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July 12, 2006 Preliminary Draft: Please Do Not Cite or Circulate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

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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”,

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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).

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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.

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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.

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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

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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

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(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

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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 ) .

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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.

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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).

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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.

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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.

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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.

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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

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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