log dimvt, s.t. dimvt ≤ D. (4.1)
{dimvt}
m∈M,v∈Vit,dimvt>0 m∈M,v∈Vit
Players’ outside options, i.e. other entertainment activities, are included in
all players’ choice sets as v0 ∈ Vit. dimvt ≥ 0 denotes the time spent in the corre-
sponding mode, version and period. D represents the total time spent in all forms
of entertainment in each period. Player preference γimvt takes the form
χimvt ◦ (γ̃
1−αm αm
imvt) (γ̄im,t−1) , if #(Vi,t−1) ≥ 1
γimvt =  (4.2)χimvt ◦ γ̃imvt, if #(Vi,t−1) = 0
where
γ̃imvt = exp (ηi + ξm + ξv + ξt + ζimvt) , γ̄im,t−1 = γimv′,t−1|v′=v̄ . (4.3)i,t−1
4Players’ game duration is in the units of second. In our data, there is no observation with
dimvt ∈ (0, 1).
96
γ̃imvt represents the “contemporary component” of the game preference, which in-
cludes mode-specific preference ξm, game-specific preference ξv, period-specific pref-
erence ξt and individual random effect ηi ∼ N(µη, σ2η). ζimvt ∼ N(0, σ2ζ ) represents
other unobserved utility components that are independent across modes, versions,
time and individuals. γ̄im,t−1 represents players’ game preferences in the most recent
game version in the previous period. χimvt ∈ {0, 1} is a random process to fit the
data patterns that players only play certain game modes and game versions, with
the probability form constructed as
 exp(a0m + a1mγimv,t−1) , for newest game in the portfolio
 1 + exp(a0m + a1mγimv,t−1)Pr(χimvt = 1) =  exp(a0m + a1mγimv,t−1 + a2m) , for other games
1 + exp(a0m + a1mγimv,t−1 + a2m)
(4.4)
The presence of player’s game preference in the previous period in this functional
form captures the empirical pattern that longer playing time is associated with
higher future play probabilities. We allow such correlation to vary across game
modes, and also between PB and NPB sessions as captured by a2m.
Players’ optimal time allocation {d∗imvt} solves (4.1), and by normalizing play-
ers’ preferences towards the outside option as γi0t = 1, it takes the form
 0, if γimvt = 0
d∗imvt =  ∑ , (4.5)γimvt D, if γimvt > 0
1 + m′∈M,v′∈V γim′ ′it v t
This solution form can be interpreted as if a player plays individual sessions
repeatedly, and for each session the player only chooses one version-mode combina-
97
tion. In this way, players’ playing time for each mode-version is determined by its
relative game preference with respect to others.
With the optimal time allocations, players’ indirect utilities conditional on the
game portfolio Vit and game preference γit = {γimvt}m∈M,v∈V , areit
∑ ( )
V γimvtu( it,γit) = γimvt log ∑ D , (4.6)
1 + m′∈M,v′∈V γim′v′tm∈M,v∈Vit,γimvt>0 it
which is used to facilitate the computation of players’ values under different game
purchase decisions.
4.3.2 Game purchase decision
In the game franchise that we study, new versions are released every year,
and players keep buying new game versions to be added to their portfolios. There
are two periods between each two consecutive gam4e releases: “pre-holiday” which
starts from the game release and ends at Nov 15th, and “holiday” which covers the
rest of annual cycle until the next game release.
From this piont, we denote the most recent game available for purchase as “new
game”, and all the other games as “old game.” When a new game is released, a player
chooses from the following options: (1) pay the full retail price p to buy the game in
pre-holiday period; (2) pay the discounted price δp to buy the game in post-holiday
period; (3) not buy the game. To simplify the computation, assume that players
only evaluate the purchase decisions based on their value in the current period, or
in another word, players’ lifetime value of buying the new game is proportional to
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the value in the current period.
To formalize the discussion of purchase decisions, we make the following as-
sumptions.
Assumption 1 Players keep at most two game versions at any time; when a player
already has two versions in his portfolio and buys another game, the oldest version
is automatically removed.
Assumption 2 A player has access to all the game modes, denoted as M, for all
the games in his portfolio.
Assumption 3 Players can only buy the most recent game version in each period.
For the newest version in period t, denoted as v̄t, a player who is eligible to
buy the game compares his value of buying and not buying the new game and make
his purchase decision accordingly.
Since a player knows his game preferences towards the owned games Vi,t−1 at
the time of purchase decision, his value of “no-purchase” is deterministic and takes
the form
uNo-Buyit = u(Vi,t−1,γit = {γimvt}m∈M,v∈V − ) (4.7)i,t 1
To evaluate the utility of buying the new game, assume that a player receives a
random shock ζ̃imvt ∼ N(0, σ2ζ ) for the new game when he decides on the new game
purchase, and this random shock is not observable to the econometrician. With this
shock, the player can calculate his preference for the new game, and his value of
99
“purchase” is (denote Vit as the updated game portfolio after purchase)
uBuyit = u(Vit, {γimvt}m∈M,v∈V ) (4.8)it
The player will buy the game if the additional value brought by the new game
is larger than a time-specific threshold pt. Denote players’ purchase behavior as
sit ∈ {0, 1}, the player’s purchase probability is
( ∣∣ )
Pr(s = 1) = Pr uBuy − uNo-Buyit it it ≥ pt∣Vi,t−1, {γimvt}m∈M,v∈V − (4.9)i,t 1
which completes the model setup of players’ purchase and play decisions.
4.4 Estimation
Our model parameters, as summarized in Table 4.8, are estimated using max-
imum likelihood function over players’ observed play and purchase activities. In the
rest of this section, we provide detailed description on how the likelihood function for
players’ game play activities and game purchase decisions, as well as the estimation
algorithm imposed in the estimation.
4.4.1 Likelihood function of game play
Denote the set of parameters to be estimated as Θ, and the set of a player’s
state variable after the purchase decision and before time allocation decision at
period t as X1it = {Vit,γit,γi,t−1}. For each mode and version in the portfolio,
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Table 4.8: List of parameters to be estimated
Function Count
A. Utility function
a0m, a1m, a2m Pr(simvt = 1) 12
B. Specification of γimvt
ξm Mode FE 4 (1 default)
ξv Version FE 5 (1 default)
ξt Time FE 2 (1 default)
uη, ση Distribution of ηi 2
C. Specification of εimvt
αm Correlation within game modes 4
σζ Distribution of ζi 1
αp Value threshold for purchase 2
conditional on the value of individual random effect ηi, the log likelihood function
of observed playing time, dimvt is
( )
fd(d 1 1imvt = d|Θ, Xit, ηi) = Y (d = 0) log(Pr(d = 0|Xit,Θ) )
+ Y (d > 0) log (Pr(d > 0|X1 ,Θ)f(d|X1it it,Θ, ηi, d >(40.)10),
where f(·) is the probability density function for dimvt, and Y (·) is the indicator
function which equals one if the condition is met, and zero otherwise.
Given the parameter value {a0m, a1m, a2m}m∈M, and game preference in the
last period γi,t−1, Pr(d > 0|Xit,Θ) can be calculated based on (4.4). To calculate the
probability density function f(d|Xit,Θ, d > 0), first impute players game preference
as γ̃ ∗ ∗imvt = dimvt/d0, then the imputed random term ζ takes the form
ζ̃imvt = log(γ̃imvt)− ηi − ξm − ξv − ξt − αmγimv′,t−1|v′=v̄ (4.11)i,t−1
101
From this expression we can see that probability density of positive game duration is
equal to φ(ζ̃imvt|Xit,Θ, ηi) where φ(·) is the density function for normal distribution
with mean zero and standard deviation of σζ .
4.4.2 Likelihood function of game purchase
Denote players’ state variables before making purchase decisions as X0it =
{Vi,t−1, {γ 1imvt}m∈M,v∈V − }, which differs from Xit in that, if the player buys thei,t 1
new game v̄ , X0t it does not include players’ realized game preference towards the new
game. In each period, the log likelihood function for the observed game purchases,
sit ∈ {0, 1}, and game play activities, {dimvt}, is
f(sit , dit = {dimv[t} 0m∈(M,v∈V |Θ, Xit it, ηi) =) ∑ ]
Y (sit = 1) l[og Pr(sit = 1|Θ, X
0 d 1
it) + E f (dimvt = d|Θ, Xit, ηi, sit = 1)
( ) ∑m,v ]
+Y (sit = 0) log Pr(sit = 0|Θ, X0it) + fd(dimvt = d|Θ, X1it = X0it, ηi, sit (=4.01)2)
m,v
where the expectation is taken over preferences in the new game.
To effectively calculate players’ game purchase probabilities, note that players’
indirect utilities take the analytic form (as in (4.6)) of
∑ ( )
U buy
γimvt
it = E γimvt log ∑ D . (4.13)1 +
m∈M ′,v∈V ∪{v̄ } m ∈M,v′∈V ∪{v̄ }
γim′it t v′tit t
To empirically evaluate this expectation, we take nr random draws of game prefer-
ences in the new game, based on the current parameter trial in the estimation, as
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{γrimvt}m∈M,v=v̄t where r = 1, 2, . . . , nr. Then players’ value of buying new games
can be calculated as (γrimvt = γimvt for preferences of old games)
( )
n
buy 1 ∑r ∑ r ∑ γrU = γ log imvtit imvt D . (4.14)nr 1 + r∈M ∈V ∪{ } m′r=1 m ,v v̄ ∈M,v′∈Vit∪{v̄ γ ′ ′t t} im v tit
Players’ values of no-purchase are deterministic as players observe their re-
alized game preferences for all their available games before making the purchase
decisions. Denote the value of no purchase as Uno−buyit , then players’ purchase prob-
abilities are
Pr(sit = 1|Θ) = Pr(U buyit − U
no−buy
it ≥ pt). (4.15)
Finally, the aggregate likelihood function sums up individual likelihood of
purchase and play behaviors, and is integrated over individual random effect as
∑∫ ∑
L(Θ) = f(sit,dit|ηi,Θ)dF (ηi|Θ) (4.16)
i t
Our estimation proceeds as follows: for each player and each period, first impute
the game preference and calculate the likelihood for the observed game duration;
then given the imputed preference value, simulate and calculate players’ purchase
probabilities. The detailed algorithm is as follows.
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Algorithm 2 Calculate likelihood function for parameter estimation
1: Generate a vector of the random effect ηi candidate values, chosen as 1% to 99%
quantiles with 1% increment.
2: for Each ηi value, each player and each period do
3: Impute players’ preferences for the games they played based on observed
game duration
4: Impute ζ from players’ preferences. Calculate its density as the likelihood
for players’ game duration.
5: Impute probabilities of game play, and calculate likelihood function for ob-
served game play choices.
6: For players eligible to buy new games, calculate their values of “buy” and
“no-buy” choices and impute their purchase probabilities.
7: end for
8: For each ηi value, calculate the aggregate likelihood function, then integrate over
all ηi based on distribution parameters.
4.5 Estimation result
4.5.1 Parameter estimates
This section reports estimation results based on 1078 players, a 2% random
sample selected from the original dataset. For each selected player, we include all
of his game sessions for all game versions and modes observed in the original data.
Parameter estimates are reported in Table 4.9.
For common utility components, which are homogeneous across all individu-
als, the fixed effect estimates suggest that players’ favorite modes are career mode
(as the base) and Occasional Play Mode, and favorite game version is G2 (as the
base) and G6. Differences in estimates across modes are higher than across game
versions. On average, players play mode in the pre-holiday season, and within-player
heterogeneity (measured by σζ) dominates cross player heterogeneity (measured by
ση).
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Table 4.9: Parameter estimates
Parameter description Param Est. Std. Err.
A. Common utility components
Career - -
ξ Instant Play -1.5556 0.0020m
Ultimate Mode -1.5300 0.0020
Occasional Play -0.8361 0.0005
G2 - -
Fixed Effect G3 -0.0963 0.0003
ξv G4 -0.1057 0.0008
G5 -0.0752 0.0012
G6 -0.0445 0.0015
Pre-holiday - -
ξt Post-holiday -0.0360 0.0015
µ -4.0516 0.0001
Random Effect η
ση 0.0239 0.0060
ζ σζ 2.1896 0.0005
B. Correlation with past game experiences
Career 0.0967 0.0001
Correlation with γ α Instant Play 0.1196 0.0001t−1 m
Ultimate Mode 0.0373 0.0003
Occasional Play 0.0769 0.0007
Career 0.7592 0.0006
Instant Play 0.6113 0.0003
a0m Ultimate Mode 0.2676 0.0118
Occasional Play 0.2275 0.0004
Career 1.3037 0.8341
Pr(d > 0) Instant Play 1.5743 0.0004a1m Ultimate Mode 0.2657 0.3597
Occasional Play 2.1730 0.5820
Career 0.5240 0.0604
a Instant Play 0.6559 0.06532m
Ultimate Mode 0.2225 0.0409
Occasional Play 0.5154 0.0505
C. Monetary preference
Price coefficient Pre-holiday 0.1685 0.0003
Holiday 0.2199 0.0003
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The second part reports estimates that determines the probability of play
and correlation with past gaming activities. Players’ playing time is correlated the
Ultimate Mode and Career Mode, and given the fact that players spend the most
time in Career Mode, we can say that it is the most correlated game mode in game
play. By comparing the estimates of a0m, we can see that players are more likely to
play in their initial game versions.
The third part reports players’ value threshold of buying the new game in each
period. In general, the additional value required for new purchase is higher during
the holiday season, mostly because of player selection: those who would wait until
holiday seasons to buy the game are less enthusiastic about the game franchise, and
the higher value threshold reflect their lower willingness to play.
4.5.2 Model fit
This paper focuses on players’ individual behavior, rather than aggregate mar-
ket level statistics. The additional data details provide more variations in identifi-
cation, but also levels up the difficulty for model fit: each individual player could be
affected by various factors not captured by the model, and exhibit higher variations
than the market average. In this section, we provide measures on how our model
structure fits the data in players’ three major decision categories: game duration,
game play probability, and game purchase probabilities.
106
Figure 4.2: Correspondence between imputed and actual game duration
14
12
10
8
6
4
2
0
0 2 4 6 8 10 12 14
Imputed log(game duration)
Game duration
Based on our model parameter estimates, we first calculate the imputed game
preference as ( )
γ̃imvt = exp ηi + ξm + ξt + αmγimv′,t−1|v′=v̄ , (4.17)i,t−1
which differs from the model structure in ζimvt as it is assumed to be mean zero.
5
Figure 4.2 plots the correspondence between predicted and actual game duration
for observations with dimvt > 0.
Based on the figure, the imputed and actual duration coordinates are clus-
tered around the 45 degree line, but with a high degree of variance. This suggests
5Another interpretation is that γ̃ measures the “predicted” component of player preference, and
ζimvt measures the unpredictable component.
107
Actual log(game duration)
that the model captures the average duration level but there are still factors not
captured by the model, and these factors could potentially affect players’ game play
decisions. To further check the model fit for the duration, Table 4.10 reports the
average imputed and actual game duration across periods, versions and modes, as
well as their standard deviations. On average, game duration fits better across pe-
riods and games than across modes, which is mostly driven by certain mode-version
combinations. More details can be found in the appendix.
Play probabilities
Given the parameter estimates, we also calculate the imputed probability of
players playing each game mode and game version in each period, and the compari-
son in this imputed probability between no-play and play observations are reported
in Table 4.11. While the predicted play probabilities are higher in the play observa-
tions than no-play observations, the differences are small compared to their standard
deviation which suggests the model cannot predict which mode and version a player
would play. To overcome this difficulty, we hold fixed the versions and game each
player actually played in the counterfactual analysis.
Purchase probabilities
Finally, we also impute players’ purchase probabilities and report them across
periods in Table 4.12. Note that in our model, players are only allowed to buy the
newest game version, so the reported imputed purchase probabilities across periods
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Table 4.10: Imputed and actual game session durations (in seconds)
Imputed Observed
Mean Std. Dev. Mean Std. Dev.
A. By period
2012 Holiday 19869 18993 27940 62653
2013 Pre-holiday 22841 21220 25203 46054
2013 Holiday 18545 17294 22961 50306
2014 Pre-holiday 20728 19292 19730 34878
2014 Holiday 17273 17892 23618 55269
2015 Pre-holiday 21005 19643 23763 46971
2015 Holiday 17611 17462 24392 53382
2016 Pre-holiday 21754 20334 23648 45961
2016 Holiday 18198 18333 21138 43681
B. By game
G2 16326 35613 18034 45465
G3 18801 38909 19915 43984
G4 24752 43435 21866 51007
G5 21253 35682 23066 47398
G6 32365 47787 26437 49874
C. By mode
Career 52474 66080 37948 61992
Instant Play 16937 24272 11374 21000
Ultimate Mode 16534 25481 26276 64432
Non-game 2293.7 3601.2 6372 19118
Occasional Play 9809.4 12724 23761 47279
Note: Observation units are player-game-mode-time specific.
Only observations with positive game play are included.
are also across different game versions as indicated in the first column.
In general the model predicts the purchase instances well as the predicted
purchase probabilities for non-buyers are around 0.2 and for buyers are around 0.9.
109
Table 4.11: Imputed probabilities of game play between play and no-play observa-
tions in players’ most recent version
Play observations No-play observations
Mean Std. Dev. Mean Std. Dev.
A. By period
2012 Holiday 0.3286 0.1029 0.2787 0.1027
2013 Pre-holiday 0.3426 0.1146 0.2921 0.1041
2013 Holiday 0.3383 0.1134 0.2948 0.1051
2014 Pre-holiday 0.3454 0.1103 0.2982 0.1064
2014 Holiday 0.3426 0.1106 0.2945 0.1061
2015 Pre-holiday 0.3529 0.1075 0.2953 0.1063
2015 Holiday 0.3497 0.1109 0.2939 0.1064
2016 Pre-holiday 0.3472 0.1140 0.2974 0.1062
2016 Holiday 0.3389 0.1115 0.2976 0.1063
B. By mode
Career 0.4921 0.0230 0.4882 0.0190
Instant Play 0.5608 0.0367 0.5568 0.0374
Ultimate Mode 0.2911 0.2427 0.2809 0.2394
Non-game 0.4709 0.0669 0.4677 0.0674
Occasional Play 0.5347 0.0064 0.5333 0.0040
Table 4.12: Imputed purchase probabilities between buyers and non-buyers
Buyers Non-buyers
New game Period
Mean Std. Dev. Mean Std. Dev.
G3 2013 Pre-holiday 0.2521 0.0622 0.8302 0.0683
2013 Holiday 0.1640 0.0648 0.8760 0.0746
2014 Pre-holiday 0.2351 0.0782 0.8536 0.0765
G4
2014 Holiday 0.1430 0.0502 0.9058 0.0544
2015 Pre-holiday 0.2392 0.0773 0.8653 0.0761
G5
2015 Holiday 0.1633 0.0555 0.9088 0.0593
G6 2016 Pre-holiday 0.2445 0.0810 0.8716 0.0675
2016 Holiday 0.1652 0.0599 0.9155 0.0491
4.6 Counterfactual analyasis
In this section, we simulate players’ game play activities based on two potential
game mechanism changes that could be of interest for the video game publishers:
110
restriction of game access to new game version only, and removal of past game
preferences.
Single-game restriction
As is illustrated in the data section, around 13% to 20% of players continue to
play their old games after buying the new games, which makes it natural for firms
to wonder what would happen if these players are restricted to play their newest
game version only. After all, when these players have no access to their old games,
they should spend more time in their new games, and higher playing time in the
new game can facilitate even higher game duration in the future through correlation
in the game preferences.
To see how players would reallocate their playing time in the new games, we
simulate players game duration by restricting them playing in the newest game
version in their portfolios. We hold the mode-version each player actually played
and players’ purchase decisions fixed as the same with the actual observations. The
results are reported in Table 4.13.
From the table we can see that, players play more in the new game, but the
extent of such game play increase is very limited to the scale of 0.3%. This suggests
very weak substitution in players’ game duration between the old and the new game,
and removing players’ access to their old games will significantly reduce their playing
time.
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Table 4.13: Comparison of game duration with and without the single-game restric-
tion
Original Single-game restriction
Period
New game Old game New game
2013 Pre-holiday 9934 3019 9985
2013 Holiday 5975 1917 5996
2014 Pre-holiday 4385 1064 4384
2014 Holiday 4595 1692 4606
2015 Pre-holiday 4688 1183 4691
2015 Holiday 4435 1441 4452
2016 Pre-holiday 4899 1313 4922
2016 Holiday 4079 976 4083
Average 5374 1576 5390
Note: numbers reported are average duration (in seconds) in each
version-mode-period that players played.
Correlation in intertemporal game preferences
One of the data patterns in the data is that players spend consistently high or
low time in certain game modes over time, and this persistence cannot be explained
by common utility factors like game mode fixed effect and individual random effect.
To evaluate how these correlated game preference in the past affect players’ current
game play activities, we change players’ game preferences, originally in the form of
χ 1−αm αm imvt ◦ (γ̃imvt) (γ̄im,t−1) , if #(Vi,t−1) ≥ 1γimvt =  (4.18)χimvt ◦ γ̃imvt, if #(Vi,t−1) = 0
to
γimvt = χimvt ◦ γ̃imvt (4.19)
In another word, players are treated as if they have no prior playing expe-
112
riences, although their game purchase records and game portfolios in each period
are unaffected. Table 4.14 compares players’ game duration with and without the
previous game preferences.
Table 4.14: Comparison of game duration with and without game preferences
Original With no previous preference
Period
New game Old game New game Old game
2013 Pre-holiday 9934 3019 7970 2852
2013 Holiday 5975 1917 5597 1751
2014 Pre-holiday 4385 1064 3507 985
2014 Holiday 4595 1692 4350 1619
2015 Pre-holiday 4688 1183 3831 1118
2015 Holiday 4435 1441 4100 1307
2016 Pre-holiday 4899 1313 3903 1225
2016 Holiday 4079 976 3746 882
Average 5374 1576 4625 1467
From the table, when players’ game preferences are only determined by con-
temporary component γ̃imvt, players on average spend 13.9% less time (from 5374
to 4625) in their new games, and 6.9% less time (from 1576 to 1467) in their old
games.
4.7 Conclusion
This paper provides a framework to analyze video game players’ multi-version
consumption behavior in the video game industry. In this framework, players al-
locate their playing time across game versions and game modes in their portfolios,
and their purchase decisions of new game versions are also endogenously determined
by the additional value brought by players’ portfolios. This framework is developed
113
to fit two patterns found in the data, where players are observed to continue to play
their old games after buying the new versions, and they spend consistently higher
time in certain game modes over time.
Given the parameter estimates, we conduct two sets of counterfactual analy-
sis by simulating players’ game activities under two alternative model alternative.
When players are restricted to play their newest game only in the portfolio, players
spend on average 0.3% more time in their new game while they completely stop
playing the old game, which suggests very weak substitutions across game versions
in players’ portfolios. When we remove players’ past game experiences from their
current game preferences, players spend on average 14% less time in the new game,
and 7% less time in the old game, which suggests strong intertemporal correlation
in players’ game preferences.
In the next step, we will further relax players’ choices in the counterfactual
analysis by allowing them to change their purchase decisions from the data, and
re-evaluate the impacts of alternative game designs, like the single-game restriction,
on players’ play activities through their purchase changes. It is also worthwhile to
study how players’ purchase intentions for the new game would vary across their
past game experiences, and examine how common marketing strategies like targeted
discount would change players’ play and purchase activities.
114
4.8 Appendix: Supplemental summary statistics
Table 4.15 reports statistics based on game session level, as compared to player
level in Table 4.1. One significant difference from the player level statistics is that
number of sessions and average session duration in the Ultimate mode is higher than
career mode, while the session count and session average duration are not. This
suggests that ultimate mode is played by relatively less players with each player,
which is also consistent with the high standard deviation for the ultimate mode.
115
Table 4.15: Summary statistics: by game sessions
(a) Game session count
Game Version
G2 G3 G4 G5 G6
Career 95,876 305,131 339,275 379,602 376,141
Instant Play 57,890 87,438 126,465 184,970 147,041
Game Mode Ultimate Mode 18,882 95,928 209,438 492,554 464,937
Non-game 56,180 14,954 16,700 12,600
Occasional Play 96,474 222,748 165,973 173,936 318,249
(b) Average session duration (seconds)
Game Version
G2 G3 G4 G5 G6
Career 4966.20 3710.15 3923.51 4175.99 4019.06
Instant Play 2582.54 3460.45 3227.59 3087.91 2679.24
Game Mode Ultimate Mode 3829.36 3265.80 3482.00 3558.84 3096.44
Non-game 1762.77 1467.86 873.89 1348.55
Occasional Play 4637.72 3824.48 4712.42 5135.74 3614.58
(c) Standard deviation of game duration (seconds)
Game Version
G2 G3 G4 G5 G6
Career 5278.83 4550.10 4693.03 4986.39 4124.25
Instant Play 3796.91 4097.38 4426.34 6035.28 4210.36
Game Mode Ultimate Mode 3815.01 3622.08 4101.47 4887.49 3875.17
Non-game 2957.91 2271.58 2170.36 4629.76
Occasional Play 4669.90 4556.51 5090.76 7061.29 4946.02
Notes: All players who have played at least one game session in any game are in-
cluded.
116
Table 4.17: Imputed and actual game duration by game mode and version
Imputed Actual Difference
G2 40944.41 27900.76 13044
G3 43257.92 34744.04 8514
Career G4 55510.35 40208.36 15302
G5 48213.91 41084.46 7129
G6 71162.91 42013.31 29150
G2 13443.12 7822.75 5620
G3 13398.06 11342.42 2056
Instant Play G4 18931.81 12225.94 6706
G5 15416.23 12295.3 3121
G6 22237.7 11508.45 10729
G2 12597.58 27109.37 14512
G3 12001.79 15840.33 3839
Ultimate Mode G4 14170.85 20018.06 5847
G5 16649.87 29564.68 12915
G6 22686.89 35258.37 12571
G2 2758.367 11350.73 8592
G3 2698.665 4202.941 1504
Non-game G4 1900.088 1727.875 172
G5 1334.252 2961.453 1627
G6 - - -
G2 7835.61 27043.21 19208
G3 8116.8 20728.86 12612
Occasional Play G4 11069.44 24846.95 13778
G5 8294.879 23630.92 15336
G6 13173.69 24879.55 11706
117
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