Dynamics of Pricing in the Video Game Console Market: Skimming or Penetration?
Hongju Liu
July 12, 2006
Preliminary Draft: Please Do Not Cite or Circulate
Abstract
The 32/64-bit video game console market was largely characterized by the competition
between Sony PlayStation 1 and Nintendo 64. Historical data on prices of game consoles show
that the price of PlayStation declined over time – consistent with price skimming. At the same
time, marginal costs declined even faster than prices. In effect Sony’s markup increased –
consistent with penetration pricing. In this paper, I reconcile these two findings – while the
existence of heterogeneous consumer segments provides an incentive to skim the market, this
incentive is overshadowed by the competing incentive to penetrate the market quickly and take
advantage of the indirect network effects that exist between consoles and games. To analyze
firms’ pricing decisions, I first estimate a demand system that allows for indirect network effects
and consumer heterogeneity, and then proceed to solve for firms’ equilibrium pricing policies
under falling marginal costs. Indirect network effects and consumer heterogeneity introduce
dynamics to firms’ pricing decisions. Since an analytical solution is difficult to obtain, I
numerically solve for the Markov perfect equilibrium in firms’ dynamic pricing game. The
predicted prices follow similar patterns to the observed ones, i.e. prices fall but markups increase.
Without network effects markups would have been decreasing instead of increasing. Without
heterogeneity but with network effects PlayStation price would have increased even though its
marginal cost declined. I also perform policy experiments while taking into account adjustments
in prices under alternative policy regimes.
1. Introduction
Price skimming and penetration pricing are two frequently recommended pricing strategies for
new product launch. Price skimming involves charging a relatively high price at first and
lowering it over time. The objective is to “skim” off those consumers who are willing to pay
more. In contrast, penetration pricing is a strategy in which the initial price is set relatively low
in hopes to “penetrate” the market quickly and secure a significant market share.
This paper examines pricing behavior in the 32/64-bit video game console market, which
was largely characterized by the competition between Sony PlayStation1 and Nintendo 64.
Historical data show that the price of PlayStation declined over time. This seems to indicate price
skimming – Sony priced high initially for hard-core gamers, and cut prices later to attract casual
gamers. Such a view was echoed by a Wall Street Journal article in March 2004, commenting on
a price cut for Microsoft Xbox:1 “By many estimates, the latest cycle has peaked because hardcore gamers already have bought their consoles and their favorite games. Now the industry has
to focus on casual gamers and other price-conscious consumers, and it is betting that price cuts
will lure them.”
However, similar to many other high-technology products, game consoles exhibit falling
marginal costs over time. Based on the estimates by industry analysts, the marginal cost of
PlayStation declined even faster than its price. In effect the markup actually increased over time.
This pattern is consistent with the common belief that console makers often incurred substantial
1
“Game Gambit: Microsoft to Cut Xbox Price”, Wall Street Journal, March 19, 2004.
1
losses on hardware in early stages of product life cycle. For example, a recent Wall Street
Journal article mentioned: 2 “Hardware makers like Sony often lose money on the sale of
consoles in their early days on the market.”
Why would markups rise over time? The video game industry exhibits indirect network
effects under which the value of a console critically depends on the availability of its
complementary good – games. A console will be more attractive to consumers when more games
are available. On the other hand, as the installed base of a console becomes larger, software
vendors are more likely to develop games for it.
This mutually-enhancing feedback cycle between hardware and software provides an
incentive for penetration pricing. Hardware firms may be willing to cut early prices in order to
build up the network and attract more games. This incentive was highlighted by the following
paragraph from the 1999 annual report from President Clinton’s Economic Advisors: “In
network markets it may be a matter of competitive necessity to price below cost in order to
penetrate the market quickly, gain a lead in installed base, and raise expectations that a product
will deliver a large network benefit.”
Therefore the increasing markup of PlayStation reveals that Sony may have engaged in
penetration pricing, in spite of the falling price which is seemingly an indication of price
skimming. Indeed, the existence of heterogeneous consumer segments provides an incentive to
skim the market. But this incentive seemed to be overshadowed by the competing incentive to
penetrate the market quickly and establish a large installed base.
2
“The Power Players”, Wall Street Journal, February 18, 2006.
2
To analyze the price patterns in the console market, I first estimate a demand system that
allows for indirect network effects and consumer heterogeneity, and then proceed to solve for
firms’ equilibrium pricing policies under falling marginal costs. Since current prices affect future
network sizes and future distributions of consumers from different market segments, firms’
pricing decisions are inherently dynamic. These dynamics are captured by a dynamic oligopoly
pricing game. Given the difficulty in obtaining an analytical solution, I use numerical dynamic
programming techniques to solve for the equilibrium pricing policies. The equilibrium concept is
the Markov perfect equilibrium in pure strategies.3
With firms’ equilibrium pricing policies, I simulate the market competition between Sony
and Nintendo in the 32/64-bit video game console market to predict the prices in each month.
The predicted prices follow similar patterns to the observed ones, i.e. prices fall but markups
increase. Without network effects I find that markups would have been decreasing instead of
increasing. The drop in PlayStation price is predicted to be 87% more than the observed one.
Without heterogeneity but with network effects PlayStation price would have increased even
though its marginal cost declined. The predicted increase in PlayStation markup is more than
four times the observed one.
Network effects, consumer heterogeneity, and falling marginal costs are common features of
many high-technology markets. This paper attempts to empirically model firms’ dynamic pricing
decisions in an oligopoly market characterized by such features. When firms set prices during a
new product launch, there are important tradeoffs to be made. Price skimming may help to
3
Maskin and Tirole (2001) provide a concise treatment of the MPE concept.
3
recover the product development cost earlier, but the network growth can be slow. Penetration
pricing may lead to fast diffusion, but initial profitability could suffer. This model sheds light on
such tradeoffs.
Previous empirical studies have examined the importance of network effects without
formally modeling firms’ pricing decisions. In these studies it is difficult to evaluate firms'
potential policy shifts, because any perturbation in the market environment would naturally
induce firms to price differently. In this paper, by solving the dynamic pricing game I am able to
perform policy experiments while taking into account adjustments in prices under alternative
policy regimes.
In markets with network effects, the importance of preemption and first-mover advantage is
frequently emphasized. I evaluate the impact of a first-mover advantage using the proposed
model. As observed in the data, given some head start Sony would become the market leader.
However, given a similar head start Nintendo would have won the console war.
The success of PlayStation can be largely attributed to its advantage in game variety. If
Nintendo had attracted more game publishers, it would be in a better competitive position. In fact,
a 10% increment in the number of N64 games would have helped Nintendo surpass Sony and
take the lead.
A major decision faced by the 32/64-bit console makers was the choice between cartridge
and CDROM storage format. I examine the tradeoff involved in this decision. It appears that
Nintendo would be more vulnerable if it had adopted the CDROM format, unless the CDROM
format could help it increase its number of game titles by more than 40%.
4
1.1 Relationship to the Literature
Within a growing literature on network effects, 4 several theoretical papers examine firms’
pricing decisions. Dhebar and Oren (1985, 1986) analyze the optimal pricing strategy of a
monopolist in a market with network effects. Xie and Sirbu (1995) examine the dynamic pricing
behaviors of an incumbent and a later entrant by incorporating network effects into a diffusion
model. They find that an increasing price can be optimal under strong network effects. In these
studies, the optimal price trajectories are established as open-loop controls. In contrast I apply
numerical dynamic programming methods to obtain a closed-loop solution, which is more
relevant to managerial decision making in an empirical context. In addition, these studies need to
keep their demand specifications simple in order to derive tractable analytical solutions. Instead,
I adopt a more realistic demand model that can be fitted to real data.
This stream of research on pricing in network economies fits in a separate theoretical
literature that develops dynamic pricing models to incorporate the evolution of costs and demand.
Studies of monopoly markets include Robinson and Lakhani (1975), Dolan and Jeuland (1981),
Kalish (1983, 1985), Mahajan, Muller, and Kerin (1985), Horsky (1990), Krishnan, Bass, and
Jain (1999). Studies that extend to oligopoly settings include Thompson and Teng (1984), Rao
and Bass (1985), Eliashberg and Jeuland (1986), Dockner and Jorgensen (1988). Again their
4
Koski and Kretschmer (2004) provide a comprehensive survey.
5
demand systems might be somewhat restrictive for real-world applications, and they typically
solve for open-loop pricing solutions.
On the empirical side Nair (2005) solves the dynamic pricing problem of PlayStation game
providers facing declining consumer valuations over time, and finds price skimming to be
optimal. This paper differs from Nair (2005) in that I study an oligopoly market with declining
marginal costs and network effects, while he works with a monopoly market with constant
marginal costs and no network effects.
This paper also extends the empirical literature on measuring network effects using actual
industry data. Among others Gandal (1994), Economides and Himmelberg (1995), Saloner and
Shepard (1995), Brynjolfsson and Kemerer (1996) examine markets with direct network effects.
Bayus and Shankar (2003), Ohashi (2003), and Park (2004) estimate indirect network effects
using the installed base of consumers, and essentially treat indirect network effects as direct ones.
Gandal, Kende, and Rob (2000), Dranove and Gandal (2003), Basu, Mazumdar, and Raj (2003),
Clements and Ohashi (2005), Karaca-Mandic (2004), and Nair, Chintagunta, and Dubé (2004)
study various aspects of indirect network effects using data on the availability of complementary
products. None of these studies explicitly models the dynamic pricing decisions of hardware
firms.
2. The 32/64-bit Video Game Console Market
6
The video game industry has seen substantial growth over the past two decades. In 2005, revenue
for video game hardware, software, and accessories totaled $10.5 billion in the US according to
NPD Group, while in comparison movie box-office receipts came in at $8.99 billion according to
Motion Picture Association of America.
Since the rise and fall of Atari, there have been several generations of game consoles.5 The
focus of this paper is on the 32/64-bit generation whose life cycle extended roughly from 1995 to
2001. There were three players in the generation, namely Sony PlayStation (PS), Nintendo 64
(N64), and Sega Saturn. Sega encountered a series of production and distribution problems with
Saturn (Coughlan 2001). As the result it only captured a small market share and exited from the
market early. Thus I restrict attention to the duopoly competition between PlayStation and
Nintendo 64. The time period of this study starts in September 1996 when Nintendo launched
N64 in the US market. At that time PlayStation had been on the market for a year. Figure 1
displays the prices of both consoles.
Similar to many other high-technology products, game consoles exhibit declining prices
over time. Prima facie, this looks like price skimming. The rationale is that firms target game
enthusiasts first, and then move to mass market through price cuts. On the other hand, it is
widely believed that console makers often incurred substantial losses in early stages of product
launch. An initial deep loss has been a repeated pattern for PlayStation, PlayStation 2, Xbox and
Xbox 360.6 This indicates that although prices declined, since firms went from making a loss in
5
See Coughlan (2000) for an overview of the industry structure, and Coughlan (2001) for a brief history.
6
“Shakeup at Sony: What's the PlayStation Costing?” Alexander & Associates, 2002; “A $500 million gamble”,
7
the early periods to breaking even or making profits later on, marginal costs must have dropped
even faster than prices. As a result markups might have increased.
Although these firms never disclosed their cost information, some industry analysts have
tried to estimate the production costs of various consoles by adding up the bill of materials for
parts and factory assembly costs. For example, when Sony launched PlayStation in September
1995, the production cost was estimated to be $260. 7 When Nintendo 64 was launched in
September 1996, Nintendo was said to be able to manufacture a cartridge-based console at $160
per unit, while a Sony PlayStation was believed to cost $210 each – a drop of $50 from the time
it was launched.8
To describe how marginal costs, cjt, declined over time, I assume that the rate of decline was
proportional to the current marginal cost level, i.e.
dc jt
dt
= −b j c jt .
The above differential equation gives rise to a marginal cost curve that decreases exponentially
over time:
c jt = a j exp( −b j t )
(1)
Consequently my assumption on costs implies exogenously falling marginal costs over time. Is
this a reasonable assumption? In principle multiple reasons may contribute to cost declines,
CNET News.com, November 15, 2001; “In this game, Microsoft is more David than Goliath”, Business Week,
November 19, 2001; “Microsoft loses money on each Xbox”, Reuters, November 24, 2005.
7
See “Shakeup at Sony: What's the PlayStation Costing?” by Alexander & Associates (2002). Factory profits are
excluded.
8
See “Japan Electronic Games” by Morgan Stanley Dean Witter (1998), and “Video Game Industry Outlook” by
CIBC Oppenheimer (1998).
8
including drops in input prices, supply-side economies of scale, and learning-by-doing. But game
consoles are very similar in design and build to personal computers. Actually most components
of a game console, such as chips, memory, data storage devices, etc., are widely used in other
industries. I believe economies of scale and learning-by-doing in console production may not be
as important as dropping component prices in explaining falling marginal costs. Therefore I
focus on exogenously falling marginal costs induced by drops in input prices.
For PlayStation, cost estimates are available at two points in time, which can determine the
two parameters in (1). But for Nintendo 64 I know the initial cost was $160 but I still need the
rate of decline, for which I assume that the marginal costs in the console market and in the PC
market decline at roughly the same rate. Using the producer price index (PPI) for computers, I
estimate the rate at which the price of computers declined. I further assume that the average
margin remained stable in the PC market during the period of this study, which implies that the
marginal cost of computers declined at the same rate as the price. Therefore the same rate of
decline is used for Nintendo 64.
With retail prices and marginal costs, the retail margin is needed in order for us to calculate
wholesale markups. Consistent with the estimates of industry experts, I use a constant retail
margin of 20%.9 In Figure 2 I plot the prices, marginal costs, and wholesale markups of both
consoles.
9
According to “Retailers cash in on PlayStation”, BBC News (2004), an average console gives a retail margin of 20-
25%. In a separate report by Merrill Lynch analyst Henry Blodget in March 2001, a 17% retail margin was used to
analyze the profitability of Microsoft Xbox.
9
The marginal cost of PlayStation decreased at a faster pace than that of Nintendo 64. This is
reasonable because Nintendo decided to stay with the old cartridge format for games so it could
reuse its existing production facilities. In contrast Sony adopted the relatively new CDROM
format, which raised the production cost initially but became much cheaper later on.
Although PlayStation price declined over time, the increasing markup reveals that Sony
might have tried to penetrate the market. The incentive came from the fact that the console
market is a two-sided market to which Sony was a new entrant. The success of a game console
critically depends on the availability of its games. Sony needed to establish a sizeable installed
base quickly to help convince third-party game publishers to deliver more games for PlayStation.
In the next section I build a structural model to investigate whether the observed price
patterns can be supported as an equilibrium outcome of dynamic price competition between
Sony and Nintendo.
3. Model
Consider an oligopoly market with J competing hardware firms. Each firm offers a single
hardware product, indexed by j. These hardware products are mutually incompatible, meaning
that the software developed for one hardware product cannot be used on another. Assume
software is supplied in a monopolistically competitive, free-entry industry.
10
Time t is discrete. In each time period a consumer decides either to buy one of the hardware
products, or to buy none of them and wait until the next period. A consumer exits the market
after making a purchase.
The timing of the game is as follows. At the beginning of each period, hardware firms make
pricing decisions and software firms make entry decisions based on existing installed bases of
hardware products. Given hardware prices and software varieties consumers make purchase
decisions.
3.1 Demand for Hardware
Consumer i’s conditional indirect utility function from choosing hardware product j in period t is
specified as
U ijt = α ij − β i p jt + γ i N λjt + ξ jt + ε ijt .
(2)
This specification is very similar to the one derived by Nair, Chintagunta, and Dubé (2004) using
a CES utility framework. αij captures consumer i’s intrinsic preference toward product j. pjt is the
price of hardware product j in period t. Njt is the number of software titles compatible with
hardware product j in period t. According to (2), a consumer’s utility from a hardware product
depends on the number of compatible software titles. Consequently the indirect network effect is
summarized into a function of the software variety. As pointed out by Clements and Ohashi
(2005), a limitation of this specification is that it may not be able to incorporate heterogeneity in
11
software quality – A consumer’s utility is affected not only by the number of software titles, but
also by the quality of them.
There could be other factors that are not captured by the model and hence contribute to the
ξjt term, which represents unobserved demand shocks specific to product j and period t.
Advertising is an important example of such factors. The other error term, εijt, represents an
individual consumer’s taste toward product j.
Following Besanko, Dubé, and Gupta (2003) and Nair (2005), a latent-class approach is
used to capture consumer heterogeneity. Every consumer belongs to one of the R segments. Each
segment r is characterized by a distinct set of parameters {αrj, βr, γr}.
In each period t, a consumer is choosing among the J competing hardware products and an
outside option (j=0). The indirect utility from the outside option is normalized to be
U i 0t = ε i 0t .
Consumers’ heterogeneous tastes, εijt, are assumed to follow independent type-I extreme-value
distributions. The market share of hardware product j within segment r is given by:
srjt =
exp(α rj − β r p jt + γ r N λjt + ξ jt )
J
1 + ∑ exp(α rk − β r pkt + γ r N kt + ξ kt )
.
(3)
λ
k =1
Let Mrt be the size of segment r at time t. The demand for hardware product j is
R
Q jt = ∑ M rt srjt .
r =1
3.2 Software Provision
12
(4)
Let Yjt be the installed base, or equivalently the cumulative sales of hardware product j up to
period t–1. It gives the total number of consumers who might be interested in purchasing a
software title that is compatible with hardware product j. Base on Yjt, many symmetric singleproduct software firms decide whether to offer a software title for hardware product j in period t.
Assume free entry. These software firms keep entering the market until each firm earns zero
profit. As in Nair, Chintagunta, and Dubé (2004), and Clements and Ohashi (2005), the number
of software titles for hardware product j, Njt, is determined by a software provision equation:
ln N jt = κ j + ϕ j ln Y jt + υ jt .
(5)
With ϕj>0, equation (5) indicates that a larger hardware installed base will attract more
software titles to be developed. On the other hand, with γ>0, equation (2) indicates that more
software titles will lead to higher demand for the corresponding hardware product. This interplay
between hardware adoption and software provision generates a mutually enhancing feedback
cycle – the indirect network effect.
3.3 Pricing of Hardware
Hardware firms collect revenues from two sources – hardware sales and software royalties. A
royalty fee is levied by a hardware firm for each sale of a software title compatible with its
hardware product. To quantify the amount of software royalties that a hardware firm receives, I
assume that on average hardware firm j will receive fj dollars of software royalties after selling
13
each unit of hardware product j. Therefore assuming a constant retail margin of 1–τ, the profit
function is specified as
π jt = (τ p jt − c jt + f j )Q jt .
(6)
In a static framework, firms set prices to maximize single-period profits. However, in a
durable good market with heterogeneous consumer segments and indirect network effects, firms’
pricing decisions not only determine current profits, but also affect future market conditions and
hence future profits. With heterogeneous consumer segments, different prices in the current
period will result in different segment sizes in future periods. With indirect network effects, a
lower current price leads to higher hardware sales and more software titles, which in turn makes
the product more attractive in later periods. A higher current price would leads to the opposite.
Therefore, firms’ pricing decisions are inherently dynamic. Firms set prices in order to
maximize the expected present value of total profits over a planning horizon:
⎡T
⎤
E ⎢ ∑ δ k −tπ jk ⎥ .
⎣ k =t
⎦
A finite horizon T is chosen for the purpose of the empirical application. δ is a discount factor. In
principle firms could look at the entire history of past states and actions when setting prices. For
simplicity I restrict attention to those games in which firms’ pricing strategies depend only on the
current state, denoted by St.
The state vector St consists of {Yrjt}, the vector of installed base of each hardware product in
each segment. It summarizes all the payoff relevant information in period t. Njt is related to Yjt
14
according to the software provision equation (5). Let Mr0 be the initial size of segment r. Mrt is
just a function of Yrjt:
J
M rt = M r 0 − ∑ Yrjt .
j =1
The marginal cost, cjt, declines exogenously over time. In any period t marginal costs are
determined according to (1). In a finite horizon problem firms pricing strategies are specific to
each time period, and therefore cjt does not enter the state space. Note that cjt does become a state
variable when solving an infinite horizon problem.
The state transition rule is straightforward. Given the current state, actions, and realizations
of error terms, the state variable Yrjt evolves according to
Yrj ,t +1 = Yrjt + M rt srjt .
Therefore the state transition density P(St+1|St, pt), which is the probability of having a new state
St+1, is determined by the joint distribution of ξt and υt.
3.4 Equilibrium
Given the current state St, the profit function can be written as
π jt ( St , pt , ξt ,υt ) .
Firms are assumed to set prices before the error terms are realized. Therefore firms’ pricing
decisions are based on the expected profit function
π jt ( St , pt ) = E[π jt ] = ∫ π jt ( St , pt , ξ ,υ )dP(ξ ,υ ) .
15
Denote firm j’s pricing strategy by σj, which is a vector of its pricing strategy in each time
period σjt: St → pjt. Under a strategy profile σ={σ1,…,σJ} which lists the pricing strategies of all
firms, the expected present value of firm j’s total profits starting from period t is given by
⎡T
⎤
V jt ( St | σ ) = E ⎢ ∑ δ k −tπ jk ( S k , σ k ( S k )) | St , σ ⎥ .
⎣ k =t
⎦
(7)
Given some guess about competitors’ strategy profile σ-j = {σ1,…,σj-1,σj+1,…,σJ}, firm j will
choose a pricing strategy σj that maximizes Vjt(St|σ) for any t. In equilibrium the Bellman
equation must be satisfied
{
}
V jt ( St | σ ) = sup π jt ( St , p jt , σ − jt ( St )) + δ ∫ V j ,t +1 ( St +1 | σ )dP( St +1 | St , p jt , σ − jt ( St )) .
p jt
(8)
Intuitively firm j just looks for the best response to σ-j.
The equilibrium concept is the Markov perfect equilibrium (MPE). An MPE is a strategy
profile σ such that no firm j would deviate from σjt(St) in any subgame starting from state St, or
formally, for any state St, any firm j, and any alternative price pjt,
V jt ( St | σ ) ≥ π jt ( St , p jt , σ − jt ( St )) + δ ∫ V j ,t +1 ( St +1 | σ )dP( St +1 | St , p jt , σ − jt ( St )) .
Due to the complexity of computing mixed strategy equilibria, I focus on pure strategies. Note
that the existence or uniqueness of an MPE in pure strategies is not guaranteed. This is different
from the contraction-mapping results in the single-agent dynamic programming models.
However, what is relevant here is the existence of an equilibrium at the estimated parameter
values, which can be verified by the convergence of the numerical solution algorithm. As to the
uniqueness, I compute the equilibrium from various starting values to check for any evidence of
multiple equilibria.
16
4. Empirical Strategy and Estimation
In this section I estimate the proposed model using data from the 32/64-bit video game console
market. Based on these estimates, I proceed to solve for firms’ equilibrium pricing strategies in
the subsequent section. Since the demand parameters are estimated without imposing supply-side
restrictions, it is possible to compare different supply-side models based on their ability to
explain the observed price patterns. A similar approach has been taken by Benkard (2001), Dubé,
Hitsch, and Manchanda (2004), and Nair (2005).
4.1 Estimation of Hardware Demand
I have monthly data on price, unit sales, and the number of games for PlayStation and Nintendo
64. Summary statistics of the data can be found in Table 1. An outstanding feature of the data is
the jump in sales for both game consoles during Thanksgiving and Christmas holidays. Therefore
holiday dummies are used to control for such effects. Since the Thanksgiving effect is
significantly smaller in magnitude than the Christmas effect, they are estimated separately.
The aggregate nature of the data limits the amount of heterogeneity that can be identified. I
assume that consumers are heterogeneous in their preferences toward game consoles but
homogeneous in other parameters. In the console market people differ a lot in their interests in
game consoles. Hardcore gamers place much higher value on new game consoles than casual
17
gamers. Thus I believe it is most important to account for the heterogeneity in consumer
preferences. Differences in preferences translate into differences in price elasticities as well.
Empirically the demand estimation is based on the following specification,10
U ijt = α rj + θ1 I Nov + θ 2 I Dec − β p jt + γ N jt + ξ jt + ε ijt .
(9)
Parameters are estimated in a Generalized Method of Moments (GMM) framework. The moment
conditions are based on the assumption that demand shocks are orthogonal to a vector of
instrumental variables. Because the components of a game console are very similar to those of a
computer, it is reasonable to expect the prices of computers and computer storage devices are
correlated with console prices but uncorrelated with the demand shocks in the console market.
Therefore, I use lagged PPI for computers and computer storage devices as instrumental
variables.11
Demand shocks ξjt are not directly observed. But following Berry, Levinsohn, and Pakes
(1995), I can back out ξjt from the demand equation (4) given a set of parameter values. The
contraction-mapping property makes this inversion computationally efficient.
To determine the number of different segments in the market, I keep adding segments until
one of the segment sizes is not statistically different from zero.12 Two segments are revealed
10
Note that Njt appears in linear form. I tried to estimate the model with a power function Njtλ but the exponent λ
cannot be precisely estimated and the hypothesis λ=1 is not rejected. Therefore following Clements and Ohashi
(2005), I use a linear specification.
11
These variables are interacted with console dummies to make the effects brand specific.
12
A similar approach has been taken by Besanko, Dubé, and Gupta (2003), and Nair (2005).
18
from the data. The demand estimates are presented in Table 2.13 Standard errors are obtained
using a bootstrap procedure.
Although in the first segment console preferences are not significantly different from zero, a
Wald test (p-value < 0.01) indicates that Nintendo 64 enjoys a significantly higher preference
over PlayStation. A couple of reasons may contribute to Nintendo’s competitive advantage in
this aspect. Nintendo had been extremely popular in the console market ever since 1980’s, but
Sony, although a strong player in many other markets, was new to game consoles back then.
Furthermore, Nintendo 64 is a 64-bit console, which renders faster and better graphics than the
32-bit PlayStation.
Consumers in segment 1 have much higher preferences toward game consoles than those in
segment 2. It suggests that segment 1 is comprised of game enthusiasts while segment 2 includes
mass market consumers. Table 3 gives the price elasticities and game elasticities of demand for
each segment. These elasticities are averages across time. Consumers in segment 2 have higher
elasticities of demand, both to price and to game variety.
In Figure 3, I plot the quarterly adoption of game consoles by segments. In the first three
years or so, a vast majority of game consoles were sold to game enthusiasts in segment 1. Sales
to mass market consumers in segment 2 started to pick up in Q4 1999, which was right after the
price cut from $129 to $99 for both consoles. This pattern is consistent with the comments from
a Nintendo executive about a similar price cut, from $149 to $99, for the next generation
13
A market size of 50 million is used according to a Banc of America Securities Research Report, “A Tale of Two
Industries”, May 2001.
19
GameCube: “Every time a generation of technology has moved into the true mass market,
Nintendo has prospered.”14
4.2 Estimation of Software Provision
Given data on Njt and Yjt, I use a simple regression to estimate the software provision equation
(5). Since Yjt denotes the cumulative sales up to the previous period, it is unlikely that there is a
correlation between lnYjt and υjt, the contemporaneous error term in the software market.
Parameter estimates are presented in Table 4.
Although PlayStation has a smaller value for parameter φ, its value for parameter κ is much
larger. Within reasonable ranges for the hardware installed base Yjt, the effect of a much larger κ
dominates that of a smaller φ – At the same installed base, PlayStation would attract much more
games than Nintendo 64. This can be seen from the observed data. At the end of the data period
for this study, the installed base for PlayStation was approximately 45% larger than that of
Nintendo 64, but there were over 300% more games available for PlayStation – 1158 games for
PlayStation versus only 277 games for Nintendo 64.
In fact, the two companies had very different strategies regarding the software market. Sony
strived to support PlayStation with as many games as possible, partly because of the lesson
learned from the loss of its Betamax to the opposing VHS standard in the video cassette industry.
However, Nintendo enforced very strict content and quality restrictions, which limited support
14
“Nintendo GameCube Price Drops to $99”, Business Wire, September 24, 2003.
20
from game publishers. Also, Sony chose CDROM as the storage media for PlayStation games,
while Nintendo kept using cartridges, which are much more expensive to produce. A higher
production cost, plus a higher royalty fee, leaves third-party game publishers much lower gross
margins under Nintendo’s standard, despite the fact that N64 games were priced about $20
higher than PlayStation games. 15 Therefore, Sony had a clear advantage over Nintendo with
respect to games.
4.3 Discussion
Following the literature on network effects (Ohashi 2003; Park 2004; Nair, Chintagunta, and
Dubé 2004; Clements and Ohashi 2004), I use these demand estimates to study the relative
importance of network effects vis-à-vis price-quality effects according to the following
relationship:
ln
sr1t
= [ (α r1 − β p1t ) − (α r 2 − β p2t )] + γ [ N1t − N 2t ] + [ξ1t − ξ 2t ] .
sr 2t
Subscript 1 indicates PlayStation, and subscript 2 indicates Nintendo 64. The first term on the
right-hand side measures the price-quality difference between the two consoles. The second term
measures the relative strength of the two networks. Since the residual effect represented by the
third term is relatively small and has a zero mean, I focus on the first two terms. Note that a
positive term indicates Sony’s lead, and a negative term indicates Nintendo’s advantage.
15
According to “Nintendo: At the Top of Its Game,” Business Week, June 9, 1997, the average price was $40 - $50
for PS games, and $60 - $70 for N64 games.
21
Using the observed prices and game varieties, I calculate these two terms for segment 1 and
plot them in Figure 4. The plot for segment 2 is omitted since the pattern is similar. The curve on
top corresponds to the relative strength in network effects, while the curve on bottom represents
the price-quality difference. It can be seen that PlayStation enjoys stronger network effect, while
Nintendo 64 holds price-quality advantage. The curve in the middle, which is labeled "Aggregate
Effect", is the sum of the network effect and the price-quality effect. Although Nintendo started
with a slight edge over Sony, the ever-growing PlayStation games eventually helped Sony to
overtake its rival.
5. Dynamics of Pricing
Based on the estimates from the previous section, I solve for firms’ equilibrium pricing policies
and study the resulting price patterns in the console market. Because a product life cycle of
approximately five years is widely expected in this market, a finite horizon of sixty months is
chosen for this dynamic pricing game between Sony and Nintendo. The discount factor is
assumed to be 0.995, which corresponds to an annual interest rate of 6%.
In the profit function (6), τ is assumed to be 0.8, which is consistent with the 20% retail
margin used in Section 2. In order to determine fj, the average amount of royalties that console
maker j expects to receive from each unit of hardware sale, I look up the average game royalty,
and multiply it by the software-to-hardware tie ratio, which is the ratio between the cumulative
22
number of games sold and the hardware installed base. In practice I use (f1, f2) = (72, 56), which
corresponds to average game royalties of ($9, $14)16 and tie ratios of (8, 4)17.
Royalty rates vary depending on the relative bargaining power of the parties involved. But
virtually all contracts contain confidentiality provisions that prohibit revealing the specific terms.
Various sources have mentioned that PlayStation royalty to be around $9, but put Nintendo 64
royalty in a wide range between $10 and $18. I take the average amount $14.
The tie ratios of (8, 4) indicate that an average PlayStation owner bought twice as many
games as a typical Nintendo 64 owner did. This is not surprising as PlayStation had many more
games to offer, and Nintendo games were much more expensive.
Now I solve for the MPE in firms’ dynamic pricing game. Due to the complexity of this
game, an analytical solution cannot be obtained. Therefore I numerically compute the
equilibrium by applying numerical dynamic programming techniques.18
Since it is a finite horizon game, I start from the last period and go backwards in time. In the
last period T, it becomes a static price competition as there is no future periods. Solving for the
Bertrand equilibrium, I obtain firms’ value functions, VjT(ST). For any other period t<T, I use a
Gauss-Siedel iterative scheme on the Bellman Equation (8) in order to compute firms’ value
functions Vjt(St), provided their value functions in the next period, Vj,t+1(St+1).
16
“A Tale of Two Industries”, Banc of America Securities Research Report, 2001; “Japan Electronic Games”,
Morgan Stanley Dean Witter, 1998; “Video Game Industry Outlook”, CIBC Oppenheimer, 1998; Coughlan (2001).
17
See Coughlan (2001).
18
See Judd (1998) for details on these numerical techniques.
23
The state space is discretized. Value functions are represented by their values on the grid
points. Linear interpolation is used to get the function values for those points that are not on the
grid. An alternative representation is to use Chebyshev polynomials. However, in this particular
application, the shape of value functions is not preserved well under Chebyshev polynomials.
To alleviate the concern for multiple equilibria, I compute the equilibrium using different
initial values. The same equilibrium is reached. As pointed out by Doraszelski and Satterthwaite
(2005), different iteration schemes can also lead to different equilibria. I tried both Gauss-Siedel
and Gauss-Jocobi schemes, and found no evidence of multiple equilibria.
At convergence the equilibrium pricing policies of both firms are obtained. I can then
simulate the market competition between Sony and Nintendo for five years. According to the
data, about one million units of PlayStation had been sold before Nintendo 64 entered the market.
Therefore in the simulation PlayStation is endowed with an installed base of one million units.
In Figure 5, I plot the predicted retail prices and wholesale markups, and compare them with
the observed ones. The predicted ones and observed ones follow similar patterns. Prices of both
consoles are predicted to fall, but the markups are predicted to rise, which confirms that it is
optimal for console makers to sacrifice early profits in order to build up their networks.
For the first few months, the observed prices are significantly higher than the predicted ones.
A couple of factors might contribute to this discrepancy. Firms often have limited production
capacity initially, which limits the expected gain of price cuts.19 Or firms might be targeting a
19
The latest example is Xbox 360 from Microsoft. When severe shortage occurred, a lot of Xbox 360 sold on eBay
at surprisingly high prices. See “Players Make a Game of Flipping New Xbox for a Profit on eBay”, Wall Street
24
small group of consumers with exceptionally high preference for game consoles. Unfortunately
this segment cannot be identified with the current data.
5.1 Price Patterns without Network Effects
To better understand the impact of indirect network effects on pricing, consider a market
situation in which consumers derive no benefit from software, i.e. γ=0 in the utility specification
(9). Without network effects firms’ pricing decisions are still dynamic because of the existence
of heterogeneous consumer segments, which provides an incentive for price skimming.
Therefore in such a scenario it is expected that markups would no longer be increasing.
I re-solve the dynamic pricing game with γ=0. The predicted prices and markups are plotted
in Figure 6. In lack of incentives for penetration pricing, markups for both PlayStation and
Nintendo 64 would have been decreasing over time. PlayStation price would have dropped by
$189, which is 87% more than the observed $101 drop in PlayStation price.
5.2 Price Patterns without Consumer Heterogeneity
Similarly I can examine the price patterns without consumer heterogeneity but with indirect
network effects. I assume there is only one segment in the market, and everyone has the same
preference levels which are set to be the weighted average of those for the two estimated
Journal, Nov 23, 2005.
25
segments in Table 2. Given homogeneous consumer preferences, firms would lose incentives to
exploit the consumer heterogeneity through inter-temporal price discrimination. Therefore, the
incentives for penetration pricing under network effects would be even more dominating.
Using the new parameter values, I re-solve the dynamic pricing game. The predicted prices
and markups are plotted in Figure 7. Although marginal costs declined, without consumer
heterogeneity PlayStation price would have gone up by as much as $125. The implied $237
increment in wholesale markup is more than four times the observed increment of $56.
5.3 Price Patterns under Static Pricing
I also examine the implications of a static pricing game, in which firms are assumed to be
myopic and only consider the single-period profits when setting prices. I compute the Bertrand
equilibrium in each period and simulate the market evolution. The resulting prices and markups
are plotted in Figure 8. Static pricing predicts stable markups and hence cannot explain the
observed patterns.
6. Policy Simulations
Past empirical studies on indirect network effects have not formally modeled hardware firms’
pricing decisions. Consequently in these studies it is difficult to evaluate firms’ potential policy
choices. One approach is to hold prices unchanged when perturbing other variables at firms’
26
disposal. However, such an approach may be biased because any changes in the market
environment would naturally induce firms to price differently. Therefore the adjustment in prices
should be taken into account for policy experiments. In this paper, by explicitly modeling firms’
dynamic price competition I am able to perform various policy experiments while taking into
account their implications on prices.
6.1 First-Mover Advantage
In markets with network effects, the importance of preemption and first-mover advantages is
frequently emphasized (Shapiro and Varian 1999). Since Nintendo 64 came to the market one
year after PlayStation, Sony was able to build up its installed base and game selections before
facing the fierce competition from Nintendo. In the end Sony became the winner of the 32/64-bit
console war, and continued to dominate the next generation (128-bit) console market with its
PlayStation 2 (PS2) product. It is interesting to note that once again Sony launched PS2 one year
before its opponents Xbox and GameCube.
To evaluate the impact of first-mover advantages, I use firms’ equilibrium pricing policies
obtained in Section 5 to simulate the market evolution starting from different initial states.
Specifically, I let Sony’s head start vary from negative five millions to five millions of installed
base – A negative head start for Sony indicates a head start for Nintendo with the same absolute
value.
27
Figure 9 plots the final installed base and the present value of total profits after five years
against the head start for Sony. It shows the pivotal role of a first-mover advantage in this market.
Given a head start Sony became the market leader, but with a similar head start Nintendo could
have won the console war.
However, there might be other considerations for Nintendo to delay the launch of N64. For
example, it might still want to collect more revenues from its previous generation product, Super
Nintendo Entertainment System (SNES), while Sony did not have a similar concern. The above
analysis focuses on the current generation market only.
6.2 It is All about Games
The success of PlayStation can be largely attributed to its advantage in game variety. If Nintendo
had been able to attract more game publishers, it would be in a better competitive position. To
evaluate the effect of an improvement in N64’s game variety, I increase parameter κ2 in software
provision equation (5) which will result in a corresponding increase in the number of games at
the same hardware installed base. With more games, Nintendo would receive more royalties.
Therefore parameter f2 in profit function (6) is raised by the same percentage.
For each different value of the percentage increase, I re-solve the dynamic pricing game and
simulate the market evolution starting from the observed head start of one-million installed base
for PlayStation. Figure 10 describes the market outcomes with different percentage increments
28
in the number of N64 games. It highlights the importance of games – a 10% increment in the
number of N64 games would have helped Nintendo surpass Sony and become the market leader.
6.3 The Choice between Cartridge and CDROM
Before the 32/64-bit generation, previous consoles had been using cartridges as the storage
media for video games. As CDROM technology was gaining widespread adoption, console
makers had to decide whether to switch away from cartridges. Eventually Sony adopted the
CDROM format but Nintendo decided to stay with cartridges.
CDROM format significantly reduces the manufacturing cost of games, which translates to
lower game prices and more game sales. On the other hand, since Nintendo had extensive
experience with cartridge format, it was much cheaper for Nintendo to produce a cartridge-based
system. 20 To examine the tradeoffs involved in this decision, I perform a counterfactual
experiment to find out what would happen if Nintendo 64 had adopted CDROM format. I
assume that Nintendo 64’s marginal cost increases to the same level as PlayStation’s, but in
exchange N64’s number of games and amount of royalties are both increased by a certain
percentage.
For each different assumption on this percentage increase, I re-solve the dynamic pricing
game and re-run the simulation. Figure 11 shows the results. For comparison, the final installed
20
“Japan Electronic Games”, Morgan Stanley Dean Witter, 1998; “Video Game Industry Outlook”, CIBC
Oppenheimer, 1998.
29
bases and profits under original parameter values are also included and represented by horizontal
lines. It seems Nintendo would have been strictly worse off unless the number of N64 games can
be increased by more than 40% as the result of switching to CDROM format. The lower
marginal cost under cartridge format was crucial to Nintendo 64’s market performance.
7. Conclusions
Using a structural model of heterogeneous demand and dynamic price competition, I am able to
explain the price patterns observed in the console market – PlayStation price declined over time,
but its markup increased. In equilibrium it is optimal for Sony to adopt penetration pricing due to
the existence of indirect network effects, despite a competing incentive for price skimming with
heterogeneous consumer segments in the market.
Network effects, consumer heterogeneity, and falling marginal costs are common features of
many high-technology markets. During a new product launch, the choice between price
skimming and penetration pricing can be difficult because these features offer contradictory
incentives. This model can be used by marketers to evaluate the tradeoffs between the two
options.
Several limitations of the current model leave opportunities for future research. Currently
consumers are assumed to make purchase decisions based on current prices and software
varieties. In addition, their expectation on future prices and software varieties may also affect
their decisions. They may decide whether to pay a higher price and start to enjoy now, or wait for
30
a lower price. As discussed in the appendix, this forward-looking behavior is not captured due to
the challenge it poses to keep the model computationally feasible.
Simplifying assumptions have been made regarding the software market. For example, the
indirect network effect is summarized into a function of software variety. This allows me to
abstract away from modeling the heterogeneity in game quality. It may be desirable to relax such
assumptions and develop a more elaborate model for the software market. Nevertheless, this will
be left for future extension given the focus of this paper on the pricing decisions of hardware
firms.
There have been several generations of video game consoles. This study focuses on the price
competition between the two major hardware firms within a particular generation, and takes the
market structure as given. In addition to pricing decisions, firms may strategically decide on the
timing of entry, exit, and product replacement. As an area for future work one can model these
decisions jointly.
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34
Appendix: Extension to Forward-Looking Consumers
In the presented model, it has been assumed that firms take into account the impact of current
prices on future profits, and maximize the PDV of all future profits. But consumers are assumed
to make purchase decisions based on the current-period utility. In other words, firms are forwardlooking but consumers are myopic. In this section I examine the issues involved in extending the
model to one that accommodates forward-looking consumers.
Starting from a general framework, assume consumer i’s indirect utility function from
purchasing hardware product j in period t is
U ijt = α ij − β i p jt + γ i N λjt + ξ jt + ε ijt
If hardware product j is purchased, the consumer exits the hardware market but continues to buy
software in later periods. The utility from software is
uijt = α ij + γ i N λjt + ξ jt + ε ijt .
Therefore consumers make purchase decisions based on the expected PDV of total utility from
hardware product j and its compatible software:
⎡ T
⎤
Wijt = U ijt + E ⎢ ∑ δ cs −t uijs ⎥ .
⎣ s =t +1
⎦
(10)
δc is the discount factor for consumers.
If consumer i buys none of the J hardware products and decides to wait until the next period,
she expects to get utility
Wi 0t = δ c E ⎡⎣ max {Wi 0,t +1 ,Wi1,t +1 ,...,WiJ ,t +1}⎤⎦ + ε i 0t .
Define Vijt = Wijt – εijt, j∈{0,…J}. Then
Vi 0t = δ c E ⎡⎣ max {Vi 0,t +1 + ε i 0,t +1 ,Vi1,t +1 + ε i1,t +1 ,...,ViJ ,t +1 + ε iJ ,t +1}⎤⎦ .
Using the properties of type-I extreme-value distributions, it can be derived that
⎡ ⎛ J
⎞⎤
Vi 0t = δ c E ⎢ln ⎜ ∑ exp(Vij ,t +1 ) ⎟ ⎥ .
⎢⎣ ⎝ j =0
⎠ ⎥⎦
(11)
If Vijt has a time-invariant function form for j∈{1,…J}, the functional equation (11) can be used
to iteratively compute Vi0t, the value of no-purchase option. Actually this is the case for a number
of past studies including Song and Chintagunta (2003), Nair (2005). Unfortunately expression
(10) cannot be easily simplified.
When computing Vijt, I should have already obtained firms’ equilibrium pricing policies
from period t+1 to T. In principle, I could simulate to get all the Njt from period t+1 to T, and
calculate Vijt directly. However, each of such calculation involves a high-dimensional integration
over all the ξjt. Given the frequency that this calculation needs to be carried out, the
computational burden is estimated to be overwhelming.
35
Table 1: Data Description
PlayStation
Nintendo 64
Min Mean Max Std. Dev. Min Mean Max Std. Dev.
Variable
Sales (thousands of units)
33
293 1609
295
6
Price ($)
99
126
# of Games
134
212 1005
201
28
69
125
200
30
654 1158
315
2
145
277
103
66
# of Observations
66
Table 2: Parameter Estimates for Hardware Demand
Variable
Estimate Std. Err.
Segment 1 – PlayStation (α11)
Segment 1 – Nintendo 64 (α12)
-2.1439
-1.3313
2.2845
1.9260
Segment 2 – PlayStation (α21)
-6.3805
2.7531
Segment 2 – Nintendo 64 (α22)
Holiday – Thanksgiving (θ1)
-4.6885
0.6476
1.4839
0.2090
Holiday – Christmas (θ2)
1.6450
0.2135
Price (β)
Game variety (γ)
Percentage of segment 1
0.0197
0.0117
0.0030
46.02%
0.0016
2.36%
Table 3: Elasticity of Demand
Elasticity
Segment 1
Own
Cross
Segment 2
Own
Cross
Price Elasticity
PS
-2.1779
0.3021 -2.4718
0.0082
N64
-2.3599
0.1106 -2.4637
0.0068
Game Elasticity
PS
N64
1.5849 -0.4010
0.4098 -0.0317
36
1.9746 -0.0112
0.4394 -0.0021
201
Table 4: Parameter Estimates for Software Provision
Variable
PlayStation
Nintendo 64
Estimate Std. Err. Estimate Std. Err.
κ
-4.1429
0.2943
-16.6255
0.6405
ϕ
0.6553
0.0183
1.3471
0.0407
Figure 1: Prices of PlayStation and Nintendo 64
220
PS
N64
200
180
Price
160
140
120
100
80
0
10
20
30
Month
37
40
50
60
Figure 2: Retail Prices, Marginal Costs and Wholesale Markups
(a) Retail Price and Marginal Cost
220
PS Price
PS Cost
N64 Price
N64 Cost
200
Price / Cost
180
160
140
120
100
80
60
0
10
20
30
40
50
60
(b) W holesale Markup
20
10
Wholesale Markup
0
-10
-20
-30
-40
-50
PS
N64
-60
-70
-80
0
10
20
30
Month
38
40
50
60
Figure 3: Unit Sales by Segments
6
4
x 10
Segment 1
Segment 2
3.5
3
Unit Sales
2.5
2
1.5
1
0.5
0
0
5
10
15
20
25
Quarter
Figure 4: Price-Quality Effect and Network Effect
2.5
Price-Quality Effect
Network Effect
Aggregate Effect
2
1.5
1
0.5
0
-0.5
-1
-1.5
0
10
20
30
Month
39
40
50
60
Figure 5: Retail Prices and Wholesale Markups – Predicted and Observed
(a) Retail Price
220
PS Observed
PS Predicted
N64 Observed
N64 Predicted
200
180
Retail Price
160
140
120
100
80
60
40
0
10
20
30
40
50
60
(b) W holesale Markup
20
Wholesale Markup
0
-20
-40
-60
-80
PS Observed
PS Predicted
N64 Observed
N64 Predicted
-100
-120
0
10
20
30
Month
40
40
50
60
Figure 6: Retail Prices and Wholesale Markups – No Network Effects
(a) Retail Price
250
PS Observed
PS Predicted
N64 Observed
N64 Predicted
Retail Price
200
150
100
50
0
10
20
30
40
50
60
(b) W holesale Markup
Wholesale Markup
50
0
PS Observed
PS Predicted
N64 Observed
N64 Predicted
-50
-100
0
10
20
30
Month
40
50
60
Figure 7: Retail Prices and Wholesale Markups – No Heterogeneity
(a) Retail Price
250
Retail Price
200
150
100
PS Observed
PS Predicted
N64 Observed
N64 Predicted
50
0
-50
0
10
20
30
40
50
60
(b) W holesale Markup
50
Wholesale Markup
0
-50
-100
PS Observed
PS Predicted
N64 Observed
N64 Predicted
-150
-200
-250
0
10
20
30
Month
41
40
50
60
Figure 8: Retail Prices and Wholesale Markups – Static Pricing
(a) Retail Price
250
PS Observed
PS Predicted
N64 Observed
N64 Predicted
Retail Price
200
150
100
50
0
10
20
30
40
50
60
(b) W holesale Markup
Wholesale Markup
20
0
-20
PS Observed
PS Predicted
N64 Observed
N64 Predicted
-40
-60
-80
0
10
20
30
Month
40
50
60
Figure 9: First-Mover Advantage (All numbers in millions)
25
800
700
20
500
15
Profit
Installed Base
600
10
400
300
200
5
100
PS
N64
0
-5
0
Head Start for Sony
0
-5
5
42
0
Head Start for Sony
5
Figure 10: More Games for N64
35
1000
PS
N64
900
30
800
700
Profit
Installed Base
25
20
15
600
500
400
300
10
200
5
0
5
10
15
Increase in N64 Games (%)
100
20
0
5
10
15
Increase in N64 Games (%)
20
Figure 11: More Games for a CDROM-Based N64
40
1200
PS Old
PS New
N64 Old
N64 New
35
800
25
Profit
Installed Base
30
1000
20
600
15
400
10
200
5
0
0
10
20
30
40
Increase in N64 Games (%)
0
50
43
0
10
20
30
40
Increase in N64 Games (%)
50