Competition in Standard-Setting with Network Effects

Transcription

1 Competition in Standard-Setting with Network Effects Xiao Fu January 20, 2017 Job Market Paper For the most recent version, please visit Abstract Many technology products are based on standards that require the use of patents. This paper studies the design of competing standards in industries with positive network effects where the relevant network can be either industry-wide when standards are compatible (e.g., mobile phone standards) or standard-specific when standards are incompatible (e.g., video game consoles). In a three-stage model, standards choose how many patent holders to include and then compete in the marketplace. I find that competing standards have incentives to soften competition through fragmenting their patent rights. Nevertheless, the degree of fragmentation is lessened when competition among standards becomes more intense. Moreover, compatibility among standards also affects the incentives to fragment patent rights. These results provide alternative explanations to as why standards in many high-technology industries adopt highly fragmented patent rights structure. Keywords and phrases: Standard-Setting Process, Standards War, Standard-Essential Patents, Compatibility JEL classification codes: D2; L4; L13; L15; O3 I am extremely indebted to Guofu Tan for his continuing guidance and support. I am very thankful to Laura Doval, Junjie Zhou, and Haojun Yu for their detailed advices. I also would like to thank Simon Wilkie, Yilmaz Kocer, Isabelle Brocas, Juan Carrillo, and Yanhui Wu. I have benefitted from comments by seminar participants at USC, as well as conference participants in 2016 Southern California Symposium on Network Economics and Game Theory. Ph.D. Candidate, Department of Economics, University of Southern California; xiaofu@usc.edu. 1

2 1 Introduction In several key industries,..., our patent system is creating a patent thicket: a set of patent rights requiring that those seeking to commercialize new technology obtain licenses from multiple patentees. Carl Shapiro, Navigating the Patent Thicket This Standards are technical specifications that regulate the common design of products and services. 1 Standardized industries such as mobile phones, computers, and digital media share the following key features: (i) standards promote interoperability so that differently designed products can work together, (ii) competing standards are developed in different organizations, and (iii) conforming to a standard requires the use of patents and paying licensing fees to multiple patent holders. 2 For example, in the case of mobile telecommunications, (i) standards ensure compatibility so that mobile phones from different carriers and/or makers can work together, (ii) several independent standard-setting organizations have developed dozens of competing standards over the last two decades (e.g., GSM and CDMA in the 2nd era of mobile networks), and (iii) each standard is made up of hundreds or even thousands of patented technologies owned by dozens of different firms. 3 Moreover, for each of the aforementioned industries, the economic effects of standard setting are significant because ex-ante (before a standard is designed) non-essential patents may become essential ex-post (after a standard is designed). 4 Economists and participants in high-technology industries have raised concerns about there potentially being too many essential patents, typically termed patent thicket phenomenon. 5 This paper analyzes the formation of competing standards in industries that satisfy features (i)- (iii) above. The research question is how do the certification decisions of standards interact with 1 Spulber (2016) comments that standards are specifications that affect product quality and interoperability of parts and components. Standards apply to inputs, components, and final-products that affect production costs and consumer benefits. 2 Baron and Spulber (2015) comment that in most cases, standards themselves do not grant users a right to use the patented technologies described in the standards. This right must be negotiated in private agreements with patent holders. The overall royalty burden is determined by adding all the different claims for royalties together. 3 For instance, Layne-Farrar and Lerner (2011) suggest that the W-CDMA standard covers 34 different patent owners holding 348 essential patents. 4 By definition, an essential patent is strictly necessary for the standard. That is, an end user needs licenses to each of these patents in order to comply with the standard. 5 As defined by Shapiro (2001), the patent thicket phenomenon describes a situation in which the users of a major invention must obtain licenses from multiple patent holders. Allison and Lemley (2002) suggest that this pattern seems to be consistent over time at least from the 1980s onwards. 2

3 market competition. In the model, standards affect competition by choosing how many patent holders to certify, and patent holders then independently set licensing royalties. The key insight of the analysis is that competing standards have incentives to soften competition through fragmenting their patent rights, that is, in the presence of competition, each standard always certifies multiple patent holders. Nevertheless, the degree of fragmentation is lessened when competition becomes more intense. Additionally, I show that compatibility among standards also affects the incentives to fragment patent rights. Specifically, I find that fragmentation incentives strictly increase with intra-standard network sensitivities and strictly decrease with inter-standard network sensitivities. The present analysis helps explain the choice of technologies by standards, provides an alternative explanation for the patent thicket phenomenon, and has interesting public policy implications. Overview of model The focus of the analysis is on the interaction between standard setting and market competition. The model is feasible enough to accommodate any number of standards. I posit that each standard performs a certification function, designing its technical specification based on a particular combination of patented technologies, and it is member-friendly in the sense that its objective is to maximize the total licensing revenue of its patent holders. 6 After the certification decisions have been made, patent holders independently set licensing royalties for their own patents. The certification decision of each standard thus involves a basic trade-off: covering more patent holders can increase royalties but makes the users less likely to adopt the standard. I solve for the equilibrium number of patent holders within each standard, under the constraint that patent holders are required to commit to grant licenses on nondiscriminatory terms. 7 I consider a discrete-choice model of standard implementation in a market characterized by positive network effects. The payoff a user derives from implementing a standard depends on the number of users implementing the same or compatible standard(s). For example, when a user faces a choice among competing standards, it tends to take into account the decisions of other users, 6 I refer to members as the patent holders whose inventions are included in the standard, as opposed to users referring to the implementers. 7 As acknowledged by Schimidt (2014), Baron and Spulber (2015), and Lerner and Tirole (2015), standards often require the patents included in the standards be made available by their owners with royalties that are fair, reasonable, and non-discriminatory, referred to as FRAND. The FRAND terms are the most common rules by which standards now deal with patent ownership, although standards usually do not indicate how to calculate FRAND royalties. 3

4 as a more popular standard can have a better chance to survive or win a standards war. The relevant network can be either industry-wide when standards are completely compatible (i.e., the networks of different standards are connected with each other) or standard-specific when standards are completely incompatible (i.e., each standard has its own proprietary network). I compare the equilibria for the standards with complete compatibility and complete incompatibility. Overview of results The main results of the analysis are as follows. First, I show that fragmentation of patent rights unambiguously raises licensing royalties for all the standards. The intuition behind this finding is that by delegating pricing decisions to independent owners holding strictly complementary patents, the standards credibly commit not to set royalties coordinately, therefore inducing less competition from competitors. I then show that competing standards have incentives to soften competition through certifying multiple patent holders. In other words, competition among the standards leads to the fragmented structure of patent rights, as compared to the case of a single monopoly standard. Second, I show that the degree of fragmentation is lessened when competition becomes more intense, that is, either the number of standards increases or the intrinsic payoff of the standards decreases. The intuition for this result is that increased competition would give each standard an additional incentive to cut royalties, and in consequence, the incentive to raise royalties through fragmentation is weakened. In addition, I show that both the equilibrium royalties and licensing revenue will drop dramatically once the number of competing standards exceeds two, that is, having three or more standards in the marketplace is much less profitable than two. Third, I consider the situation in which standards are able to coordinate their certification decisions. The equilibrium royalties under the aforementioned noncooperative standard-setting process are found to be typically lower than the joint-profit maximizing level. I then show that if standards can cooperate on certification, they will choose to cover more patent holders, and by so doing, they will be able to induce the joint-profit maximizing royalties in the market for patent licenses. This result suggests that cooperative certification can provide an alternative way for competing standards to collude. Finally, I incorporate network effects into the adoption of standard such that the payoff a user derives from implementing a standard also depends on the number of users implementing the same 4

5 or compatible standard(s). As mentioned earlier, the relevant network can be either industry-wide when standards are completely compatible (e.g., mobile phone standards) or standard-specific when standards are completely incompatible (e.g., video game consoles). I first explore the stable choice probabilities under such models and then characterize the equilibria. More specifically, with network effects, multiple equilibria can easily arise, even when network sensitivities are homogenous, and the equilibria may be either symmetric or asymmetric. I provide a sufficient condition under which there exists a unique symmetric equilibrium. This condition is powerful since it works for both compatible and incompatible standards. I also characterize some key properties of the asymmetric equilibria and show that weak network sensitivities can preclude the possibility of asymmetric equilibria. For the symmetric equilibria, I show that better compatibility reduces the incentives to fragment patent rights. Specifically, I find that fragmentation incentives strictly increase with intra-standard network sensitivities and strictly decrease with inter-standard network sensitivities. These results indicate that, all else being equal, patent thickets are denser when standards are incompatible (i.e., there are no inter-standard network effects) than when they are compatible (i.e., there exist positive inter-standard network effects). The remainder of this paper is organized as follows. Section 2 discusses the related literature. In Section 3, I set up a basic model of standard setting and competition without network effects, where the main assumptions and notations are introduced. In Section 4, I characterize the unique equilibrium of the basic model and establish comparative statics results. In Section 5, I incorporate network effects and different types of compatibility into the basic model. Section 6 concludes and all omitted proofs and details are presented in the Appendix. 2 Related literature This paper is closely related to several strands of literature in the fields of economics. The theoretical framework contributes to a long literature on Cournot s complementary monopolies problem and its application in vertically structured industries. While I discuss the analysis in the context of standards and patents, the model can generally be seen as a description of interaction between input monopolies in the upstream market and oligopolies in the downstream market, and therefore it can 5

6 apply to a number of different situations. The economics literature provides many examples of complementary input monopolies selling to downstream manufacturers, including copper and zinc monopolists selling to downstream producers of brass (Cournot (1838)), jet engines and avionics in aircraft component markets (Choi (2008)), and Microsoft s Windows operating system and Intel s microprocessors (Casadesus-Masanell and Yoffie (2007)). The baseline model of this paper most nearly resembles that of Tan and Yuan (2001). In their paper, two competing firms independently choose ex ante their divestiture strategies and delegate pricing decisions to the divisions. In their theory, such a divisionalization softens the price competition between the two firms. As a result, the prices and profits increase, but the total surplus is reduced. More recently, Quint (2014a) analyzes a similar environment in which each products has its components supplied by different firms. He shows sufficient conditions on a random utility model under which the pricing game has a unique equilibrium. Together, this line of literature considers a world with differentiated products that are made of nonoverlapping sets of essential inputs, each supplied by a different firm. To draw an important distinction between this paper and this line of existing works, I note that none of the papers mentioned above considers network effects. This paper also makes substantial contributions to the analysis of standardization. Many of the papers in the literature focus only on the design of a single standard (see, e.g., Farrell and Saloner (1988), Farrell and Simcoe (2012), Lerner and Tirole (2015)). 8 An important exception is Llanes and Poblete (2015). They model standard setting as a coalition-formation problem in which two groups of technology developers compete to have their own standards adopted in the market. The patent ownership in their setup is thus unconcentrated, and they allow developers to differ in two dimensions: the number of patents they hold and the value of those patents. The profits of a coalition of developers thus depend on the allocation of developers into coalitions. My paper combines these approaches and the contribution is twofold. First, I introduce a theoretical framework that is flexible enough to accommodate any number of competing standards. I show that with competition, fragmentation of patent rights has a broader interpretation. For example, in many models of a single standard, having one additional patent holder in the standard will reduce licensing revenue and the reduced revenue has to be shared with 8 Lerner and Tirole (2015) model standard setting as choosing patented technological functionalities and provide conditions under which a user-friendly standard and users form the efficient combination of technologies. Farrell and Saloner (1988) model consensus standard setting as a war of attrition with complete information, that is, two developers argue for their preferred technological solutions until one side concedes. Farrell and Simcoe (2012) extend their early work by introducing private information on the quality of solutions. 6

7 all the patent holders, e.g., see Schmidt (2014) and Quint (2014b). If that is the case, then from the standard s perspective, patent ownership must be the more concentrated the better. However, my analysis suggests that the insights we have learned from these models can be incomplete. I show that competing standards have incentives to soften competition through covering multiple patent holders. As a result, both total royalties and licensing revenue can increase for all the standards. Second, I evaluate the interaction between the certification decisions of standards and market competition. As acknowledged by Lerner and Tirole (2006), the economics literature analyzing standards has largely focused on just one role: that of a meeting room where technology developers can negotiate; therefore the strategic roles played by standards are often ignored. The final related literature is on oligopolies with network effects. In their pioneering work on markets with network effects, Katz and Shapiro (1985) consider oligopolies with positive network effects and different types of compatibility. 9 Amir and Lazzati (2011) generalizes the theory in Katz and Shapiro (1985) on oligopolistic markets with complete compatibility. They show that Cournot oligopolies with fully compatible networks will never have an asymmetric equilibrium, only symmetric equilibria are guaranteed. More recently, Amir and Gama (2015) show that oligopolies with incompatible networks may have asymmetric equilibria, even if all the firms face the same demand and costs of production. They center their attention to non-trivial symmetric equilibria and set aside the existence of asymmetric equilibria for future study. Since all the aforementioned papers focus on quantity competition, the model and many results of this paper are distinct from these papers. et al. Network effects are also discussed in the logit choice model by Anderson (1992), but only the case of symmetric equilibria under incompatible networks is briefly considered. Starkweather (2003) further modifies the logit choice model to incorporate network effects and compatibility issues. Following the theory of Miyao and Shapiro (1981), he provides a sufficient condition on network sensitivities parameters under which there exists a unique stable choice probability when products are fully incompatible with each other. The network effects in his model can be either positive or negative. However, he does not characterize equilibrium prices or provide comparative statics analysis. So the research question and analysis of this paper are still much different from Starkweather. 9 Their first model is when all the products are compatible; in the second one, all the goods supplied by different firms are incompatible; and lastly, in the case of partial compatibility, there are groups of goods that are compatible within own group but incompatible with the goods outside the group. 7

8 3 The basic framework I consider a discrete choice model of standard implementation in which users face a choice over a finite set k K = {1, 2,..., K} of distinct standards. I assume that the standard has full flexibility in defining which technologies are essential. That is, even though some technologies may not be essential for a standard ex-ante (before the standard is designed), if they are certified by the standard, they become essential ex-post (after the standard is designed). I describe next the preferences of the technology developers, end users, and standards. Technology developers (certified patent holders) There is a finite set t M = {1, 2,..., M} of symmetric technology developers, each can potentially form a standard. 10 For k K, each standard chooses members M k M and then determines the set of technical specifications based on technologies developed by its members. I first consider a situation where standards do not have any common patent holder (i.e., M k Mk = ). I will relax this assumption later by analyzing licensing with overlapping patent ownership in section 4.1. As I explain below, each end user makes a discrete choice of which standard to adopt, and therefore users single-home. This means that the only way to license patents to a particular user is to make the patents be covered by the standard she is using. I further assume that patent holders are required to commit to license their inventions at nondiscriminatory royalties. Let b kt denote the (linear) licensing royalties set by the tth patent holder of standard k for t M k. The total royalties for implementing standard k are given by b k t M k b kt. End users Demand for the standards comes from a market of total size N. I deploy a discrete-choice model of standard implementation where each user adopts the standard (or the no-adoption option denoted by 0) that gives her the highest payoff. The payoff a representative user obtains from implementing standard k is given by 10 This setting indicates that the efficient standard only certifies a single technology developer. 8

9 u k = τ k + ε k, (1) where τ k is the deterministic payoff from adopting standard k (τ 0 is normalized to 0) and ε 0, ε 1,..., ε K reflect user-specific opportunity costs of implementing the standards (or the nonadoption option), which are assumed to be i.i.d. Gumbel random variables. For k K, we have τ k = π b k, where π is the intrinsic payoff of the standards and b k is the overall royalty burden for implementing standard k. 11 Let b = {b 1,..., b K }. The above formulation yields that the choice probability for standard k takes the following fractional form Standards s k (b) = exp(τ k ) 1 + K l=1 exp(τ, for k K. (2) l) The total licensing revenue of standard k takes the following form R k = b k s k (b)n, for k K. (3) The objective of each standard is to maximize its licensing revenue R k by choosing how many patent holders to include. Timing The timing of the game is as follows: 1. Certification: standards independently choose how many patent holders to include, requiring patent holders to make a commitment to grant licenses on nondiscriminatory terms. 2. Licensing: patent holders simultaneously and noncooperatively set licensing royalties, under the constraint of the nondiscriminatory terms; Users then choose which standard to implement (or the non-adoption option) and pay licensing fees to all the relevant patent holders. My main interest is in how patent ownership is designed in stage 1 under different market structures. 11 In order to simplify the presentation and emphasize the effects of the nature of market competition on fragmentation, I assume that the intrinsic payoff is symmetric across standards and users. This simplification does not affect the qualitative results in the paper. 9

10 4 Analysis This section characterizes the equilibrium outcomes of the basic model. For an arbitrary allocation of patent holders within each standard, the equilibrium royalties will be formalized. I will then stylize the equilibrium number of patent holders and conduct comparative statics studies for certification and royalties. 4.1 Characterization Without loss of generality, I further normalize N to 1. For m = {m 1,..., m K }, the profit of the tth patent holder in standard k is given by R kt = b kt s k (b), for t M k and k K. (4) Therefore, in the second stage, the first-order condition for an interior solution is s k + b kt b k = 0, for t M k and k K, (5) which suggests that in equilibrium the royalties set by the independent patents holders are identical within each standard. b = {b 1,..., b k } must solve the following equation: The equilibrium total royalties for implementing each standard m k s k + b k b k = 0, for k K. (6) From the above equation, one can see that b depends on the number of patent holders within each standard. Given b as induced by (6), the licensing revenue function for each standard can be rewritten as R k = b k s k(b ), for k K. (7) Therefore, the equilibrium number of patent holders within each standard m = {m 1,..., m K } must solve the following equation: 10

11 (s k (b ) + b (b ) k b ) b k + b (b ) k k m k b l k l b l m k = 0, (8) for k, l K and k l. Using (6), the above equation can be rewritten as b k m k 1 (b ) m k b + k m k l k (b ) b l b l m k = 0, (9) for k, l K and k l. Now I am ready to describe the equilibrium of the two-stage game and the implications the game has for total royalties. I pay particular attention to the case of K 2. In the Appendix I show that some desirable properties of the Logit choice model leads to an easy proof of equilibrium existence and uniqueness. Proposition 1 Suppose K 2. Then, (i) For any m, the total royalties increase with the number of certified patent holders within each standard, and they are more sensitive to their own standards sizes than to the sizes of other standards. That is, b k m k > b l m k > 0 for k, l K and k l. (ii) The two-stage game has a unique equilibrium with m k = m > 1 for all k K. The results in Proposition 1 rely on the complements effect within each standard and can be generally seen as an extension of Tan and Yuan (2001) to the market with an arbitrary number of competing firms. It stems from the fact that when firms sell strictly complementary goods, their combined price will be higher than if all the goods were provided by a single monopolist. This situation was originally studied by Cournot (1838) and later termed the complements effect. In my setting, by delegating pricing decisions to independent owners holding strictly complementary patents, standards credibly commit not to set royalties coordinately, therefore inducing less competition from competing standards. can increase for all the standards. As a result, both total royalties and licensing revenue Proposition 1 suggests that considering competition among standards can shed new light on how does fragmentation of patent rights affect licensing revenues. The existing works on standardessential patents often focus on the case with a single standard. Therefore, in many models, having 11

12 one additional patent holder in the standard will reduce licensing revenue and the reduced revenue has to be shared with all the patent holders, e.g., see Schmidt (2014) and Quint (2014b). If that is the case, then from the standard s perspective, patent ownership must be the more concentrated the better. Proposition 1 implies that the insights we have learned from these models can be incomplete: in the presence of competition (i.e., K 2), standards have incentives to fragment patent rights, and in consequence, such fragmentation can increase licensing revenues for all the standards. Cooperative certification Denote the licensing revenue function specified in (7) by R(m,..., m) when standards are all symmetrically designed (i.e., m k = m 1 for all k K). The following proposition provides an interesting property of this function. Proposition 2 For any K 2, if m k = m for all k K, the licensing revenue of each standard R(m,..., m) is singled-peaked of m and reaches the maximum at m = m > m, where m is defined as in Proposition 1. Proposition 2 demonstrates that when standards are all symmetrically designed, fragmentation can increase their licensing revenue as long as the number of patent holders within each standard falls into a certain range (i.e., 1 m < m). This result also suggests that the equilibrium total royalties for implementing each standard is typically below the joint-profit maximizing level. An immediate implication of Proposition 2 is that standards will achieve the joint-profit maximizing total royalties if they are able to coordinate their certification decisions and set m k = m for all k K. Therefore, cooperative certification can provide an alternative way for competing standards to collude. To the extent that standards can achieve tacit collusion in licensing through coordinated certification, the competition policy implication of the present analysis is that antitrust agencies should consider the potential competitive effects in permitting formal cooperation between competing standard-setting bodies. Next, to illustrate the contrast between concentration and fragmentation of patent rights, I describe a set of numerical examples. I demonstrate that in the presence of competition, it is always profitable for standards to fragment their patent rights. Otherwise, a significant portion 12

13 of licensing revenue may be lost. By the following lemma, I can get analytical results for the competition among any K 1 standards under the logit choice model. Lemma 1 For any K 1, the equilibrium m and b in the two-stage game must satisfy m = (1 s(b ))b m 1 m (1 s(b ))[1 s(b ) + b s(b ) (K 1)b s(b ) 2 ] = (K 1)b s(b ) 3 where s(b) = eπ b. 1+Ke π b In what follows, I compare three certification strategies: 1. Cooperative certification: I consider the optimal symmetric certification decision. That is, I let m k = m for all k K and solve the aforementioned joint-profit maximization problem for m. Let the optimal licensing revenue be denoted by R(m). 2. Noncooperative certification: I solve for the equilibrium number of certified patent holders m by lemma 1, which generates the equilibrium licensing revenue R(m ). 3. Concentration: I ignore fragmentation and compute the licensing revenue with m k = 1 for all k K. The comparison results are illustrated in Figure 1. We can see that when K = 1, the optimal certification strategy is to concentrate patent rights (i.e., m k = m = 1 for all k K); and therefore, the licensing revenues are identical across the three cases. However, when K 2, a concentrated patent ownership is no longer optimal and case 3 always generates a smaller licensing revenue than the other two; additionally, case 2 always generates a smaller licensing revenue than case 1, as suggested by Proposition 2. 13

14 Figure 1: Comparison of licensing revenues under different certification strategies. π is fixed at 8. Integration of patent holders I now consider the situation in which given m, some patent holders may integrate, that is, either a patent holder buys up some other essential patents, or some patent holders form a patent pool to coordinate licensing. In either case, the integrated patent holders bundle their patents and license them at a joint licensing fee to users. The effects of such integration on total royalties are summarized in the following proposition. Proposition 3 Suppose K 2. Then, fix any m, (i) If some (or all) patent holders from the same standard integrate, the total royalties are reduced for all the standards. (ii) If some (or all) patent holders from different standards integrate, the total royalties are raised for all the standards. Proposition 3 shows that integration between patent holders from the same standard unambiguously reduces royalties for all the standards since the intra-standard complements effect is weakened. By contrast, integration across standards has a unilateral effect: it eliminates the competition between the merging firms, raising royalties for all the standards. 14

15 The result in Proposition 3 part (i) is obvious because by Proposition 1 part (i) we already know that the total royalties monotonically increase with the number of certified patent holders within each standard. This result is consistent with the existing literature on how patent pools of complementary patents affect royalties. 12 It then immediately follows from Proposition 1 part (ii) that the grand patent pool containing all the patents of a standard cannot be profitable for participants because in the presence of competition, a concentrated patent ownership must be undesirable (i.e, we have R k(m) m k mk =1 > 0 for any arbitrary m l with k, l K and k l). This result sheds some light on why in real-world markets many standard-related patent pools are incomplete pools, typically containing a small percentage of eligible patent owners, e.g., see Layne-Farrar and Lerner (2011) Comparative statics on royalties and certification In real-world markets, there are many factors that can affect standards incentives to certificate patent rights, including the number of competing standards, litigation cost and regulation on intellectual property protection, and asymmetry across technology developers and users. In what follows, I provide a formal analysis of two of these factors, i.e., how do the number of competing standards and the symmetric intrinsic payoff from implementing the standard affect the certification decisions and incentives to set royalties? I establish: Proposition 4 For any K 2, (i) The introduction of an independent standard lowers both total royalties b and licensing revenue R. Moreover, it also leads to a smaller number of certified patent holders within each standard m if π > 7 1. (ii) An increase in π raises b, R, and m. Moreover, it holds that lim K 1 K(K 2). π b = K 1 K 2 and lim π R = 12 A patent pool is an agreement by patent holders to license their patents as a single package to end users. The economics literature generally argues that patent pools can help solve the complements problem. For example, Shapiro (2001) shows that patent pools decrease royalties when all patents are perfect complements. However, in practice there is a lack of patent pools, in particular complete pools. 13 For example, Layne-Farrar and Lerner (2011) suggest that patent pools usually adopt either numeric proportionality rule or value-based rule for dividing royalty earnings among participants. They study the pertaining practice of nine active patent pools from different industries, which on average cover 38 percent of all standardessential patent holders eligible for pool. 15

16 Figure 2 below illustrates the comparative-statics results for m. The intuition for these results is that as market competition among standards becomes more intense, it gives each standard an additional incentive to cut royalties, and consequently, the incentives to raise royalties through fragmenting patent rights are reduced. Proposition 4 part (ii) also suggests that the upper limits of R and b will experience a significant drop once the number of standards exceeds two. In my setting, introducing a new standard does not have to incur an entry cost, but in real-world markets such a cost cannot be trivial. This result implies that if there are already two independent standards competing in the marketplace, an outside standard may not want to enter the market for the fact that having three standards is much less profitable than two. This result may shed some light on why in many hightechnology industries, such as mobile telecommunications and consumer electronics, standards (formats) wars usually happen between exactly two differently designed standards. 14 Figure 2: An example of equilibrium number of patent holders under different values of K and π 14 For a comprehensive list of standards war and participants since the 1880s, see wiki/format_war. 16

17 5 Standard setting with network effects In this section, I modify the basic logit choice model to incorporate network effects into the user s payoff. A standard is said to exhibit network effects if users value it more when greater numbers of other users adopt that same or compatible standard. That is, each standard s network can be either compatible or incompatible with that of its competitors. The relevant network can be either industry-wide when standards are completely compatible or standard-specific when standards are completely incompatible. I first characterize the stable choice probability under such models and then conduct studies on properties of the equilibria. Finally, I compare the equilibria for standards with complete compatibility and complete incompatibility. I center my attention to the effect of compatibility on the incentives to fragment patent rights. 5.1 The logit choice model with network effects Consider a market of total size N where users make a discrete choice over K distinct standards. The payoff a representative user obtains from implementing standard k is given by u k = τ k + ε k, for k K, where the deterministic part τ k is the expected payoff from implementing standard k and ε dk is an i.i.d Gumbel random variable that captures the heterogeneity in the user s opportunity cost. More specifically, we have τ k = π b k + α k x k + β kl x l, for k K, (10) l K,l k where π is the intrinsic payoff of the standard, which is assumed to be identical across standards and users; b k represent the (linear) total royalties for implementing standard k; x k is the user s perceived demand for standard k; α k is the intra-standard network effect sensitivity parameter; and β kl is the inter-standard one. I assume β kl > 0 if standards k and l are compatible with each other, otherwise β kl = 0. This specification indicates that the users perceived network value for the standard is taken to be a continuous and strictly increasing function of her perceived market coverage of that standard and other compatible standards. More precisely, for k, l K and k l, we have 17

18 α k > β kl > 0: complete compatibility, α k > β kl = 0: complete incompatibility, α k = β kl = 0: no network effects. Complete compatibility refers to the case in which all the standards on the technology market can work together. An example of such industries is mobile phone networks. As shown in Figure 3, carriers often build their cellular networks by different wireless technologies and use bilateral agreements to complete a call made to one of its subscribers by a caller from a different carrier s network. A carrier can benefit from the expansion of its competitors networks because it would be able to collect more revenue from providing termination services. Figure 3: Mobile networks based on fully compatible technology standards In contrast, complete incompatibility refers to the case in which each standard is incompatible with that of its competitor. Common examples of industries with incompatible standards include digital compact cassette, digital media formats, and video game consoles. Many observations suggest that when a producing firm faces a choice among incompatible standards, it tends to consider the number of firms which have adopted each standard, as a more popular standard will have a better chance to survive or win a standards war. Next, given the representative user s expectations x = {x 1,...x K } and total royalties b = {b 1,...b K }, the probability that she adopts standard k is given by The payoff of the non-adoption option is normalized to 0, and I assume that the network effects on τ k does not depend on the choice of the outside option. 18

19 exp(τ k ) s k (x; b, α, β, π) = 1 + i K exp(τ i) = exp(π b k + α k x k + l K,l k β klx l ) 1 + i K exp(π b i + α i x i + j K,j i β ijx j ). (11) Therefore, the above choice probability is a function of royalties and user expectations. I do not explicitly model the process through which users expectations are formed. Instead, I impose the requirement that in equilibrium users expectations are fulfilled. Self-fulfilling expectations imply that at equilibrium x k = s k N. Without loss of generality, we can normalize the total number of users N to 1, and (11) then can be rewritten as F k (s) = exp(π b k + α k s k + l K,l k β kls l ) 1 + i K exp(π b i + α i s i + j K,j i β, for k K. (12) ijs j ) For any s = {s 1,..., s K } with s k > 0 and K k=1 s k < 1, there is a unique vector b = {b 1 (s),..., b K (s)} that satisfies (12). The profit maximization problem of the tth patent holder in standard k becomes max b kt Rkt = b kt (s)s k, for t M k and k K, where s is implicitly defined by (12). The licensing revenue of standard k is given by R k = b k (s)s k, for k K. (13) where b k = t M k b kt. Each standard maximizes the licensing revenue of its members by choosing how many patent holders to include. The timing of the game is as follows: 1. Users form expectations about the size of the network with which each standard is associated. 2. Standards independently make decision on how many patent holders to include, and patent holders then noncooperatively and simultaneously announce licensing royalties for their own inventions. 3. Users make their implementation decisions, given their expectations and royalties. 19

20 5.2 Completely incompatible standards In this section, I suppose that the standards are incompatible with each other, that is, I assume β kl = 0 for k, l K and k l. In what follows, I will pay particular attention to the case with α k 1 for all k K since this case gives a lot of interesting comparative static results. The following lemma describes some interesting features of the logit choice model with positive network effects where each standard has its own proprietary network. Lemma 2 (i) Suppose α k 1 for all k K. Then, the stable choice probability s k is increasing in α k and b l and decreasing in α l and b k for k, l K and k l. Furthermore, choice probabilities are more sensitive to royalties than to the intra-standard network effect parameters. α k + b k < 0 and α l + b l > 0 for k, l K and k l. That is, (ii) The logit specification with network effects does not exhibit the independence of irrelevant alternatives (IIA) property. That is, for any three standards j, k and l, the ratio of choice probabilities of standard k and l will change as the parameters of standard j changes. Next I look into the existence and uniqueness of the stable choice probability as defined in (12). Denote S = {s R K k K s k < 1, s k > 0}. Thus, F is a continuos mapping from S to S. By Brouwer fixed point theorem, there exists at least one solution s S to (12). However, unlike the basic framework without network effects, multiple equilibria can exist. In other words, given a vector of total royalties b, there could be multiple s that satisfy (12). Lemma 3 below provides a simple sufficient condition which ensures that for any b there exists a unique s that satisfies (12). Lemma 3 For any values of {(α k, b k ) : k K}, there exists at least one s that satisfies (12). Moreover, if 0 < α k 2 for all k K, then the solution to (12) is unique and can be achieved by iteratively applying the mapping from any starting point. Lemma 3 suggests that fix b and any starting point s 0 = (s 0 1,..., s0 K ), s t converges to the unique stable solution by the dynamics s t = F (s t 1 ) if 0 < α k 2 for all k K. The logic behind this result is first acknowledged by Miyao and Shapiro (1981) under a more general setup than the present model, and it is also closely related to the network Logit specification studied by Starkweather (2003). These conditions are very powerful since they work for both incompatible and compatible standards. 20

21 By Lemma 3, we know that at least one symmetric equilibrium exists. However, the above conditions are still not sufficient for guaranteeing a unique equilibrium. An interesting feature of the present model is that multiple equilibria can easily arise, even when the network sensitivities parameters are homogeneous, and the equilibria may be either symmetric or asymmetric. Let ŝ = (ŝ 1,..., ŝ K ) denote stable choice probabilities that satisfy (12), we have the following proposition regarding the characteristics of equilibria for incompatible standards with symmetric patent rights structure. Proposition 5 Suppose standards are incompatible with each other and are all symmetrically designed (i.e., m k = m 1 for all k K). (i) When network sensitivities are identical across standards (i.e., assume α k = α for all k K), There are at most three distinct entries in ŝ. There exists no asymmetric equilibria if 2 m 1 α α and α 1 3. There exists ᾱ > 0, which depends on K and π, such that there exists a unique symmetric equilibrium ŝ 1 =... = ŝ K = ŝ if 0 < α min{ᾱ, 1}. (ii) When network sensitivities differ across standards (i.e., assume 0 < α 1 <... < α K 1), for any equilibrium, ŝ must satisfy ŝ 1 <... < ŝ K. Proposition 5 explores some interesting properties of the asymmetric equilibria. In my setting, the asymmetric equilibria can easily arise when some standards are more widely adopted because the users expect them to be so. For example, during the formats war between Blu-ray and HD DVD, some major film studios (Fox, 20th Century, Warner Bros, etc.) announced that they were willing to declare exclusive support for one format, but they wanted the format to have another studio partner before they did so. In my setting, asymmetric equilibria can arise when demand is concentrated on a single standard or a set of standards. In the case of homogeneous network sensitivities, I find that there are at most three distinct entries in ŝ and that weak network sensitivities can preclude the possibility of asymmetric equilibria. In the case of heterogenous network sensitivities, I show that there is no symmetric equilibrium and that in equilibrium the standard associated with a larger value of network effects must have a higher market share. The existence of asymmetric equilibria is set aside for future research. Moreover, Proposition 5 part (i) suggests that in the case of homogeneous network sensitivities, 21

22 a unique symmetric equilibrium can be guaranteed when α does not exceed a certain threshold. In the Appendix, I show that the threshold on α is positive, which is strictly increasing in K and decreasing in π. Interestingly, this condition works without modification for standards with completely compatible networks. I now center my attention to the special case of symmetric equilibria and consider the situation in which standards are able to coordinate their certification decisions. For the symmetric equilibria, let ŝ denote the equilibrium market share for each standard. Then, the equilibrium total royalties ˆb are given by ˆb = π + αŝ log[ŝ] + log[1 ŝk], (14) and the equilibrium licensing revenue for implementing each standard becomes R = αŝ 2 + (π + log[ 1 ŝk ])ŝ. (15) ŝ I still use m to denote the cooperative certification outcomes but add a subscript I that denotes complete incompatibility. I have the following proposition describing the cooperative certification decisions of incompatible standards. Proposition 6 Suppose 0 < α k = α 1 and m k = m for all k K. Then, for any symmetric equilibrium, R(m,..., m) is single peaked in m and reaches its maximum at m = m I, which strictly increases with α. The results above extend those in Proposition 2, which shows that if standards are able to cooperate on certification decisions, they will cover more patent rights when each standard has its own proprietary network than when there are no network effects. The impact of network effects on cooperative certification under complete incompatibility will be discussed in detail in section Completely compatible standards In this section, I incorporate inter-standard network effects into the user s payoff and focus on the homogenous case in which β kl = β > 0 for k, l K and l k. The stability condition (ow becomes 22

23 where s k = i K,i k s i. F k (s) = exp(π b k + α k s k + βs k ) 1 + i K exp(π b, for k K, (16) i + α i s i + βs i ) It turns out that many results in the case of incompatible standards still hold here. First, I find that Lemma 3 holds with a minor modification, that is, for any values of {(α k, β, b k ) : k K}, if 0 < β < α k 2 for all k K, we can conclude that the solution to (16) is unique (See A.6. Proof of Lemma 3). When the above condition holds, there exists (at least) one symmetric equilibrium. Second, the sufficient condition for the existence of a unique symmetric equilibrium holds without modification in the present setting. set aside for future research. Again, the existence of asymmetric equilibrium is In what follows, I further assume that the inter-standard network sensitivities parameters are homogenous. For the symmetric equilibria, let s denote the equilibrium market share for each standard. Then, the equilibrium total royalties b are given by b = π + α s + β(k 1) s log[ s] + log[1 sk], (17) and the licensing revenue function becomes R = [α + β(k 1)] s 2 + (π + log[ 1 sk ]) s. (18) s The following proposition describes the cooperative certification decisions of compatible standards. I add a subscript C into m to denote complete compatibility. Proposition 7 Suppose 0 < β < α 1 and m k = m for all k K. Then, for any symmetric equilibrium, R(m,..., m) is single peaked in m and reaches the maximum at m = m C, which strictly decreases with β. The results above further extend those in Proposition 2, which implies that better compatibility among standards leads to lower incentives to fragment patent rights when standards are able to coordinate their certification decisions. Since the two network sensitivities parameters α and β are found to affect m in opposite ways, the net effect matters. The impact of network effects on cooperative certification under complete compatibility will be 23

24 formalized in the next section. 5.4 Complete incompatibility versus complete compatibility In this section, I compare certification decisions for standards with positive network effects under complete incompatibility and complete compatibility. In particular, I want to see how does compatibility affect the equilibrium number of patent holders. With a particular emphasis on symmetric equilibria and homogenous network sensitivities, I first summarize the impact of network effects and compatibility on cooperative certification decisions and then center my attention to the case of noncooperative certification. Cooperative certification We already know that if standards are able to coordinate their certification decisions, there exists a unique value of m such that the joint-profit maximizing royalties can be supported as a noncooperative equilibrium outcome at the licensing stage. I denote such a value of m by m, which was already found to strictly increase with α and decrease with β at any symmetric equilibrium. Again, I use subscripts to distinguish complete incompatibility and complete compatibility. Some early results of the previous sections are summarized in the following proposition. Proposition 8 Suppose 0 < β < α 1. Then, competing standards can achieve the maximum joint profit by setting m k = m for all k K. Moreover, m strictly increases with α and decreases with β. It is straightforward that Proposition 8 implies that m I is always larger than m and m C. I now present a simple sufficient condition on π under which m C can be always larger than m. Corollary 1 For 0 < β < α 1, m C > m if π 2+log[2]. To finish this line of discussion, I present a figure that illustrates the above proposition. For any K [1, 4], I set π = 60 and plot the cooperative certification outcomes under three cases: (i) no network effects: m with α = β = 0, (ii) complete incompatibility: m I with α = 0.5 and β = 0, and (iii) complete compatibility: m C with α = 0.5 and β = 0.1. Figure 4 illustrates how m changes with three of the four aforementioned parameters, namely, α, β, and K. Since π satisfies the condition in the above Corollary, we can see that for any K, it holds that m I > m C > m. 24