The dynamics of pre-market standardization

Information Economics and Policy 24 (2012) 105–119

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The dynamics of pre-market standardization Sven Kerstan a, Tobias Kretschmer b,c,⇑, Katrin Muehlfeld d a

Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands Institute for Strategy, Technology and Organization, Munich School of Management, LMU Munich, Schackstr. 4/III, D-80539 Munich, Germany Ifo Institute for Economic Research, Germany d Utrecht University School of Economics, Utrecht University, Janskerkhof 12, NL-3512 BL Utrecht, The Netherlands b c

a r t i c l e

i n f o

Article history: Received 25 August 2010 Received in revised form 2 November 2011 Accepted 8 November 2011 Available online 23 December 2011 JEL classification: C70 L15 O32 Keywords: Standardization Network effects Preemption Standards battle

a b s t r a c t This paper studies an under-explored phenomenon: standardization arising during the technology development stage from the interplay of incentives to compete and cooperate. We identify circumstances in which a firm will prelaunch its technology (i.e., publish detailed technological specifications) and the rival abandons its own technology to support a common standard in a two-stage two-player game with network effects and licensing and a fixed deadline for technological development. We find that failure to standardize predominantly occurs for technologies with very weak or very strong network effects, and for firms with similar technological capabilities. The outcome can depend on what would be perceived by market participants as a simultaneous prelaunch: a prelaunch on the same day, during the same week, or month, and so on, depending on how time is discretized. Ó 2011 Elsevier B.V. All rights reserved.

1. Introduction Firms in network industries face a tradeoff in their decision to standardize. While industry-wide compatibility improves a technology’s chances of consumer acceptance, it also means sharing profits with other sponsors of the standard. Therefore, firms sometimes introduce competing technologies to establish a de facto industry standard in a standards battle (Arthur, 1989). The resulting technological uncertainty and the risk of being orphaned with a failing technology may prevent consumers from adopting the technology at all (Postrel, 1990; Kretschmer, 2008). Recent evidence is the lingering demand for the DVD successor

⇑ Corresponding author at: Institute for Strategy, Technology and Organization, Munich School of Management, LMU Munich, Schackstr. 4/III, D-80539 Munich, Germany. E-mail addresses: [email protected] (T. Kretschmer), [email protected] (K. Muehlfeld). 0167-6245/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.infoecopol.2011.11.002

technology, Blu-ray, which in 2008 emerged as the winner from a six-year-long standards battle. To avoid this, firms often agree on a common standard before making the technology available to final consumers. Despite its practical importance, such cooperative standard-setting has received little attention in the literature. Prior work has focused either on standard battles occurring after product introduction, or on formal standard setting organizations (SSOs) in the pre-market stage. However, anecdotal evidence shows that standardization during the pre-market stage may also result from firms’ interactions shaped by simultaneous incentives to compete and cooperate. An example is the successful formation of the Compact Disc (CD) standard (McGahan, 1993; Gandal et al., 2001).1 Given the limits of analog audio playback technologies and the emerging technological opportunities, 1 For a detailed overview see Gamharter and Kretschmer (2004) or Dai (1996).

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many major consumer electronics manufacturers2 undertook research and development in search of a new audio playback technology in the 1970s. They followed different technological trajectories ranging from Telefunken’s mechanical solution to JVC’s magnetic scanning system. Philips and Sony were both experimenting with digital optical systems and pooled their efforts in 1979. There was a strong belief that firms would need to join forces to overcome the large installed base of the two incumbent formats, vinyl and cassette tapes. To facilitate coordination, in 1978 the Japanese Ministry of International Trade and Industry (MITI) announced the Digital Audio Disc (DAD) conference for spring 1981 to bring together all major consumer electronics manufacturers to set a new audio playback standard. The conference was attended by 29 consumer electronics manufacturers, who approved two out of five technologies presented: Philips/ Sony’s CD and JVC/Matsushita’s technology. However, only the CD format was commercialized and eventually became the new audio playback standard. Presumably, this was because two events effectively preempted the DAD conference (Dai, 1996). First, Philips/Sony published the exact specifications of their technology in the so-called ‘Redbook’ in June 1980, thereby fixing their technology’s fundamental properties and making them common knowledge. Second, in response, JVC/Matsushita announced their support for the Philips/ Sony technology in January 1981, at which point Philips and Sony began granting licenses to audio equipment manufacturers and record replicators. Hence, although a committee existed to approve a standard, the two leading coalitions engaged in strategic manoeuvering during the development phase that helped them define the new standard prior to the standardization conference, thereby effectively preempting the committee’s subsequent decision. This raises a number of questions not readily answered in the literature: Why did Philips/Sony prelaunch so early and thereby risk committing prematurely to a technology? Why did JVC/Matsushita support Philips’/Sony’s technology despite having developed a serious contender for the new standard? To address these questions, we focus on the emergence and timing of a standard during technological development, i.e. prior to commercialization, resulting from strategic interaction between firms. We model a duopoly market with network effects and licensing costs. Firms compete in two stages, a development and a (Cournot) market stage. In the development stage, firms decide in each round whether to (1) prelaunch their technology by publishing its technical specifications and their royalty demands, (2) concede after a prelaunch by the rival and support the rival technology as a standard, or (3) continue developing their own technology. Our ‘prelaunch’ differs from mere product announcements because it carries a commitment to this technology. The incentives to prelaunch arise through network effects: A prelaunch followed by a concession gener2

Among the major players were Philips, Sony, The Victor Company of Japan (JVC) and its parent firm Matsushita, as well as Telefunken/Decca (German Teledec), RCA and Thompson.

ates network benefits from a single standard, resulting in higher firm profits in the market stage. The costs of standardization are twofold. First, both prelaunch and concession end a firm’s technological progress. Although a prelaunch may persuade the rival to join one’s own standard, publishing its specifications curtails further technological development.3 Similarly, concession renders further development of one’s own technology inefficient. Second, the conceding firm pays licensing fees to the prelauncher. The market stage is a simple Cournot duopoly with linear demand and network effects. Note that only technological development is modeled as time dependent. We do not model the timing of product release by the firms because we want to focus on the timing of pre-market standardization. We identify conditions under which a (successful) prelaunch will take place, when it will take place and what licensing fees will be set. We characterize these conditions as a function of the strength of network effects, firms’ technological capabilities and the time horizon of the development stage, and derive several results: Depending on parameter values, both no standardization and pre-market standardization emerge as equilibrium outcomes. Standardization can arise in different types of games in our framework: Games in which one firm prelaunches at its optimal time, different types of preemption games, and waiting games (in the form of a war of attrition). Second, we find that for large parameter ranges, the competitors agree on a joint (pre-market) standard, although at varying times depending on the particular equilibrium class. Standard battles (defined in our framework as cases in which both firms enter the market stage with incompatible technologies) arise only for firms with similar technological capabilities and require either very strong or very weak network effects. For very weak network effects, there is no sufficient incentive for standardization. For very high network effects, in turn, the incentive to own one’s own network is too strong: A firm that considers prelaunching its technology would, for very high network effects, have to offer (too) high subsidies to the rivaling firm to make it give up its own technology (i.e., network) and join the common standard. Thereby, for very high network effects, a prelaunch becomes unattractive compared to the alternative of both firms staying in and entering the final consumer market with incompatible technologies. The paper is organized as follows: In Section 2, we review the literature. In Section 3, we present our model. Section 4 contains the analysis of equilibria and comparative statics for network effect strength and changes in the firms’ technological progress functions. Section 5 contains a discussion and extensions. Section 6 concludes. There are three appendices. Appendix A.1 contains the proofs of our propositions, Appendix A.2 contains mixed strategy equilibria, and Appendix A.3 presents more in-depth reasoning about some of our results.

3 It would be relatively straightforward to assume that technological development does not cease completely, but slows down after a prelaunch. However, this would not add much insight to the model. For a similar assumption, see Regibeau and Rockett (1996).

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2. Related literature This study integrates several issues not analyzed jointly before, specifically (1) network effects, (2) pre-market standardization and (3) its timing, (4) triggered by one firm’s prelaunch (5) in an oligopoly setting. The literature on network externalities and standardization is vast – especially on post-introduction compatibility decisions (Farrell and Saloner, 1985, 1986; Katz and Shapiro, 1985, 1986, 1994; David and Greenstein, 1990; Besen and Farrell, 1994; Economides, 1996; Regibeau and Rockett, 1996; Clements, 2004; Koski and Kretschmer, 2004) – and will not be reviewed in detail. Closest to our model is Farrell and Saloner (1988), who compare the efficiency of a hybrid standardization mechanism with de facto market standardization and a committee solution. They find that hybrid standardization may be superior to either of the pure mechanisms because firms have more opportunities for coordination. Coalition formation for standard-setting in network industries has been studied by Axelrod et al. (1995) and Economides and Skrzypacz (2003). Economides and Skrzypacz (2003) study coalition formation among N firms in a two-stage game, with three main differences to our model. First, we incorporate timing in the first stage. Second, we model the effect of technological development on standardization incentives. Third, we focus on two firms to keep the model tractable. Other studies on market structure in network industries (Argenziano, 2008; Clements, 2005; Mitchell and Skrzypacz, 2006) model dynamic duopolies and analyze the evolution of a de facto (i.e. postlaunch) standard. In contrast, we analyze firms’ incentives to agree on a standard in the pre-market development stage and we specifically study the dynamics of the first stage with a simplified second stage. Our model also relates to timing games in general (Fudenberg and Tirole, 1991; Lotker et al., 2008) and in particular preemption games (Fudenberg and Tirole, 1985; Levin and Peck, 2003), waiting games such as warof-attrition games (Bulow and Klemperer, 1999; Hoerner and Sahuguet, 2011), and innovation and technology adoption games (Hoppe, 2002; Hoppe and Lehmann-Grube, 2005).4 Two key findings in that literature are that firstmover advantages may accelerate adoption through preemption – even up to the point of rent equalization across adopters (Fudenberg and Tirole, 1985) – and that late-mover advantages may exist because technologies improve over time (Hoppe, 2002). Our model captures this trade-off and we find both preemption and waiting games. Related to our paper is a study by Katz and Shapiro (1987) who analyze two firms that compete to bring an innovation to the market. Their dynamic setting allows the non-innovating firm to benefit from the rival’s innovation to varying degrees, depending on the regime of post-development dissemination of the innovation. They obtain – as we do - both patent races (driven by a preemption motive) and waiting games, and find that industry leaders introduce minor innovations, but develop major innovations only if imitation is difficult.

4 See Baye and Hoppe (2003) who relate innovation games to rentseeking games.

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However, while Katz and Shapiro (1987) are primarily interested in the timing of an innovation, the identity of the innovating firm (leader or follower) and the effect of different regimes of post-innovation dissemination, we study the effect of network effects and technological capabilities on compatibility decisions. Further, Katz and Shapiro (1987) assume that players can produce and innovate in each round. In contrast, we consider a multi-round development stage in which firms decide whether and when to publish their increasingly ‘mature’ technology prior to launch. Their model captures ongoing process R&D, where the effect of an innovation is an immediate cost reduction, while ours captures new product development for which a standard may or may not be agreed on.5 Further, our model has no incumbent, and we assume that imitation without licensing is not possible. Our model also resembles models of oligopolistic competition with some prior stage of competition, e.g., networks formation (Billand and Bravard, 2004), or research and development (R&D). Typically, firms make decisions on R&D investment in the first stage and compete in the product market in the second stage (D’Aspremont and Jacquemin, 1988; Amir et al., 2000). Recent work has extended these models by adding another stage prior to R&D investment. This preceding stage captures decisions such as the knowledge sharing rate in cooperative R&D (Sakakibara, 2003), or an incentive scheme for the firm’s management (Kraekel, 2004). Our model structure is similar with two major exceptions: First, we focus on timing (not intensity) decisions in the first stage.6 Second, we model a network market. This shifts the focus to the issue of (in-)compatibility and its consequences for the market stage. We also draw on work on strategic preannouncements. The literature on preannouncements studies conditions under which advance communication (e.g., in the form of product preannouncements) arises as an equilibrium strategy (Haan, 2003; Gerlach, 2004). Typically, preannouncements are modeled as public statements which reveal little about precise product specifications. Instead, they usually announce the impending release of a new product and the envisaged release date. However, these statements often turn out to be untruthful (Haan, 2003): The new product is released with great delay, if at all. Our notion of a prelaunch differs from such preannouncements. The commitment value of a prelaunch in our paper exceeds that of a preannouncement. That is, a prelaunch resembles the presentation of a prototype. The rationale for a prelaunch is to be so specific in describing the new technology and its interfaces as to let rivals assess its quality as industry standard for the consumer market. This limits the possibility of changing the core (interface) features of the technology after the prelaunch. Hence, a prelaunch essentially commits the firm to commercializing the technology in the prelaunched format.

5 We study a ‘technology revolution’ as noted by Shy (1996). Shy (1996) considers a related problem, the frequency of new technology adoption in network industries, but takes a demand-side perspective. 6 In this sense, the model presented here is similar in spirit to Gilbert and Harris (1984).

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Finally, work on strategic information disclosure (Gill, 2008; Gordon, 2004; Jansen, 2008) and licensing is relevant to our model. While different in modeling approach, the literature on strategic information disclosure shares our idea of strategically motivated publishing to induce the rival to adopt a certain behavior (e.g., ‘cut R&D intensity’ in Gordon, 2004; ‘concede’ in our model). While licensing mechanisms are not central to our study and we adopt a rather simple design, the determination of license fees in our model draws on the literature on licensing in oligopoly (Giebe and Wolfstetter, 2008). 3. The model Consider two firms 1 and 2. Information is complete and perfect. The game has two stages. The first stage is a timing game with a fixed time horizon, sliced into N rounds (on discretizing in timing games see Lotker et al., 2008). It describes the development phase of a new technological standard. Firms do not make profits or incur costs in this stage.7 The second stage is a Cournot game and models product market competition. 3.1. Technology development stage In each of the first N  1 rounds of the development stage each firm chooses one of the following three actions:  Stay in (S),  Prelaunch (P),  Concede (C), In the final round N the only options are ‘Stay in’ and, if a prelaunch has taken place in a prior round, ‘Concede’. ‘Stay in’ means continuing the development of the standard. ‘Prelaunch’ means publishing the technological specifications and royalty demands/subsidy offers if the opponent adopts the standard. It ends the firm’s development efforts of the standard (although not necessarily for the product).8 ‘Concede’ stands for a firm ending its development and announcing that it will support the rival standard and pay royalties/ receive subsidies. Each firm can prelaunch only once, and prelaunching implies that the firm cannot make any more moves in the first stage of the game. A firm will also concede only once (if at all), which, in this case, is its final move in the development stage. So a firm must either stay in until the end of the development stage, stay in until it prelaunches, or stay in until it concedes. Once one firm has prelaunched, the actions available to the rival are limited to ‘Stay in’ and ‘Concede’. This is based on the assumption that a prelaunch (unlike a mere preannouncement) implies a commitment to the particular technology so that a firm will not concede after having prelaunched.9 Our reading of a prelaunch resembles the 7 This is a simplifying assumption. Allowing for costs of development would create further incentives to prelaunch and save money on further development. 8 We do not model subsequent product development, that is, the design and implementation of soft’ features that do not matter for the interoperability of the technology. 9 This assumption makes sense for the two-firm case. With additional firms, prelaunching remains an option as long as there are at least two firms who might concede, and have not yet prelaunched.

prelaunch of the Compact Disc discussed earlier. The quality of the technology that firm i 2 {1, 2} has developed until round n of the development stage is given by its technological progress function ai(n), which is strictly increasing in n. If firm 1 prelaunches, it publishes the technological standard it will introduce. This ends the firm’s development. The round M in which it does so thus determines the final technological quality of its standard to be a1(M). A concession also ends a firm’s development. Concession means that the conceding firm 2 will enter the market stage with the opponent’s technology: a2 = a1(M). We denote the final value of a firm’s technology by ai, without indication of the final round. Note the distinction between a2(n) as a function of the rounds n as opposed to the final value a2. If firm 2 concedes, a2 is set by firm 1’s quality, i.e. a1(M). A prelaunch also requires the prelaunching firm to fix its demands for royalty payments m (or subsidies if m < 0) in the round of the prelaunch.10 3.2. Cournot market stage We now formalize the Cournot market stage. Depending on the outcome of the first stage, the firms either use the same technology – the standard – (‘compatibility’) or different technologies (‘incompatibility’). For compatibility, the inverse demand function for firm i is

pi ¼ ai þ dðqi þ qj Þ  bðqi þ qj Þ;

i – j:

ð1Þ

For incompatibility it is

pi ¼ ai þ dqi  bðqi þ qj Þ;

i – j:

ð2Þ

Here ai is the quality of firm i’s technology as determined in the first stage, qi is the quantity that firm i produces, d indicates the strength of network effects and b is the slope of the inverse demand curve. Ceteris paribus, both products are perfect substitutes. The parameters b, d and the functions ai(n) and aj(n) are exogenous (although ai is not). Normalizing marginal production cost to zero, firm i’s payoff with incompatible technologies is:

pi ¼ qi pi :

ð3Þ

For compatible technologies (firm i prelaunched, firm j conceded), the prelauncher receives m qj from firm j as royalties (or, if m < 0, pays subsidies), while firm j pays (receives) the same amount. The payoffs are

pi ¼ qi pi þ mqj pj ¼ qj pj  mqj :

ð4Þ ð5Þ

Without loss of generality, we choose b = 1. Further, we define c  b  d = 1  d to simplify the notation. Our inverse demand function then becomes

pi ¼ ai  cðq1 þ q2 Þ:

ð6Þ

under compatibility and for incompatibility we obtain

pi ¼ ai  cqi  qj :

ð7Þ

10 We could also assume that m is exogeneously determined, for example by a regulatory authority. In our model, m is the compensation demanded by the prelauncher for letting the conceding firm use its technology or the subsidies offered by the prelauncher to induce the rival to concede.

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4. Equilibria

pi ¼ c

A strategy for a firm consists of two parts: The first relates to the timing stage, the second to the Cournot stage. The latter consists of a production quantity for each possible outcome of the timing stage. The former consists of an action for all possible histories in each round. Most of this information is redundant – the only possible history up to the first prelaunch is that both firms stayed in every round so far – and a strategy is characterized by  a round M from which onwards a firm would prelaunch, and the m it would set, and  a maximum m such that it would concede if the opponent prelaunches before M. We solve for subgame perfect Nash equilibria by backward induction. After deriving equilibrium quantities, we calculate payoffs in the market stage, which depend on the final value ai of the first stage. Knowing how payoffs depend on ai lets us determine the equilibrium in the timing stage. To ensure an interior solution, we impose the following two restrictions:

c > 0:

ð8Þ

and

2c P

ai 1 P ; i – j: aj 2c

ð9Þ

Combining (8) and (9), we get

cP

1 2

ð10Þ

with equality iff the technologies at the end of the timing stage are equal. In other words, our model is only applicable if less than half of the slope of the demand curve is compensated for by the network effect. This also implies that at the end of the development stage no firm’s quality can be more than twice that of its opponent:

2P

ai 1 P ; i – j: aj 2

ð11Þ

4.1. Cournot market stage For incompatibility, equilibrium quantities are:

qi ¼

2cai  aj  qin ; 4c2  1

ð12Þ

while for compatibility (w.l.o.g., firm i prelaunches, firm j concedes) we find

ai ðnÞ þ m  qcom P ; 3c ai ðnÞ  2m  qcom qj ¼ C : 3c

qi ¼

ð13Þ

2cai  aj 4c2  1

109

2 ð15Þ

and for compatibility (prelaunch by firm i in round n, concession by firm j in some later round), they are

pi ¼

  ðai ðnÞ þ mÞ2 ai ðnÞ  2m þm 3c 9c

ð16Þ

pj ¼

ðai ðnÞ  2mÞ2 : 9c

ð17Þ

Equilibrium payoffs and quantities show that in the case of incompatibility, the only factor discriminating between the firms is the quality of their technologies, ai, and, as expected, the firm with the better technology has a larger market share and higher profit. With compatibility, firms use the same technology, so that payoffs only differ in who pays and who receives royalties m. The prelauncher has the larger market share and higher profits (given m > 0). The prelauncher’s choice of m will be analyzed in the first stage. 4.2. Technology development stage By pXi ðnÞ we denote the equilibrium payoff for firm i from the chosen strategy with X 2 {S, P, C} where n refers to the round in which a prelaunch (by any of the firms) occurs – if at all. If both firms stay in until the end, the payoff is denoted by pXi . First, note that firm i can always secure at least the payoff pSi , given by (15) with ai = ai(N) and aj = aj(N), if it plays ‘stay in no matter what’. Should the rival respond to this by prelaunching in round n, then firm i’s payoff would yield pSi ðnÞ, given by (15) with ai = ai(N) and aj = aj(n). Firm i will only consider prelaunching if a prelaunch is at least as profitable as the lowest payoff from staying in, i.e. if

pPi ðnÞ P pSi

ð18Þ

where pPi ðnÞ are profits from successfully prelaunching in round n (i.e. the opponent concedes – when this happens does not matter in our model). We refer to (18) as the ‘weak prelaunch condition’ (WPC). The payoff from an unsuccessful prelaunch ((15) with ai < ai(N)) is always less then pSi . So in equilibrium firm i will only prelaunch if firm j finds it more profitable to concede than to stay in until the end, i.e. if for firm j (17) is greater than (15) with aj = aj(N). We solve this condition for m to obtain an upper bound on m11:

m6

  1 2caj ðNÞ  ai ðnÞ ai ðnÞ  3c : 2 4c2  1

ð19Þ

Since the prelaunching firm sets royalties (or subsidies) m, it can always make concession attractive to the opponent, at the extreme by offering subsidies. The prelauncher’s

ð14Þ

Substituting these into the payoff functions, we find the equilibrium payoffs. For incompatibility, equilibrium profits are

11 We do not index m by firms (mi, mj) as the context makes clear which m is meant.

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optimal choice for m is indeed the largest m allowed by (19), denoted by m⁄.12 We now substitute (16) and (15) into the WPC (18), and then insert m⁄. We solve for ai(n) and find 10aj ðNÞc3 2c   ð20Þ 1  13c2 þ 16c4 1  13c2 þ 16c4 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi u u a2j ðNÞ  4ai ðNÞaj ðNÞc þ 4a2i ðNÞc2 þ 5a2j ðNÞc2 t 25a2j ðNÞc4 þ ð1  13c2 þ 16c4 Þ1

ai ðnÞ >

with ‘’ if (1  13c2 + 16c4) is positive and ‘+’ otherwise. In this explicit form the WPC is more useful for our analyses. Note that if (20) holds in round n, it will hold for all subsequent rounds as well, because ai(n) is strictly increasing in n. This condition is necessary for a prelaunch, but if it holds for both firms, it need not be sufficient, because a prelaunch is not necessarily more beneficial than a concession. This is ensured by a stronger condition, the ‘strong prelaunch condition’ (SPC):

pPi ðnÞ > pCi ðnÞ

ð21Þ

where pCi ðnÞ is firm i’s payoff if it concedes to a prelaunch by firm j in round n (see (17)). pPi ðnÞ is firm i’s payoff if it prelaunches in round n and the rival concedes. We substitute the payoffs and solve for ai and find 10aj ðNÞc3 2c   ð22Þ 1  13c2 þ 16c4 1  13c2 þ 16c4 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   u u a2j ðnÞ  4ai ðNÞaj ðnÞc þ 4a2i ðNÞc2 þ 5a2j ðNÞc2 t 2 4 25aj ðNÞc þ ð1  13c2 þ 16c4 Þ1

ai ðnÞ >

with ‘’ if (1  13c2 + 16c4) is positive and ‘+’ otherwise.13 The difference between Eqs. (20) and (22) is subtle: They differ only by the final qualities of the products, aj(n) and aj(N). If we rule out large jumps in technological progress (such that most of the progress is made in a single round; for details see Section 4.3), we find that if the SPC (21) holds in round n, it will hold in all subsequent rounds. Given the significant role that the SPC plays for the analysis, some further explanation is in order. Let firm j be such that the SPC is not satisfied before round nj 2 {2, . . . , N}. In that case, by definition of the SPC, we have pPj ðnÞ < pCj ðnÞ for all rounds n 2 {1, . . . , nj  1}. Besides, we know that pCj ðnÞ is defined such that pCj ðnÞ ¼ pSj for all rounds n 2 {1, . . . , N  1}. It follows that, for all rounds n 2 {1, . . . , nj  1}, we have pPj ðnÞ < pCj ðnÞ ¼ pSj and firm j will never prelaunch before round nj in equilibrium. Also, note that the WPC always holds before the SPC does. The weak and strong prelaunch conditions are the tools for classifying the equilibria that arise in our model. 12 This can be seen as follows: The prelauncher wants to maximize (16), which is quadratic in m and has a negative second derivative with respect to m. It has a maximum at m ¼ ai2ðnÞ. For m < ai2ðnÞ, the payoff is increasing in m. But (19) restricts the prelauncher to choose m < ai2ðnÞ (from (9)), and the maximum value allowed by (19) is the best choice. This implies that the conceding firm’s concession profit is equal to its profits from staying in. Note that we assume that a firm concedes if it is indifferent between conceding and staying in. 13 If the right hand side of the equation is not real, the SPC is never satisfied.

4.3. Classification of equilibria We first classify all games that arise in our framework and then determine the subgame perfect equilibria for each class. All results require that the technological progress functions are increasing in rounds, have no large jumps14 and that the aforementioned restrictions apply. For simplicity, assume that firm 1 prelaunches first in cases where there is a prelaunch. The case with reverse ordering is analogous. We state the classification as a lemma: 4.3.1. Classification lemma All games fall into one of the following classes: 1. No Action Games. The WPC (18) is not met, neither for firm 1 nor for firm 2 by round N  1. 2. Late Prelaunch Games. (i) There is only one firm for whom the WPC (18) is met by round N  1, or (ii) the WPC is met for both firms, but the SPC (21) is only met for one firm by round N  1. 3. Early Preemption Games. The WPC (18) is met for both firms by round N  1. The SPC (21) is also met for both firms, but for firm 1 from round n1 on, and for firm 2 from round n2 on, with n1 – n2. 4. Preemption Wars. The SPC (21) is met for firm 1 and firm 2 simultaneously from round n on. 5. Wars of Attrition. The WPC (18) is met for both firms before round n 6 N  1, but the SPC (21) is not met for either firm by round N  1. These classes exhaust all combinations of weak and strong prelaunch conditions applying or not applying to the firms, so we have captured all possible games. The classes are mutually exclusive by construction. In Section 4.4 we illustrate how the classification of the games depends on the strength of network effects and the technological progress functions. We now give the pure strategy equilibria for different game classes. (All proofs can be found in the Appendix, which also discusses mixed strategy equilibria for our model.) Proposition 1. For ‘No Action’ games, the unique pure strategy equilibrium is: Firm 1 : If the opponent prelaunches and sets m 6 m⁄, concede and produce qcom C . Otherwise, stay in until the final round and produce qin. Firm 2 : Same. The outcome in ‘No Action’ games will be that both firms stay in until the end, enter the market with incompatible technologies and produce equilibrium quantities. No firm will prelaunch because it is more profitable for both to stay in and compete. An example of a ‘No action’ game is given by:

a1 ðnÞ ¼ a2 ðnÞ ¼ n; c ¼ 1; N ¼ 250:

ð23Þ

14 d A sufficient condition is ai ðNÞ > dn aj ðnÞ, i.e. in no round may a firm’s technological progress jump by more than the final value of the opponent’s technology.

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Proposition 2. For ‘Late Prelaunch’ games, the unique pure strategy equilibrium is: Firm 1 :If firm 2 prelaunches and sets m 6 m⁄, concede ⁄ and produce qcom C ; if it sets m > m , stay in until in the end and produce q . If firm 2 does not prelaunch, prelaunch in round N  1 and set m = m⁄. If firm 2 concedes, produce qcom P , otherwise produce qin. Firm 2 :If firm 1 prelaunches and sets m 6 m⁄, concede and produce qcom C . Otherwise stay in until the end and produce qin. The outcome of ‘Late Prelaunch’ games is as follows: Firm 1 prelaunches in the penultimate round N  1, and firm 2 concedes in the final round N. This is because firm 2 prefers staying into prelaunching throughout the entire development phase, while firm 1 finds prelaunching more profitable from round n < N onwards. Firm 1 could therefore profitably prelaunch from round n onwards. However, it will continue developing until it prelaunches in round N  1. An example of a ‘Late Prelaunch’ game is given by:

a1 ðnÞ ¼ n; a2 ðnÞ ¼

4n ; 5

3 4

c ¼ ; N ¼ 250:

ð24Þ

We can use (20) to see that for firm 1 the WPC holds from round 231 and the SPC from round 239 onwards, while for firm 2 neither hold in any round. Firm 1 then prelaunches in round 249, and firm 2 concedes in round 250. Proposition 3. For ‘Early Preemption’ games, the unique pure strategy equilibrium is: Firm 1 :Stay in until firm 2 prelaunches or until round n2  1 is reached.15 If firm 2 prelaunches before round n2  1, concede if m 6 m⁄ and produce ⁄ qcom C ; if m > m , stay in until the end and produce qin. If firm 2 has not prelaunched before round n2  1, prelaunch in round n2  1 and set m = m⁄. If firm 2 concedes, produce qcom P . If firm 2 does not concede, produce qin. Firm 2 :Stay in until firm 1 prelaunches or round n2 is reached. If firm 1 prelaunched and set m 6 m⁄, ⁄ concede and produce qcom C ; if m > m , stay in until the end and produce qin. If round n2 is reached without a prelaunch of firm 1, prelaunch in round n2 and set m = m⁄. If firm 1 concedes, produce in qcom P , otherwise q . The outcome for ‘Early Preemption’ games is a prelaunch by firm 1 in round n2  1, followed by concession by firm 2. For firm 1, prelaunching is preferred to staying in or conceding to a prelaunch from round n1 onwards. But firm 1 can increase payoffs by developing its technology further. However, firm 1 must avoid being preempted by firm 2 that would prelaunch from round n2 onwards. Firm 1 will continue developing until round n2  1 and will then prelaunch to preempt firm 2. An example is given by:

15

Round ni is the round from which on firm i’s SPC holds.

a1 ðnÞ ¼ n; a2 ðnÞ ¼

49n ; 50

2 3

c ¼ ; N ¼ 250:

ð25Þ

We can use (20) to see that from round 234, the WPC is satisfied for firm 1. This is true for firm 2 from round 240. The SPC (22) holds for firm 1 from round 239, and for firm 2 from round 242. So firm 1 prelaunches in round 241, just before the rival prefers prelaunching to conceding. This is illustrated in Fig. 1. A more extreme form of a preemption game is summarized in Proposition 4: Proposition 4. For ‘Preemption Wars’, the two pure strategy equilibria are: Firm 1 : If firm 2 prelaunches before round n1 and sets ⁄ m 6 m⁄ concede and produce qcom C ; if m > m , stay in in until the end and produce q . If firm 2 has not prelaunched before round n1, then prelaunch in round n1 and set m = m⁄. If firm 2 concedes, proin duce qcom P , otherwise produce q . Firm 2 :If firm 1 prelaunches before round n2 + 1 and sets ⁄ m 6 m⁄ concede and produce qcom C ; if m > m , stay in until the end and produce qin. If firm 1 does not prelaunch until then, prelaunch in round n2 + 1, and set m = m⁄. If firm 1 concedes, produce in qcom P ; q otherwise. The other equilibrium is analogous, but with firms’ roles reversed. The outcome for ‘Preemption Wars’ is that firm 1 prelaunches in round n1 and firm 2 concedes subsequently or vice versa. An example is given by

2 3

a1 ðnÞ ¼ a2 ðnÞ ¼ n; c ¼ ; N ¼ 250:

ð26Þ

We can use (20) to see that for both firms the WPC (20) is satisfied from round 236, and by using (22) we find that the SPC is satisfied from round 240 onwards. Hence the prelaunch will take place in round 240. Proposition 5. For ‘Wars of Attrition’, the two pure strategy equilibria are: Firm 1 : If firm 2 prelaunches in any round and sets ⁄ m 6 m⁄, concede and produce qcom C ; if m > m , stay in in until the end and produce q . If firm 2 has not prelaunched yet, prelaunch in round N  1 and set m = m⁄. If firm 2 concedes, produce qcom P , if not, produce qin. Firm 2 : Never prelaunch. If firm 1 prelaunches and sets m 6 m⁄, concede and produce qcom C ; if it sets m > m⁄, stay in until the end and produce qin. The other equilibrium is analogous, but with firms’ roles reversed. The outcome for ‘Wars of Attrition’ is in some sense the opposite of a ‘Preemption War’: W.l.o.g., firm 1 prelaunches in round N  1 and firm 2 concedes (the prelauncher’s profits increase over time). An example is given by:

a1 ðnÞ ¼ a2 ðnÞ ¼ n; c ¼

39 ; 40

N ¼ 175:

ð27Þ

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P1: Successful Prelaunch P1: Concession P2: Successful Prelaunch P2: Concession

Payoff

15000

10000 Stay In 1

Stay In 2 5000

0 225

230

WP1

SP1 WP2

SP2

245

250

Round Fig. 1. Payoff structure for an ‘Early Preemption’ game. ‘Stay in 1’/‘Stay in 2’ indicate the firms’ final payoffs from not prelaunching or conceding. ‘WP1’/ ‘WP2’(and ‘SP1’/‘SP2’) are the earliest times the weak (strong) prelaunch conditions are satisfied for the firms.

This concludes our analysis of the pure strategy equilibria. For some of the game classes, mixed strategy equilibria exist, but they do not change our results qualitatively. While for ‘Preemption Wars’ and the ‘Wars of Attrition’ mixed strategy equilibria have the advantage of being symmetric, they suffer from the common instability of mixed strategy equilibria as a small deviation from the equilibrium strategy by one firm induces the opponent to select one of its pure strategies. See Appendix A.2 for details. 4.4. Comparative statics Our model has four degrees of freedom: The strength of network effects (1  c), the firms’ technological progress functions ai(n) and aj(n) and the number of rounds N. The classification lemma relates these fundamental parameters to the game classes via expressions (20) and (22). To get an intuition of the effects of variations in the strength of network effects and technological progress functions, we classify a large number of games (see Fig. 2 below). Keeping the number of rounds fixed at N = 250, we vary 1  c over the permissible range from 0 to 0.5. We also scale one firm’s progress function via a parameter x. Technologically similar firms represent cases with x close 1. We use a1(n) = n and a2(n) = x n, and let x vary between 0.9 and 1.0, so firm 1 is (weakly) stronger than 2. Each point in the (c, x) plane then corresponds to one particular game. After classifying this game via the classification lemma, we indicate the game class by coloring the point at coordinate (c, x) in a shade of gray. Game classes are shaded in their order in Propositions 1–5: ‘No Action’ (lightest), ‘Late Prelaunch’, ‘Early Preemption’, ‘Preemption War’, ‘War of Attrition’ (darkest). For the values above we obtain Fig. 2.

One striking feature in Fig. 2 is that ‘Preemption Wars’ occur only on the horizontal axis (where firms have identical technological progress functions) and in a number of ‘spikes’ below. ‘Wars of Attrition’ are found only in small pockets towards the left and the right end of the horizontal axis. ‘No Action’ games appear as a small triangular structure at the far left and the far right of the horizontal axis. The horizontal axis is embedded in a large structure containing ‘Early Preemption’ games. Firm 1 as the stronger firm will prelaunch early in these games. The largest, lighter gray area contains ‘Late Prelaunch’ games, where again firm 1 prelaunches. Hence, for most parameter combinations, we obtain either a ‘Late Prelaunch’ or an ‘Early Preemption’ game. It is intuitive that a ‘Preemption War’ or a ‘War of Attrition’ will only take place if both firms’ technologies are of similar quality. That is, situations where both firms compete for setting the industry standard only occur if they are close technological competitors. The further down in Fig. 2, the stronger firm 1 is relative to its opponent. Consequently, we first obtain ‘Early Preemption’ games, and then ‘Late Prelaunch’ games. Interestingly, even without network effects, late prelaunch games may occur if the firms are sufficiently dissimilar (see Fig. 2). The reasoning behind this is that, if the technologically more advanced firm prelaunches, it can demand royalties from the other firm. The other firm will accept as it gets access to a better technology and can make at least the same profit as with its own technology. Note that while the ‘spikes’ are a specific property of our model – as discussed in Section 4.4.2, they are caused by the discrete nature of time in our game – such patterns are expected in a wide class of timing games with discrete time. As continuous time can be seen as an idealization and is often less realistic than

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Fig. 2. Illustration of the game classes in (c, x) space with a1 = n, a2 = xn, 0.5 < c < 1. White indicates a parameter combination ruled out by our restrictions, and the shading of gray indicates the game class emerging at a (c, x) combination.

discrete time, such patterns may well be common in timing games describing real world phenomena.16

4.4.1. The network effect symmetry of the classification In this subsection we give a qualitative explanation for some important features of Fig. 2, for example the fact that increasing network effects can have a ‘non-monotonic impact’ on the classes of games. We first illustrate how network effects affect the round n from which onwards the SPC is satisfied, and how this in turn impacts the distribution of game classes across the parameter space, i.e. the shape of Fig. 2. We then give some intuition for the impact of network effects on n. First, note that there appears to be a (non-linear) symmetry in Fig. 2. There is a value of network effects (at c  0.7, or, equivalently, 1  c  0.3), which divides the diagram into two similar halves. For each game in the left half of the diagram there appears to be a corresponding one in the right half, although both halves depend differently on the fundamental parameters. For example, there are nine spikes containing ‘Preemption War’ games in the left half, and nine such spikes in the right half. However, the tip of the spike is at a slightly different x, while the spikes (and indeed the whole diagram) are stretched in the c-direction for larger c, and squeezed for c smaller than 0.7. This is because the round n from which onwards the SPC holds is a convex function of c (Fig. 3), as is the WPC. Around c  0.7, this function has its minimum.17 So a small change in network effects does not affect the time at which the SPC (and WPC) is satisfied at c  0.7. The identity of the prelaunching firm is therefore stable, meaning that a large range of x-values generates ‘Early Preemption’ games rather than ‘Preemption Wars’, which have no clearly defined leader (and two equilibria). Moving away from 1  c  0.3,

the round n at which the SPC holds increases for both increasing and decreasing c, but at different rates (see Fig. 3). This explains why the two halves of Fig. 2 are not simply mirrored, but mirrored and stretched. For example, we can see in Fig. 3 that the SPC is satisfied from round 240 onwards for 1  c  0.18 in the left half of the diagram. To the right, the SPC holds from round n = 240 for 1  c  0.4, i.e. at a different distance to 1  c  0.3. So the symmetry, and hence some of the surprising results, such as finding ‘Wars of Attrition’ and even ‘No Action’ games for high network effects (i.e. close to values of 0.5), are a consequence of the shape of n as a function of c (see Fig. 3). Turning to the second part of the explanation, we will now give a qualitative explanation for the link between network effects and earliest prelaunch times. Given that firm 2 does not prelaunch, the profit for firm 1 increases with the round n in which it prelaunches, simply because its technology is more advanced in later rounds (Fig. 1). Similarly, the conceder’s profits decrease with the round n in which the opponent prelaunches. The intersection of these two functions defines the time at which the SPC is satisfied. Increasing the value of c has two countervailing effects: First, it lowers the concession profits and raises the prelaunch profits. The result is that the SPC is satisfied earlier.

n 252.5 250 247.5 245 242.5

1 0.1 16

An immediate implication of continuous time would be that preemption wars would only happen if firms developed identical technologies, an unlikely scenario in real life. 17 The precise location of the minimum depends on the value of x.

0.2

0.3

0.4

0.5

237.5

Fig. 3. Round n in which the SPC is satisfied as a function of the strength of the network effect 1  c, for x = 0.95.

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Second, the shape of profits as a function of the round changes (Fig. 1). They become generally flatter, i.e. less dependent on network effects c. This results in the SPC being satisfied later. In the left half of Fig. 2, the first effect dominates, in the right half the second. The value of x (which characterizes the quality of one firm’s technology relative to the rival’s technology) has a small impact on the effects. In Fig. 2, for example, the ‘neutral’ value of c around which the games are mirrored is slightly smaller for large x than for small x. Starting from some intermediate value of network effects then, we find that both increasing and decreasing network externalities delay the time for which the firms’ (weak and strong) prelaunch conditions are met (Fig. 3). This means that the prelaunch occurs later both for the ‘Preemption War’ spikes and the ‘Early Preemption’ games between the spikes. At both extreme ends, the firms’ SPCs (indicating a preference for prelaunching over conceding) are not fulfilled before the final round N, while the WPCs still are. Firms then play a ‘War of Attrition’, in which both prefer concession to staying in, but would rather not prelaunch themselves. With a further decrease/increase in network effects, we obtain ‘No Action’ games. The intuition for this differs on the right and the left hand sides of the graph. If the strength of network externalities decreases further when they are already weak (see Fig. 4), gains from standardization decrease and standardization becomes unprofitable.18 For strong network effects (see Fig. 5), the intuition is more subtle. Further increases in the strength of network effects affect the profits from staying in more than prelaunch and concession profits. As the prelaunching firm sets the license fees such that the rival ‘just’ prefers conceding to staying in, the increasing attractiveness of staying in requires the prelaunching firm to lower the license fee until it eventually has to offer subsidies to make the rival give up its own technology (see (15)–(17) for details). As a result, at some point firms prefer to concede rather than prelaunch until, in the extreme, a prelaunch becomes so unattractive that both firms prefer to stay in rather than agree on a standard prior to the market stage (although both would prefer even more to concede to a prelaunch undertaken by the rival). 4.4.2. Granularity of discrete time So far, we focused on network effects and technological capabilities. However, an important element of our model is the decision how to slice time into discrete rounds. Should a prelaunch by two companies be considered simultaneous if it occurs in the same month, or rather the same day? To understand the effect of granularity consider the effects of changing the number of rounds N. This concerns the slicing or granularity, not necessarily the

18 This is true only at the x = 1 axis and very close to it (the precise value depends on the number of rounds N of the game) Away from that axis, there are games with prelaunches even without any network effects. Here, when the technologically advanced firm prelaunches, it can demand royalties from the other firm. The other firm accepts as it gets access to a better technology and can earn at least the same profit as with its own technology.

duration of the development stage (the final technological quality may remain unchanged). We find that increasing the number of rounds leads to more but smaller spikes.19 The spikes’ height (in the direction of the parameter x) and width (in the c-direction) decrease with the number of rounds N. That is, increasingly smaller changes in the strength of network effects suffice to generate different outcomes. Recall that the spikes exist because for two similarly strong firms, the rounds from which the relevant prelaunch conditions are fulfilled may coincide although one firm is stronger. For N ? 1, in contrast, this could not happen and ‘Preemption Wars’ could not appear for x – 1. Further, for the N ? 1 case, the two ‘War of Attrition’ spikes on the left and right of the c axis shrink away, and so do the ‘No Action’ spikes at the far ends. The intuition is that in the limit N ? 1, as soon as firms differ even slightly in their technological abilities, the prelauncher’s identity is predetermined. So most of the rich structure of the discrete time game disappears in the limit. To summarize, in discrete time, whether the prelaunch conditions are satisfied in the same round or not, and hence which game class emerges, depends on the granularity of decision-making. We expect this effect to appear in a wide class of timing games.

5. Discussion In our model, failure to standardize – that is, both firms enter the market stage with incompatible technologies – occurs only when network effects are either very weak or very strong and firms have similar technological capabilities (or for a coordination failure when firms play mixed strategies, see Appendix A.2). Hence, standards battles emerge only in a rather limited parameter range. This has two interpretations. First, it stresses the importance of coordinated standard-setting, a phenomenon which is underrepresented in the literature on standards and network effects. Second, it suggests that standards battles may be driven by forces outside the scope of our model. For example, firms might play a dynamic game in the market stage, which would generate more extreme long-term market outcomes, so that a standards battle becomes relatively more attractive as the payoffs from winning it get amplified. Further, welfare losses are more likely the more similar the qualities of the two firms’ technologies are. Inefficiencies in our model may occur either due to ‘premature’ technology introduction prior to round N  1 (the ‘Preemption Wars’ or ‘Early Preemption’ scenarios in our model), due to a failure to standardize during the development stage (the ‘No Action’ scenario or coordination failure when firms use mixed strategies), or due to standardization on the (slightly) inferior technology, which may happen if the weaker firm gets to prelaunch in the ‘War of Attrition’ scenario. ‘No Action’ games, ‘Wars of Attrition’, and ‘Preemption Wars’ occur indeed only for nearly identical firms. Firms with very different technological capabilities (resulting in a ‘Late Prelaunch’) do not engage in value-destroying competition. Rather, they jointly introduce the better standard when it is fully developed, 19

A graphical illustration of this is available from the authors.

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115

Fig. 4. Enlargement of the top left area of Fig. 2.

Fig. 5. Enlargement of the top right area of Fig. 2.

and the less capable firm prefers adopting the competing standard to releasing its own version. We now discuss possible variations and extensions to our model. First, it would be interesting to allow for bargaining over license fees. Related, variations in the postinnovation dissemination regime as in Katz and Shapiro (1987) may yield interesting insights. For example, what would happen if imitation was feasible and costless? In our model, this would imply that m = 0, i.e. the prelaunching firm will cannot charge any licensing fees nor will it offer subsidies to the rival. The SPC would disappear with pPi ðni Þ ¼ pCi ðni Þ. A firm becomes indifferent between prelaunching and conceding, but whether it would prefer any of these to staying in until the end depends on the strength of network effects and the technological progress functions. Symmetric firms would always prefer prelaunch/concession, unless network effects were either non-existent or very strong (i.e., c very close to 0 or 0.5). If firms prefer prelaunch/concession, any successful

prelaunch that would be observed would occur in the last possible round (N  1), which implies that technological quality is maximized, and the underlying game would be reduced to a coordination game. Absent network effects, none of the firms has an incentive to prelaunch or concede. For very strong network effects (i.e., c close to 0.5), the incentive for maintaining incompatibility emerges from the higher prices that firms can charge in the incompatibility case, compared to a joint standard. In other words, if network effects are very strong, compatibility increases firms’ quantities so much that the corresponding prices decline such that profits are lower compared to incompatibility. For asymmetric firms, the weaker firm always prefers entering with a joint standard based on the competitor’s technology. Whether the stronger firm prefers entering the market with incompatible technologies or prefers the weaker rival to join its superior technology depends on parameter values. In any case, the stronger firm would neither prelaunch nor concede to a prelaunch by the weaker

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firm, so it will stay in and introduce its superior technology, which will then be adopted at no cost by the weaker rival. It would also be interesting to consider the possibility of an endogenously arising time horizon (e.g., resulting from decreasing marginal returns from development and/or increasing development costs). For symmetric firms, this would not change the qualitative results of our model. For asymmetric firms, firms might want to enter the market at different points in time, which complicates our analysis. However, if both prelaunch conditions for both firms hold prior to the earliest time at which one firm would want to enter the market, the general mechanisms would remain intact. Further, our model assumes deterministic technological progress.20 It would be interesting to incorporate uncertainty of technological development. A model with incomplete information in which firms are uncertain about their own and/or the rival’s technological progress functions might be more realistic in some cases. In such a setting, we speculate that unsuccessful prelaunches might emerge in equilibrium, unlike in our current setting. Also, in many strategic situations, more firms are involved, e.g., direct competitors or complementors such as software suppliers or hardware producers without their own R&D. More generally, in games with several stages, it might be interesting to consider not only the possibility of additional competitors that are structurally similar (i.e., they compete in both stages), but also of firms that compete only in the development or the commercialization phase. Their presence might give rise to interesting signaling effects. Finally, we discuss briefly how our results inform some of the puzzles arising from our opening example, the emergence of the CD standard. Philips/Sony’s prelaunch prior to the DAD conference suggests that there was an element of preemption involved. While we cannot say how much JVC/Matsushita’s technological progress affected Philips/Sony’s timing of the prelaunch, we can speculate that the approval of JVC/Matsushita’s technology at the DAD conference implies that they could have also prelaunched their technology as a viable alternative to the winning standard. The benefits from standardization were significant, however, rendering concession a preferable option for JVC/Matsushita to entering a standards battle with their own, viable technology. Clearly, the CD example exhibits many additional interesting aspects beyond those captured here. For example, the drive towards extensive licensing of CD technology by Philips and Sony (including granting very favorable terms to JVC/Matsushita) may be an indicator that technological competition was relatively tight (as the license fees demanded in our model decrease in the strength of the licensee), but the dynamics of licensing to multiple suppliers is not an issue we discuss in detail.21

20 It should be noted that our results hold for a large variety of different technological progress functions. Results are available from the authors. 21 For a discussion of this, see Shepard (1987).

6. Conclusion In this paper, we studied the emergence and timing of a technological standard prior to release. In a simple twostage game, we characterize the circumstances under which a firm would prelaunch their technology, hoping that the rival adopts it and pays licensing fees. We classify our results depending on the strength of network effects and firms’ technological capabilities for a given time horizon. The model captures several phenomena and strategic variables that matter in pre-market standardization, such as the tradeoff between preemption motives and technological development, and the likely outcomes in terms of preemptive standardization, last-minute agreements, and failures to standardize. Depending on the firms’ technological progress functions, the strength of the network externalities and the (time) granularity of the development stage, the outcome belongs to one of five different game classes ranging from no standardization outcomes to cases in which the firms’ behavior (prelaunch and subsequent concession) leads to the adoption of a joint standard. Competitors agree on a joint standard in most cases, although the timing differs depending on the equilibrium class. Standard battles with incompatible technologies arise only for firms with very similar development capabilities and when network effects are either very strong or very weak (or in case of a coordination failure). ‘‘Wars of Attrition’’ emerge only in situations with similar firms and rather weak or rather strong network effects (for somewhat less extreme values of network effects than those for which we find standard battles). Finally, we observe that the dependence of the game classes on the parameters exhibits a surprisingly complex structure. This is a consequence of the discrete nature of time, and the notion of ‘‘at the same time’’, which depends on the way time is discretized. In reality, there will always be events which should be considered as ‘‘at the same time’’, although one happens before the other. In our case, a prelaunch by both firms on the same day, one just before lunch, one just after, should probably be considered as taking place ‘‘at the same time’’ (although a continuous time model would treat the two events as taking place at different times). The complexity of the structure and its dependence on the precise time slicing emphasize the importance of choosing between continuous and discrete time in modeling such strategic situations and, in the case of discrete time models, of choosing the appropriate length of rounds. Acknowledgments Part of this research was conducted while Katrin Muehlfeld was a research fellow at the Department of Management at LSE whose hospitality is gratefully acknowledged. ESRC (Grant PTA-026-27-0083) and the NET Institute provided financial support. Benedikt Gamharter provided excellent research assistance. We are grateful for useful comments provided by participants at EARIE (Amsterdam) and IIOC (Boston), and at seminars at LSE, CEP and the University of Frankfurt. We thank Rafael Gomez, Marco Haan, Bernd Irlenbusch, Mariana Stamm, Arjen

S. Kerstan et al. / Information Economics and Policy 24 (2012) 105–119

van Witteloostuijn, and in particular a referee and an associate editor for helpful comments on earlier versions. The usual disclaimer applies. Appendix A A.1. Proofs Proof of Proposition 1. We need to prove three things: First, that the given strategies really constitute a subgame perfect equilibrium, second, that such games exist, and third, that the equilibrium is unique. We first check all possible alternative strategies in the timing stage. Any deviation from the strategy in Proposition 1 involves a prelaunch by some firm. But by construction the games considered in Proposition 1 are such that, for either firm, irrespective of its opponent’s actions, prelaunching is less profitable than staying in. The production quantities are equilibrium quantities by construction (see Section 4.1). This shows that the strategies define an equilibrium. The existence of such games is proved by the example just after the proposition. The uniqueness is obvious: We showed that in equilibrium, both firms will stay in until the end of the timing stage. Given that, the unique quantities derived in Section 4.1 are the only equilibrium solution. The strategies in Proposition 1 therefore define the unique subgame perfect equilibrium. h

117

drop to just above the Stay In profit). It could also decide not to prelaunch at all, which, again, is easily seen to generate a lower payoff than the proposed strategy. Any deviation on firm 2’s side leads to lower payoffs: Prelaunch before round n2 is by construction not as profitable as waiting until round n2. Should round n2 be reached without firm 1 prelaunching, then firm 2 could deviate by not prelaunching, which is again, by construction, less profitable than the proposed strategy. Existence of such games is proved by the example just below Proposition 3. That the equilibrium is unique can be seen by exhausting all possible alternatives: Strategies in which both firms do not prelaunch, or would prelaunch in rounds that deviate from those given in Proposition 3, exhibit incentives for firms to deviate unilaterally, and hence do not define equilibria. Hence the only equilibrium is the one we described. h Proof of Proposition 4. The proof is analogous to the proofs of Propositions 1–3. h Proof of Proposition 5. The proof is analogous to the proofs of Propositions 1–3. h A.2. Mixed strategy equilibria

Proof of Proposition 2. We proceed as in the proof of Proposition 1. To show that we are dealing with an equilibrium, we first observe that by construction, firm 2 has no incentive to prelaunch at any time, and its strategy must be to stay in (and concede to a prelaunch, should it be profitable). For firm 1, there are several ways in which it could deviate: It could prelaunch before round n, but that leads to lower profits than the proposed strategy. It could prelaunch in some round k with n 6 k < N  1. Again, this is a less profitable option than the proposed strategy, because it would not reap the extra profits from her increased technological standard. It could also not prelaunch at all, but again, by construction of the case, this is less profitable. Hence for either firm, any deviation from the proposed strategy lowers its payoff and hence we have showed that we are dealing with an equilibrium. Existence is proved by the example just after the proposition. Uniqueness is shown by considering all alternative strategies for both firms: Firm 1 could prelaunch earlier, but whatever firm 2’s reply, could always do better than that by sticking to the proposed strategy. It could not prelaunch at all, but again, could do better than that by sticking with the proposed strategy. Similarly for firm 2. Hence the only equilibrium is the one we described. h

For the timing stage, a firm i’s mixed strategy consists of a set of prelaunch probabilities pni for each round n, depending on the history of play up to the particular round, plus a specification of the alternative choice (either Stay In or Concede) for the remaining probability 1  pni . In the model presented here, the history of play can simply be characterized as whether a prelaunch has already taken place, or not. In the first case, the firm either stays in until the end, or concedes (at an unspecified time during the timing stage), depending on the respective pay off. Therefore, we can further simplify this brief characterization of mixed strategy equilibria by focusing on the prelaunch probabilities alone, that is on a firm’s probability to prelaunch in each given round (provided, no prelaunch has taken place, yet), i.e. pni . To determine theses period-specific probabilities in equilibrium, we first observe that in any game class, the expected payoff E(pi) for firm i in round N  1 (the last round in which prelaunching is allowed), is given by

Proof of Proposition 3. That the proposed strategy defines an equilibrium can be seen by checking all possible deviations for either firm in the timing stage: Firm 1 could prelaunch earlier (but this is less profitable because it would enter the market with a lower quality), or later (in which case the rival would preempt it and its profit would

where pN1 denotes firm i’s probability of prelaunching in i round N  1, while pPi ðN  1Þ stands for firm i’s payoff for a successful prelaunch in round N  1 and pCF i ðN  1Þ stands for firm i’s payoff in case of a coordination failure (both firms prelaunching in round N  1Þ; pCi ðN  1Þ is the payoff for conceding to the opponent (who prelaunches

  Eðpi ðN  1ÞÞ ¼ pN1 1  pN1 pPi ðN  1Þ i j pN1 pCF þ pN1 i j i ðN  1Þ   N1 C N1 pj pi ðN  1Þ þ 1  pi     pSi ðN  1Þ 1  pN1 þ 1  pN1 i j

ð28Þ

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in round N  1) and finally pSi ðN  1Þ stands for the payoff for staying in until the end. To find the period-specific prelaunch probabilities pN1 in equilibrium we demand i @ Eðpi ðN  1ÞÞ ¼ 0. This is the case for @pN1 i

pN1 i

¼

p

P j ðN

pPj ðN  1Þ  pSj :  1Þ  pSj þ pCj ðN  1Þ  pCF j ðN  1Þ

ð29Þ

This defines a firm’s prelaunch probability as part of its equilibrium strategy for the timing stage, given that round N  1 was reached. In earlier rounds the prelaunch probabilities are



pni

¼

pPj ðnÞ  E pSj ðnÞ







pPj ðnÞ  E pSj ðnÞ þ pCj ðn þ 1Þ  pCF j ðnÞ

ð30Þ

  where E pSj ðnÞ is the expected payoff from staying in during the current round n and prelaunching with probability pki (according to (30) in each subsequent round k with n < k < N  1 and with probability pN1 in round N  1. i The formulae (29) and (30) define both firm’ prelaunch probabilities for all possible rounds, which are the central ingredient to the mixed strategy equilibria. For both, ‘‘Preemption War’’ games and ‘‘War of Attrition’’ games, there are mixed strategy equilibria given by. Firm 1 :If firm 2 prelaunches before round n1 and sets m 6 m⁄ then concede and produce quantity qcom C . If m > m⁄, then stay in until end and produce quantity qin. From round n P n1 onwards, act according to the following strategy in every round: If firm 2 has not prelaunched until round n, then prelaunch in round n with probability pn1 given by Eq. (30) and, if the prelaunch takes place, set m = m⁄. If firm 2 concedes to this prelaunch, produce quantity qcom P , while if firm 2 responds by staying in until the end, produce quantity qin. If firm 2 also prelaunches in round n1, then produce quantity qin. If no prelaunch took place in round n, repeat the above steps for n + 1. Firm 2 :As firm 1, but roles of firm 1 and firm 2 reversed. Similarly, there is an analogous equilibrium for ‘‘Early Preemption’’ games. A.3. More on Network Effects and Technological Capabilities The structure of the ‘‘spikes’’ along the horizontal axis warrants further discussion. We first comment on the pattern of ‘‘alternating’’ games (‘‘Preemption War‘‘ and ‘‘Early Preemption’’ games) just below the horizontal axis. Consider a game with weak network effects in which one firm (here, wlog, firm 1), is slightly stronger than the opponent, such that the game belongs to one of the (dark shaded) spikes, i.e. the game is a ‘‘Preemption War’’ game (see Fig. 4). A small decrease in network effects (i.e. moving to the left) switches the game to an ‘‘Early Preemption’’ game. Another small decrease in network effects, i.e. going further left, switches the game back to a ‘‘Preemption Wars’’ game, and so on. The reason for this ‘‘alternating pattern’’ over a range of values for c towards both ends

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