Licensing a technology standard

International Journal of Industrial Organization 47 (2016) 33–61

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International Journal of Industrial Organization www.elsevier.com/locate/INDOR

Licensing a technology standard✩ Chun-Hui Miao∗ Department of Economics, University of South Carolina, Columbia, SC 29208, United States

a r t i c l e

i n f o

Article history: Received 9 October 2014 Revised 1 February 2016 Accepted 9 February 2016 Available online 12 May 2016 JEL Classification: D4 L1 G2 Keywords: Licensing Monop olistic comp etition Patent p o ol Royalty Technology standard Vertical control

a b s t r a c t I examine the optimal licensing strategy of the owner of a proprietary technology standard in a monopolistically competitive industry. The standard owner can be either an outsider inventor or a joint venture of downstream firms. I find that (1) a simple revenue royalty replicates the integrated monopoly outcome; (2) a patent p o ol cannot do better than adopting a non-discriminatory licensing policy that offers higher royalty rates to p o ol memb ers than to nonmembers; (3) if the standard owner also sells a complementary go o d, then it may choose a decentralized marketplace as a commitment not to maximize licensing revenue. Implications to the use of RAND pricing in standard settings are discussed. © 2016 Elsevier B.V. All rights reserved.

1. Introduction The last half century witnessed the growing importance of technology standards. Numerous industries rely on technology standards to deliver consumers a diverse yet ✩ This paper was previously circulated under the title “How to license a technology standard”. I am grateful to Tony Creane, Joshua Gans, Michael Waldman, seminar participants at the 2011 International Industrial Organization Conference, the 2011 Midwest Theory Conference, the 2012 ALEA Annual Meeting, the 2013 China Meeting of the Econometric Society, the 2013 REER Conference, Hunan University, Shandong University, USC – Columbia, two anonymous referees and the Editor for helpful comments and suggestions. All remaining errors are mine. ∗ Tel.: +1 8037772583. E-mail address: [email protected]

http://dx.doi.org/10.1016/j.ijindorg.2016.02.001 0167-7187/© 2016 Elsevier B.V. All rights reserved.

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compatible selection of products. Movies/music have become widely distributed and easily accessible to consumers through the development of successive generations of standard formats; the ubiquitous Microsoft Windows operating system gives users unprecedented computing power through a broad range of applications; eBay provides an e-commerce platform for millions of buyers and sellers to trade a myriad of go o ds.1 In all the above examples, a company or a partnership (henceforth, a standard owner) either owns a proprietary technology standard or controls a common platform on which other firms can develop applications. Due to its control over the technology standard, the standard owner can sell access to the standard or the platform through licensing contracts. The purpose of this paper is to examine a standard owner’s optimal licensing strategy in a monop olistically comp etitive industry.2 I consider several types of ownership, including an outsider inventor, a joint venture of downstream firms (i.e., insider inventors) such as a patent p o ol, and a standard owner (e.g., the platform) that also sells a complementary go o d. I find that either a two-part tariff containing a fixed fee and a per-unit royalty (henceforth, output royalty), or a revenue-sharing royalty (henceforth, revenue royalty), maximizes an outsider inventor’s licensing revenue, though a revenue royalty is more appealing due to its simplicity and its low information requirement: first, in the basic setting it is sufficient to use a revenue royalty alone to maximize licensing revenue without the use of another payment instrument; second, the implementation of a revenue royalty requires less information than the implementation of the two-part tariff. Furthermore, I find that both schemes replicate the integrated monopoly outcome and provide a greater product variety than royalty-free licensing. Building on these findings, I examine the optimal licensing strategy of a patent p o ol. I find that non-discriminatory licensing requires p o ol memb ers to pay higher royalty rates than nonmembers,3 for part of its licensing payment is “rebated” back when a p o ol member receives its share of the licensing revenue. Moreover, since the integrated monopoly profits can be obtained by an outsider inventor who has no incentive to discriminate, the patent p o ol can do no better than mimic an outsider inventor and adopt a nondiscriminatory licensing policy. Therefore, even in the absence of antitrust concerns, a patent p o ol may find it beneficial not to use discriminatory licensing. This also means that any use of discriminatory licensing cannot be simply attributed to the patent p o ol’s motive to monopolize the downstream market. Taken together, the above findings lend support to the US Department of Justice’s rule-of-reason approach to discriminatory licensing in patent p o ol agreements.4 1 Other familiar examples include, but are not limited to, Apple iPod and its “Made for iPod” accessories, credit card networks and merchants, and various trademark franchises. 2 Strictly speaking, a standard itself is not a property right and cannot be licensed. In this paper, I use the phrase “license a standard” as shorthand for “license the proprietary technologies that are necessary to implement a standard”. 3 Perhaps we can call it reverse-discrimination, but as shown later, reverse discrimination in nominal royalty rates is only being used to achieve parity in “real” royalty rates. 4 The finding also supports a lenient stance towards mergers between a patent p o ol memb er and a downstream producer. A case in point is the recent merger between Microsoft and Nokia, which won world-

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Maximizing licensing revenue, however, may not be the optimal strategy for a standard owner when it also sells a complementary go o d essential to the use of downstream products. Since downstream products are usually bought after initial purchases of the complementary go o d, the standard owner faces a time-consistency problem: a payment scheme that maximizes licensing revenue lowers consumers’ willingness to pay for the complementary go o d b ecause they exp ect higher downstream prices.5 In the absence of commitment power (to licensing terms), the standard owner may choose to use a decentralized marketplace as a commitment to fixed-fee licensing, as opposed to royalty-based schemes that maximize licensing revenue. Following early contributions of Kamien and Tauman (1984;1986) and Katz and Shapiro (1985;1986), a large b o dy of literature has studied the optimal payment scheme in technology licensing, but it mostly deals with the licensing of process innovations.6 This omission apparently is not due to a lack of empirical relevance, as is evident from the above examples, or a lack of concern among policy makers. In fact, standard-setting b o dies require participants to license any essential patents on “reasonable and nondiscriminatory terms” (RAND) before adopting any standards, and there is an ongoing debate about how “reasonable” terms should be defined and whether antitrust authorities should enforce non-discriminatory licensing.7 The omission, however, is perhaps understandable: as a special case of vertical relationships, technology licensing, and especially the licensing of a standard, shares much in common with franchising, which has been extensively researched and has a literature of its own (see Blair and Lafontaine, 2005 for an excellent survey). Indeed, many models of franchising can be easily adapted to study issues related to technology licensing. However, due to its main focus on the retailing industry, the franchising literature has only given these issues casual treatment. This paper aims to correct this omission by examining models tailored to the specific nature of technology licensing.

wide antitrust approvals despite the fact that Microsoft holds approximately 200 patent families that are part of the technology standard necessary to build an Android smartphone, a direct competitor to Nokia phones. According to Microsoft: “It has never been our intent to change our (licensing) practices after we acquire the Nokia business, so while we disagreed with the premise that our incentives might change in the future, we were happy to discuss commitments (that the acquisition should not impact our licenses signed in the past or historical practices) on this basis.” http://blogs.microsoft.com/blog/2014/04/ 08/chinese- ministry- of- commerce- approves- microsoft- nokia- deal. 5 If the downstream market is concentrated instead, then the same timing issue can lead to a hold-up problem (Gans, 2012). He finds that revenue sharing, rather than fixed fees, can resolve the hold-up problem. 6 There are a few exceptions: Kamien et al. (1988) consider the licensing of a new product; Lemarié (2005) focuses on the licensing of a demand-enhancing innovation; Stamatopoulos and Tauman (2008) study the licensing of quality-improving innovations. In a recent paper, Ménière and Parlane (2010) consider licensing of complementary patents underlying a technology standard. Their main concern is on whether problems such as royalty-stacking can be overcome via the use of fixed fees, but they do not consider the licensing strategy of patent p o ols, nor do they address RAND pricing. 7 In 2002, the U.S. Department of Justice and the U.S. Federal Trade Commission conducted a series of Hearings, entitled “Competition and Intellectual Property Law and Policy in the Knowledge-Based Economy”, to examine the Agencies’ approach toward analyzing conduct involving intellectual property rights. Many of the hearings were devoted to topics such as standard licensing and patent p o ols. “Antitrust Enforcement And Intellectual Property Rights: Promoting Innovation And Competition”, U.S. Department of Justice and the Federal Trade Commission (2007).

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The present study contributes to the growing literature on patent p o ols and standard setting. This literature addresses questions on how to design a patent p o ol, including a patent owner’s decision to participate in the p o ol, the sharing rule among participants and the welfare properties of patent p o ols.8 The existing literature typically takes the licensing schemes as given, but does not address their optimality. The findings of the present study can therefore fill a gap in the literature. This paper is also related to an extensive literature known as the “leverage theory”, which centers on the question whether a firm with a monopoly in one market can leverage its market power into related markets (for a recent synthesis, see Rey and Tirole, 2007. My result that a vertically integrated standard owner can extract downstream profits via non-discriminatory licensing can be seen as another application of the “one monopoly rent” theorem (Bork, 1978; Director and Levi, 1956). Most closely related is a small but emerging literature that addresses nondiscriminatory licensing within a standard-setting context. Swanson and Baumol (2005) argue that the need for the “nondiscrimination” component of the RAND obligation principally arises from possible acts of foreclosure by a standard owner who competes in a downstream market, but not by an outsider inventor. Recognizing the difficulty of accounting for a patent holder’s own licensing fee, they propose that the “efficient component pricing rule” (ECPR) be used to determine whether a standard owner has engaged in anticompetitive discriminatory licensing. However, Geradin (2008) and Crane (2010) observe that the Swanson–Baumol proposal assumes a single patent holder as the standard owner, but in reality standards are typically owned by patent p o ols that have multiple members and a multiplicity of licensing fees can be consistent with the ECPR. Therefore, the Swanson–Baumol proposal may be difficult to implement in practice. Layne-Farrar (2010) synthesizes existing theories of price discrimination in traditional markets and those of technology licensing outside of standard setting. Drawing lessons from these theories, she recommends a rule-of-reason approach for discriminatory licensing involving technology standards. All ab ove papers rely on informal arguments and focus on the normative aspect of RAND pricing. In contrast, this study uses a formal model and builds on the positive analysis of the optimal licensing strategy of a patent p o ol to discuss its policy implications. Finally, since this paper is at the intersection of several streams of literature, it is worthwhile to precisely delineate its scope. First of all, this paper focuses on the payment scheme, which is but one dimension of a licensing contract. Other licensing terms, including grantback clauses, partial-po ol licensing and exclusivity in patent p o ols, are also of great interest to industry practitioners and policy makers. In this regard, the present study is complementary to Lerner et al. (2007) (henceforth LST-07), which introduces a theoretical framework to analyze the licensing terms associated with patent

8 Notable contributions include, but are not limited to, Shapiro (2001), Aoki and Nagaoka (2004), Kim (2004), Lerner and Tirole (2004), Lerner and Tirole (2007), Dewatripont and Legros (2008), Schmidt (2009), Gilbert and Katz (2010) and Layne-Farrar and Lerner (2011).

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p o ols, and empirically tests a set of predictions on the use of grantbacks and independent licensing. Second, similar to LST-07, I focus on ex post licensing, i.e., licensing by the standard owner after its investment has been made and the standard has been set. Therefore, important issues related to ex ante R&D of a technology, adoption of a competing standard or formation of a patent p o ol are beyond the scope of this paper. The remaining of the paper is organized as follows: Section 2 sets up the basic model. Section 3 studies the optimal licensing strategy of an outsider inventor. Section 4 considers a patent p o ol consisting of multiple downstream firms and discusses the model’s implications to the issue of non-discrimination licensing. Section 5 examines the case in which the standard owner also sells a complementary go o d essential to the use of downstream products. Section 6 concludes. Any formal proofs omitted from the main text are contained in the appendix.

2. The basic model In this section, I introduce the basic elements of my model, including consumers’ preference and firms’ production technology. Following Spence (1976) and Dixit and Stiglitz (1977), I adopt a consumer utility function that is symmetric in the outputs of each product and has a constant elasticity of substitution (C.E.S.) between products. Products are differentiated over many characteristics. I denote by n the number of different products, i the index of available products, xi the output and pi the price of product i. When the number of products n is greater, the greater is “product variety”. All consumers are assumed to be identical and have an income of I. A representative consumer’s β/ρ  n utility function is U = x0 + α 0 xρi di , where x0 is the consumption of a competitively supplied numeraire go o d, α > 0 and 0 < β < ρ ≤ 1.9 The constant elasticity of substitution between any two products is 1/(1 − ρ) > 1. Following Spence (1976) and Perry and Groff (1985), I assume that the downstream industry is characterized by what Koenker and Perry (1981) calls “perfect” monopolistic competition. Under this assumpn ρ ∂ tion, ∂x xi di = 0 in the symmetric solution. 0 i As in standard models of monop olistic comp etition, I assume that each product is produced by one and only one firm, so there is a one-to-one correspondence between products and firms. All the products are produced at a constant marginal cost of c, and each variety of products is developed at a fixed cost of F. Under free entry, F represents the entry cost. To maintain symmetry among the firms, I assume that each faces the same cost function, that is, c and F are the same across firms. In order to guarantee finite entry, both c and F are assumed to be strictly positive. At the same time, F is assumed to be so small that n is sufficiently large and that i can be treated as a continuous variable.10 9 These are standard parameter restrictions in C.E.S. models. In particular, β < ρ implies a diminishing marginal utility for each go o d as a function of the quantity of the composite good. 10 Even when firms’ entry costs increase as a result of a fixed licensing fee, our assumption of a large n is justified because the optimal fixed licensing fee f∗ is proportional to F, as shown below.

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Fig. 1. A monopolistic competition model of technology licensing.

The standard owner licenses the technology standard to firms either by a fixed fee, an output royalty, a revenue royalty, or any linear combination of the three. Without loss of generality, the standard owner can be seen as choosing a three-part tariff T = f + xr + spx, where f is the fixed fee, r is the rate of output royalty and s is the rate of revenue royalty. Players make moves in the following order: 1. The standard owner announces the licensing payment scheme, represented by a triplet (f, r, s), and makes a take-it-or-leave-it offer to every firm (see Fig. 1); 2. Firms simultaneously and independently decide whether to accept the offer and become a licensee. Only licensees enter the market. Each of them incurs a total cost of F + f; 3. The firms that enter set prices to compete and the representative consumer decides how much to purchase from each firm; 4. Firms make royalty payments, if any, to the standard owner. The solution concept is the subgame-perfect equilibrium. The equilibrium as a function of the payment scheme set by the standard owner is characterized by a triplet (x, p, n), where n represents the number of licensees as well as the number of downstream products available to the consumer. In the remainder of the paper, for notational simplicity, the subscript i is suppressed when it is unambiguous. In addition, if a licensing scheme uses only one of the instruments, instead of a multi-part tariff, then I use FF to denote a fixed fee scheme, OR an output royalty, and RR a revenue royalty. 2.1. Discussion of assumptions It is perhaps worthwhile to explain in more detail the modeling choice of my paper with regard to the product market competition. In models of technology licensing involving process innovations, it is typically assumed that licensees compete in a homogeneous product market.11 However, these models are ill-suited for studying the licensing 11 Notable exceptions include Muto (1993), Poddar and Sinha (2004), Hernandez-Murillo and Llobet (2006), but none of these papers considers issues related to technology standard such as product variety.

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of technology standards. First, the optimal licensing strategy is trivial in a market of homogeneous producers: the standard owner always grants an exclusive license in order to obtain the monopoly profit.12 More importantly, the nature of standard setting means that different products work together through a common specification. The very reason why a standard is adopted is that consumers value the variety of products brought out by their interoperability; any mo del of homogeneous go o ds will fail to capture this essential feature of technology standards. The same is true for some models of product differentiation such as spatial models and random choice models, in which a consumer is typically assumed to patronize only one producer. In contrast, the C.E.S. model embeds a consumer’s preference for variety into her utility function. This means that a wide diffusion of technology standards, as observed in the real world, can naturally arise in the model. The modeling choice of downstream competition among potential licensees makes this paper closely related to several studies in the vertical control literature. Perry and Groff (1985) also use the C.E.S. monopolistic competition model to characterize downstream competition, but their main focus is on the welfare properties of vertical integration. While they obtain a result identical to mine in which a two-part tariff replicates the integrated monopoly outcome, they do not consider revenue royalty.13 Schmidt, (1994) considers revenue royalty for a franchiser who offers an intangible trademark and finds that revenue royalty, rather than profit royalty, can curtail intrabrand competition and maximize franchising revenue. In his paper, a consumer buys from only one of the firms differentiated by their geographic locations, so the issue of product variety is a moot point. Last but not least, neither of the above-mentioned papers addresses the many issues arising from the specific context of technology standards, which is the focus of the present paper. Another common method of licensing, but not considered in this paper, is the auction method. It has been shown that auction is more profitable than fixed-fee licensing for a cost-reducing innovation (Kamien and Tauman, 1986; Katz and Shapiro, 1986), because the opportunity cost of being a licensee is lower under an auction than under fixed-fee licensing so one has a greater willingness to pay for a license in an auction. In my model, however, the opportunity costs are the same under both schemes, since the technology standard is an essential input, without which a firm cannot compete. Therefore, auction has no advantage over fixed-fee and there is no loss of generality from limiting our attention to the combination of fixed fees and royalties. Last, since the results below may also apply to the pricing of intangible properties other than technology standards, it is important to clarify the essential elements of the model in order to see its applicability as well as its limitation: first, the model requires 12 Since technology standard is an essential input, without which a firm cannot compete, it is analogous to a “drastic innovation”, for which fixed-fee exclusive licensing is optimal (Kamien and Tauman, 1986). 13 This is not a loss in their model: since there is a positive variable cost for the production of the intermediate input in their model, the optimal contracts require at least two instruments even when revenue royalty is used, as shown in the online appendix (Section B.2) of this paper.

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the licenses to be essential inputs for potential licensees; second, a licensee needs only one unit of the input, which has a zero variable cost to supply; third, consumers value variety and make purchases from multiple licensees. Examples given in the introduction all contain these elements. 3. Optimal licensing strategy by an outsider inventor In this section, I consider an outsider inventor as the standard owner. More specifically, the standard owner is a non-practicing entity or a R&D specialist that only licenses the technology standard to downstream firms, but does not engage in downstream production itself. In this setting, it is natural to focus on an equilibrium in which all licensees are offered the same licensing term by the standard owner.14 The main issue here is the impact of different licensing environments on profitability, welfare and product variety. 3.1. Equilibrium under free entry The consumer’s optimality condition for choice of xi yields (equating MRS across go o ds)  pi = αβX β−ρ xρ−1 , where X = i

n

0

1/ρ xρi di

.

(1)

Given the inverse demand function (1), licensee i solves max (1 − s)pi xi − (c + r )xi , xi

(2)

and the first-order condition is (1 − s)ραβX β−ρ xρ−1 − (c + r ) = 0. i

(3)

Plugging (1) into (3) and taking into account symmetry between licensees, we find the downstream prices: pi = p =

(c + r ) , for all i. (1 − s)ρ

(4)

This means that a licensee’s profit π equals x(c + r )(1 − ρ)/ρ. Under free entry, π = F + f. Therefore, xi = x =

ρ F +f , 1−ρ c+r

(5)

14 This assumption will be further justified when we compare the equilibrium outcome with the integrated monopoly outcome in Section 3.1.2.

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n +f n and x0 = I − 0 xi pi di = I − F1−s 1−ρ . Substituting (4) and (5) into (1), we obtain that +r αβnβ/ρ−1 xβ−1 = (1c−s . Solving, we find the equilibrium number of licensees: )ρ 



c+r n = (1 − s)αβ ρ

β 

F +f 1−ρ

−ρ 1−β ρ−β

.

(6)

3.1.1. Revenue royalty maximizes licensing revenue The standard owner must maximize its licensing revenue subject to the monopolistically competitive equilibrium in the downstream stage of the industry. Its total revenue is R = nT = n(f + xr + spx). Hence, 

−ρ  β  1−β ρ−β  c+r F +f ρ F +f 1 F +f R = (1 − s)αβ r+s f+ ρ 1−ρ 1−ρ c+r 1−s 1−ρ β

   ρ  1−ρ β−ρ  ρ c+r F +f f s r = A(1 − s) ρ−β +ρ + (1 − ρ) , ρ 1−ρ F +f c+r 1−s



(7) where A = A(α, β, ρ) > 0. Differentiating R with respect to f, r, and s, respectively, we obtain a set of first-order conditions:   r ρ s 1 (F + f ) 1 + + 1−ρc+r 1−s1−ρ   ρ(1 − β) ρ F +f s F +f = r+ (8) f+ , ρ−β 1−ρ c+r 1−s 1−ρ   ρ F +f ρβ ρ F +f s F +f c= r+ (9) f+ , 1−ρ c+r ρ−β 1−ρ c+r 1−s 1−ρ   1 F +f ρ ρ F +f s F +f = r+ (10) f+ . 1−s 1−ρ ρ−β 1−ρ c+r 1−s 1−ρ Since (8) + (9) = (10), there are only two independent equations, implying that the optimal licensing strategy can be implemented by a combination of at most two instruments. Solving (9) and (10), we get s = 1 − β(cρc+r) . Plugging it back into (9),   +r ) 1− β(cρc ρ F +f ρβ ρ F +f F +f we find 1−ρ c+r c − ρ−β f + 1−ρ c+r r + β(c+r) 1−ρ = (f c − rF ) (c+rβρ )(β−ρ) = 0, i.e., ρc

ρ r c ∗ and = . Consider a two-part tariff in which s = 0 , we obtain f = F − 1 f F β

r ∗ = c βρ − 1 . Both increase with ρ, the elasticity of substitution.15 Alternatively, consider a tariff in which r = 0; from (8) and (10), we obtain f = 0 and s∗ = 1 − β/ρ.16 It ∂2 ∗ is easy to verify that ∂s 2 R(0, 0, s) ≤ 0 at s . Therefore, we can conclude that It is tedious but not difficult to verify that the Hessian is negative semi-definite at (f∗ , r∗ ). Very few papers examine the determinants of royalty rates. Among them, Becker and Lu (2009) find that royalty rates are positively correlated with price markups. My result is consistent with their finding. 15

16

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Proposition 1. If the standard owner is an outsider inventor, then it can maximize its licensing revenue by using either of the two schemes: (i) a two-part tariff T T = f ∗ + r ∗ x, where f ∗ = F (ρ/β − 1) and r ∗ = c(ρ/β − 1); or (ii) a pure revenue royalty RR = s∗ px, where s∗ = 1 − β/ρ. Under the above two schemes, TT or RR, the equilibrium outcome is the same and is characterized by a triplet (x∗ , p∗ , n∗ ), where ρ F , 1−ρ c c p∗ = , β

x∗ =



αβ 2 n = ρ ∗

−ρ  β  1−β ρ−β F c . ρ 1−ρ

(11) (12)

(13)

3.1.2. Comparison with vertical integration To see the intuition b ehind Proposition 1, it is instructive to compare the market outcome resulting from the optimal tariff and the integrated monopoly outcome. An integrated monopolist’s profit is the industry revenue minus the total fixed costs of entry: max (p − c)xn − nF, where p = αβnβ/ρ−1 xβ−1 . n,x

(14)

ρ F Solving the monopolist’s problem, we get x = 1−ρ p = βc and n = c, −ρ   β

1−β ρ−β αβ 2 c F . Comparing these solutions to (11)−(13), we can see that ρ ρ 1−ρ

both TT and RR lead to the same number of firms, output p er firm, and price as the integrated solution.17 It is not surprising that a two-part tariff can replicate the integrated monopoly outcome, since a symmetric equilibrium can be completely characterized by two variables, the size of the industry, n, and the price level, p. The fixed fee and the output royalty provide the two degrees of freedom necessary to replicate the integrated monopoly outcome. Interestingly, a pure revenue royalty can also replicate the integrated monopoly outcome.18 While both licensing schemes are revenue-equivalent, a pure revenue royalty’s simplicity and low information requirement make it a more appealing one:19 in order to 17 Perry and Groff (1985) discuss several vertical control mechanisms that can attain the integrated outcome that maximizes profits for an upstream monopolist, but all of them require at least one of the payment instruments along with some vertical restriction, such as resale price maintenance or quantity forcing. 18 The generality of this result remains an open question and awaits further research. A recent paper by Shy and Wang (2011) finds that a pure revenue royalty is more profitable than a pure output royalty in a model of Cournot competition and they use this observation to explain why credit card networks adopt proportional fees rather than fixed per-transaction fees. Boohaker and Miao (2012) extend their model to incorporate free entry and find that the same result holds for all downward-sloping demand functions, but that the integrated monopoly outcome can be replicated by a revenue royalty only if the entry cost is zero. 19 The result appears to be consistent with the finding of Bousquet et al. (1998) that revenue royalties are important in practice, particularly in hi-tech industries. According to their estimate, over 90% of the royalty contracts offered by CNET (the research center of France Telecom) specifies a revenue royalty.

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use the two-part tariff, the standard owner needs to learn not only consumers’ preference parameters, but also licensees’ costs, whereas only the former is needed for the revenue royalty. 3.2. Welfare Next I consider the welfare properties of the above equilibrium. The representaβ/ρ  n n (F + f ) tive consumer’s indirect utility is V = I − 0 xi pi di + α 0 xρi di = I − (1n−s )(1−ρ) +

β ρ F +f α n1/ρ 1−ρ . Plugging (6) in, we can simplify and rewrite V as c+r 



c+r I + α(1 − β) (1 − s)αβ ρ

ρ 

F +f 1−ρ

−β 1−ρ ρ−β

(15)

The social surplus W = V + R. Substituting (7) and (15) into W and simplifying, we get 

−β ρ  1−ρ ρ−β c+r F +f W = I +α (1 − s)β ρ 1−ρ    1−ρ ρ × 1 + (1 − s)β f +r −1 . F +f c+r ρ ρ−β



(16)

From (16), it is easy to verify that social surplus decreases with f, r or s and is maximized at (0, 0, 0), i.e., the rates chosen by a profit-maximizing standard owner result in lower social welfare, relative to the first-best. This is not surprising, since a positive royalty increases the marginal cost of a licensee who in turn raises its price while a fixed fee increases the entry cost of licensees thereby reducing product variety. 3.2.1. Comparison with royalty-free licensing Although completely free licensing achieves the first-best, it provides no R&D incentive and is thus clearly impractical. More often discussed among industry practitioners and government regulators is the so-called “royalty-free licensing”, i.e., fixed-fee licensing.20 Several standard-setting organizations require patent holders to commit to royalty-free licensing before incorporating the patent into a standard and there are debates on whether 20 The term “royalty-free licensing” is sometimes loosely used to refer to free licensing (e.g., W3C RoyaltyFree (RF) Licensing Requirements at http://www.w3.org/Consortium/Patent- Policy- 20040205/), but it is generally not the same. Typically, royalty-free licensing requires a licensee to pay upfront a one-time fee that does not depend on either output or revenue (“What does ‘Royalty Free’ mean?”, Alex Wild, Scientific American, January 10, 2012 ). For example, AP Images, a division of The Associated Press, stipulates that “A limited amount of the Content may be ‘royalty free’ material that is licensed for an unlimited number of uses for a one-time flat fee.”, http://www.apimages.com/uns/splash/default.aspx?url=legal/licenseterms. html; in a recent case involving the ubiquitous “Ethernet” computer networking standard, the Federal Trade Commission requires a patent licensing company to offer royalty-free licenses for a one-time fee. “In the Matter of Negotiated Data Solutions LLC.” FTC File No. 051 0094.

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royalty-free licensing is the best means for technology dissemination and limiting opportunistic behavior of patent holders.21 At the same time, fixed-fee licensing is also of interest from the positive perspective. In order for the standard owner to use either a two-part tariff or a revenue royalty, it must monitor licensees’ output levels. In cases where the monitoring effort is too costly, licensing contracts with royalties are not enforceable, leaving fixed-fee licensing the only option. Below I compare the equilibrium properties of fixed-fee licensing with those of the optimal licensing strategy, i.e., revenue royalty. Proposition 2. (i) Fixed-fee licensing is less profitable than revenue royalty for the standard owner, (ii) social welfare is higher under fixed-fee licensing than under revenue royalty, (iii) consumer welfare under fixed-fee licensing is higher under revenue royalty. Proof. In the appendix.



Similarly, we can show that analogous results hold when comparing output royalty and revenue royalty: ROR < RRR , WOR > WRR , VOR > VRR . In sum, both consumer surplus and social welfare from a revenue royalty are lower than those from either fixedfee licensing or output royalty. This means that a requirement of royalty-free licensing can potentially raise social welfare and benefit consumers. It should be noted, however, that this result addresses only static efficiency but not dynamic efficiency.22 A recurring theme in antitrust regulation is that a policy that promotes static efficiency may be detrimental to dynamic efficiency, and therefore, the above result should not be seen as an endorsement of the royalty-free licensing rule. In fact, the following result shows that royalty-free licensing is not an effective means to promote technology diffusion: Proposition 3. Among licensing schemes based on a single instrument, the number of varieties offered to consumers is lowest under fixed-fee licensing and highest under output royalty, i.e., nFF < nRR < nOR .23 Proof. In the appendix.



Interestingly, Proposition 3 predicts that imposing a royalty-free licensing requirement could narrow, not widen, technology diffusion, relative to what is obtained under royaltybased licensing schemes.24 The reason is not difficult to understand: without a royalty, 21 “Competition Concerns When Patents Are Incorporated Into Collaboratively Set Standards”, Chapter 2, Antitrust Enforcement And Intellectual Property Rights: Promoting Innovation And Competition, U.S. Department of Justice and the Federal Trade Commission (2007). 22 In the realm of intellectual prop erty p olicies, static efficiency is concerned with the welfare cost of ex p ost monop oly pricing distortions, whereas dynamic efficiency refers to the welfare b enefit of creating ex ante R&D incentives to develop better technologies (Segal and Whinston, 2007). 23 I am grateful to an anonymous referee for suggesting this analysis. 24 It should be noted, however, that the output of each product incorporating the technology is greater, i.e., xFF > xRR .

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the standard owner tries to extract licensing revenue by increasing the fixed fee, thus raising the entry cost and reducing product variety. 3.3. Extensions Before concluding this section, I consider two minor variants of the basic model and show that revenue royalty-based payment schemes can be easily adapted to implement the optimal licensing policy in a variety of standard-related environments. 3.3.1. Exogenous entry In the basic model, I assume free entry. But in some industries, there may be a limited number of entry, which restricts the number of p otential licensees. To complete the analysis, here I investigate this possibility. Clearly, we are only interested in the case where the number of licensees is constrained by the limited entry. In other words, I consider the case where n is fixed and n < n∗ . Since n is fixed, entry is no longer an issue, it is without loss of generality to set F = 0. Proposition 4. If n is fixed and n < n∗ , then the standard owner’s licensing revenue is maximized by a two-part tariff that contains a fixed fee and either an output royalty or a revenue royalty; the optimal royalty rates are the same as in Proposition 1; the two schemes replicate the integrated monopoly outcome. Proof. In the appendix.



The result contained in Proposition 4 is in line with the finding of Hernandez-Murillo and Llobet (2006) that a two-part tariff containing a fixed fee and either an output royalty or a revenue royalty implements the optimal allocation in a model of licensing a cost-reducing innovation to monopolistic competitors.25 The intuition behind the result is straightforward: the royalty part of the tariff can be used to regulate the downstream price, while the fixed-fee part allows the standard owner to extract the remaining producer surplus. 3.3.2. Cost of technology licensing The basic model also assumes that technology licensing is costless. Here I relax this assumption by assuming that it costs the standard owner t for every additional license, though the interpretation of the cost varies with industries. For example, an iPhone App (and its updates) has first to be approved by Apple before it is available in the iTunes online store and we can think of t as the cost of examining and approving an App. 25 Since Hernandez-Murillo and Llobet (2006) consider only the case of exogenous entry, revenue royalty and output royalty are completely equivalent in their model and the former offers no advantage. Their main contribution is to show that the optimal licensing contract serves two purposes: separation of heterogeneous licensees and regulating the degree of competition in the downstream market.

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Proposition 5. If the cost of technology licensing is t, then the standard owner’s licensing revenue is maximized by a fixed fee and a revenue royalty, where f = t and s = s∗ . Proof. In the appendix.



The above licensing scheme appears consistent with that of the Apple iTunes Store, which charges App develop ers a fixed fee of $99 p er year plus 30% of the sales revenue.26 4. Optimal licensing Strategy by a p o ol of downstream firms As Katz and Shapiro (1986) point out, when analyzing licensing, it is important to distinguish two basic patterns of patent ownership, both of which arise in practice. The first pattern is that of an outsider inventor who has no financial interest in the downstream firms; the second pattern is that of licensing entity owned by one or more of the downstream firms. The second one is particularly relevant to the licensing of technology standards, which often build on a number of innovations made by firms active in the downstream markets. In order to facilitate adoption of the standards, owners of complementary patents often form patent p o ols that license their patents in a single package and divide up the proceeds. At the same time, a number of authors have shown that the optimal licensing strategy can be quite different, depending on whether the licensor itself is involved in downstream competition. First put forward by Shapiro (1985) and later confirmed by Wang (1998) and Kamien and Tauman (2002), it has been shown that royalty is superior to fixed fee for an insider inventor of a cost-reducing innovation in a duopoly, whereas the opposite is true for an outsider inventor.27 The reason is that licensing the innovation through a royalty raises a rival’s cost, thereby accomplishing the patent holder’s two objectives at once: a low rent for the rival and a high price for consumers. The result established in these papers implies that the optimal licensing policy of an insider inventor is necessarily discriminatory: the patent holder uses the innovation for free, while other licensees must pay royalties to use. In contrast, in this paper, although I cannot rule out discriminatory licensing policies as optimal, I find that a patent p o ol cannot do better than adopting a “non-discriminatory” licensing policy under which p o ol memb ers pay higher royalty rates than nonmembers.28 Consider the following mo del. Suppose that downstream firms have the same production technology and the same free entry condition as in the basic model, but the standard is owned by some of the downstream firms, who form a patent p o ol that licenses to both 26

Source: iOS Developer Program, http://developer.apple.com/programs/ios/distribute.html. Sen and Tauman (2007) point out that while pure output royalty is still optimal when there are two firms other than an incumbent inventor, a two-part tariff is optimal for larger industries. 28 Schmidt (2009) studies the welfare effects of vertical integration when a technology standard is based on several patents owned by different firms. His mo del incorp orates a more general downstream market, but he takes the licensing scheme as given and interprets integration simply as the right to free licensing. 27

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members and nonmembers.29 Let the member firms be indexed by j, where j = 1, 2, . . . , m and 2 ≤ m < n∗ .30 I assume that a member firm receives a share of the total licensing revenue, i.e., Rj = σj R, where Rj is the licensing revenue received by member firm j, σ j is the share of firm j and R is the total licensing revenue collected by the patent p o ol. Hence, m  j=1

σj = 1 and

m 

Rj = R.

(17)

j=1

The allocation of licensing revenue among pool members is pre-determined, possibly based on some exogenously specified sharing rule.31 In other words, σ j is taken as given in the present model. I further assume that efficient bargaining ensures that p o ol members share a common objective of maximizing the sum of their profits earned in the downstream market and the licensing revenue collected from all downstream firms. The patent p o ol can use any mechanism of the form (f, r, s), like the outsider inventor, but that the patent p o ol can elect to give its members special treatment (e.g., free licenses) if it so desires. 4.1. Main result Upon first glance, the patent pool’s problem appears rather complicated, because asymmetry has to be taken into account when we consider downstream competition. Hence, the standard solution method for a symmetric equilibrium no longer applies. Indeed, given the degree of freedom offered to the patent p o ol in terms of the licensing scheme and the inherent difficulty with asymmetric firms, a full characterization of the optimal licensing scheme appears beyond reach. Fortunately, a full solution may be unnecessary: since the best outcome possible for the patent pool is the integrated monopoly outcome, the p o ol can do no b etter than simply replicate it. There are at least two ways of doing this, according to the following proposition: Proposition 6. A patent pool can maximize its total profits by either (i) offering a revenue royalty and setting sj = s∗ /(1 − σj ) for pool members and s = s∗ for nonmembers; or (ii) spinning off a financially independent patent-holding company, which licenses the 29 Strictly speaking, patent pools do not own the standard; instead, a pool is a contractual agreement among member firms to provide a sp ecific typ e of license to use a bundle of patents and to redistribute the royalty revenue. In other words, p o ol memb ers own the patented technologies that are necessary to implement a standard issued by the standard setting organization (SSO). 30 If n∗ ≤ m, then there will no licensing to non-p o ol memb ers so the issue of nondiscriminatory licensing becomes a moot point. 31 While many patent p o ols employ numeric proportionality rules (Layne-Farrar and Lerner, 2011), where p o ol memb ers are paid royalties on the basis of the number of patents contributed, Layne-Farrar et al. (2007) propose that patents covering “essential” technologies with a greater contribution to the value of the standard and without close substitutes before the standard gets adopted should receive higher royalty payments after the adoption of the standard. Since σ j is an exogenous variable in the model, my result does not vary with the sharing rule used by the p o ol.

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standard via a revenue royalty s = s∗ to all licensees and keeps all licensing revenue as its profits.

Pro of. (i) A p o ol memb er’s p ost-entry profit has two parts: one is the profit from its downstream product and the other is from its share of the licensing revenue, both of which are only realized after downstream sales take place. Thus, given the inverse demand function (1), a p o ol memb er solves   max [(1 − sj )pj − c]xj + σj 

xj



n

si pi xi di

n

1(i = j)si pi xi di + max [(1 − sj + σj sj )pj xj − cxj ]

= σj 0

(18)

0

xj

(19)

Comparing (19) to (2), we can see that the maximization problem of a p o ol memb er is identical to that of an independent downstream firm if 1 − sj + σj sj = 1 − s∗ , i.e., sj = s∗ /(1 − σj ). At the same time, the maximization problem of a nonmember is identical to that of an independent downstream firm. This means that the downstream quantity/price pair (x, p) resulting from (sj , s∗ ) replicates an outsider inventor’s choice, characterized by Proposition 1. In addition, it is easy to verify that the post-entry benefit of participating in downstream competition for a pool member is F. (Note that the incremental benefit of participating in downstream competition for a pool member exceeds its downstream profit because of the gain in additional licensing revenue.) Therefore, (sj , s∗ ) also yields the same number of downstream products as in (6). Since (x, p, n) uniquely determines the equilibrium, we can conclude that (sj , s∗ ) allows the patent p o ol to replicate the equilibrium chosen by an outsider inventor, which in turn replicates the integrated monopoly outcome. (ii) is obvious. 

Proposition 6 shows that a patent p o ol cannot do better than adopting a nondiscriminatory licensing policy that offers higher royalty rates to pool members than to nonmembers. Furthermore, a member firm’s royalty rate increases with its revenue share in the patent p o ol. While the juxtaposition of the two words “nondiscriminatory” and “higher” may appear confusing upon first glance, the intuition underlying Proposition 6 can be illustrated with a very simple numerical example. Suppose that a p o ol memb er’s revenue share is 50%, then for every dollar of its royalty payment, it will receive half a dollar back. This means the “real” royalty rate, i.e., the increase in marginal cost, is only half of the “nominal” rate that it has to pay. Thus, in order to replicate the integrated monopoly outcome, in which all downstream firms have the same effective marginal cost, the member firm’s “nominal” royalty rate needs to be twice that of a nonmember. More generally, a pool member’s “real” royalty rate sj = sj − σj sj is

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always smaller than the “nominal” royalty rate sj . Therefore, it must pay a higher royalty rate in order for its marginal cost to equal that of a nonmember.32 4.2. Robustness It is not difficult to see that the patent p o ol’s optimal licensing strategy can also be implemented via a two-part tariff containing a fixed fee and an output royalty as in Proposition 1. In addition, if entry is exogenous (i.e., n is fixed), then an analogous result, but based on Proposition 4, applies. In particular, if the patent p o ol uses an output royalty-based two-part tariff, then the “real” output royalty rate for a p o ol memb er equals rj = (1 − σj )rj , where rj is the “nominal” rate. This means that the optimal rate for a

p o ol memb er has to b e rj = r ∗ /(1 − σj ) > r ∗ , where r ∗ = c βρ − 1 is the rate for a nonmember. One caveat for part (i) of Proposition 6 is that its implementation requires at least two members for the patent p o ol, i.e., m ≥ 2. This is because with a single patentee σj = 1 and thus its “real” royalty rate is always zero regardless of the “nominal” royalty rate.33 Thus, for the case of a single patentee, the approach described in part (ii) is more suitable.34 In this approach, the parent company (the patentee) either spins off its technology licensing business and transfers its intellectual properties to the spunoff company, or, equivalently, sells off its production arm. Either way results in two independent companies, one sp ecializing in patent licensing and the other specializing in downstream production. Original shareholders of the parent company receive their return on investment in the form of either a special dividend or stocks of the spun-off company. Examples of this approach are abundant.35 Another caveat is that the above results are obtained under the assumption of complete symmetry among downstream firms. Admittedly unrealistic, it nevertheless serves as a useful starting point for further exploration, especially on issues involving nondiscriminatory licensing, since results under complete symmetry are the cleanest and easiest to interpret. In a recent paper, Crane (2010) laments that “Given the importance of the RAND commitment as an antitrust fix to the SSO-patent p o oling problem, it is surprising that there has not been more attention given to the meaning of the nondiscrimination prong. If RAND commitments are to be a successful fix, the ‘nondiscrimination’ prong will need to b e b etter understoo d and articulated.” Below, I will argue that the above analysis provides us some valuable lessons on understanding the issue of

32 Note that a higher rate itself will not discourage a firm from joining the p o ol, since only memb ers of the p o ol can share the licensing revenue. 33 The same observation has also been made by Swanson and Baumol (2005) and Crane (2010). 34 Similarly, if σ j is sufficiently large, then the revenue royalty rate sj given by Proposition 6 may be greater than 1, which is unusual in practice. I am grateful to an anonymous referee for this observation. 35 “AudioFAX Strikes License Deal With Cisco for AudioFAX Fax Technology”, PR Newswire, Jun 19, 2002; “PDL BioPharma to Spin Off, List Biotechnology Unit”, Beth Jinks, Bloomberg,Apr 10, 2008; “uWink Completes Spin-Off Transaction”, Business Wire, Mar 4, 2009; “Aware Announces Plans to Spin-Off Patent Licensing Operations”, PR Newswire, Sept. 24, 2010.

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non-discriminatory licensing. A last point to make is that Proposition 6 does not rule out the use of other licensing schemes, such as royalty-free cross-licensing or “equal-rate” licensing, in which all firms pay the same royalty rate. In fact, “equal-rate” policies are more widely used in practice than the one proposed here Serafino (2007). The likely cause is the existence of transaction costs, which are not modeled in this paper but whose effects are quite obvious, as the “equal-rate” rule is easier to implement and verify, thereby lowering transaction costs. Another possible cause is the so-called “sales leakage”, namely, sales revenue reported by a licensee is lower than the actual sales, which reduces the effective royalty rate, among other effects Horn and Zisk (1993), Yuan and Krishna (2008). If the leakage is more severe for nonmembers than for members, who usually get closer scrutiny, then an “equal-rate” policy will imply higher rates for members, approximating the policy shown in Proposition 6.36

4.3. Non-discriminatory licensing Lessons from Proposition 6 are two-fold. First, equating non-discriminatory licensing to equal royalty rates is misleading.37 Since part of the royalty payment is “rebated” back to the p o ol memb ers, the “real” royalty rate for a p o ol memb er can b e quite different from the “nominal” royalty rate written in the licensing agreements.38 Paying the same “nominal” royalty rate still confers p o ol memb ers a distinct cost advantage over nonmembers and can potentially have the effect of foreclosing competition. For an antitrust authority or a standard-setting organization to simply stipulate non-discriminatory licensing without precisely defining its meaning is an open invitation for confusion and controversy.39 Second, a major concern of proponents of non-discriminatory licensing is that patent p o ol memb ers may receive favorable licensing terms, e.g., a lower royalty rate, thus

36 According to Blum (2010), licensees routinely underpay the licensors by 20–30%. Some disputes are resolved via lawsuits. “Philips accuses Taiwan optical disc maker Lead Data of royalty underpayment”, DigiTimes, Dec.26, 2008. 37 Other commentators have expressed a similar view. Gilbert (2011) argues that “It is artificial and counterpro ductive to imp ose a definition of non-discrimination that requires identical licensing terms for every licensee.” According to Brooks and Geradin (2011), the majority of the Special Committee members of the European Telecommunications Standards Institute agrees that non-discriminatory “does not necessarily imply identical terms”. 38 In a model that analyzes the impact of vertical integration among patent p o ol memb ers, Kim (2004) makes the same observation, but he assumes that “nominal” royalty rates are set to be equal. 39 In a recently published communication from the European Commission (“Guidelines on the Applicability of Art 101 of the Treaty on the Functioning of the European Union to horizontal co-operation agreements”, OJ C 11, Jan. 14, 2011.), the language of non-discriminatory licensing is repeatedly used, but its precise definition is never given.

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disadvantaging nonmembers and in some cases leading to market foreclosure.40 For example, Swanson and Baumol (2005) suggest that:41 While discrimination in license fees is a valid concern, for intellectual property: those instances when the owner of the IP uses it as an input in a downstream market where competitors also require the IP for the same purpose. A licensor exercising bottleneck market power that discriminates in licensing in order to handicap its competitors and favor its own downstream sales can create or enhance market power in downstream markets for standard-compliant products and services. While the above concern is certainly valid, my model cautions against overreaction, for a patent p o ol gains nothing from adopting a discriminatory policy against downstream competitors. In the present model, exactly the opposite occurs: a profit-maximizing patent p o ol not only has an incentive to offer nonmembers the same royalty rate, but also goes as far as making sure it is the “real” royalty rate to equalize.42 The reason has been clear to many commentators: a patent p o ol as the standard owner has an incentive to grow the market, not to use a high royalty rate to kill the market.43 Although one may still argue, based on the welfare analysis above, that the royalty rates set by a patent p o ol are to o high from the society’s standpoint, at least with respect to non-discriminatory licensing, it appears that the interest of a patent p o ol is aligned with that of standard-setting organizations. Thus, if a patent p o ol does imp ose different royalty payments, its motivation cannot be solely anticompetitive.44 A blanket decree of banning discriminatory licensing can be harmful if the use of latter is based on efficiency considerations.45 40 Another form of discrimination is to give preferential treatment to early adopters of a standard Gilbert (2011), owned by either an outsider inventor or an insider, but it is usually not a source of anticompetitive concern. As Hovenkamp et al. (2001) succinctly puts it: “The only plausible anticompetitive explanation for [discriminatory licensing] is as an act of foreclosure by a vertically integrated monopolist.” 41 For another example, see “Cross-Licensing and Patent Pools”, M. Howard Morse, Prepared Testimony Before the U.S. Department of Justice Antitrust Division and Federal Trade Commission Hearings on Competition and Intellectual Property Law and Policy in the Knowledge-Based Economy, April 17, 2002. 42 It would be desirable to show how much profit is lost if the patent p o ol is restricted to nominally equal licensing fees, but it is technically challenging since the differences in real rates will create asymmetry among downstream firms, with a few patent p o ol memb ers enjoying cost advantages. 43 See, e.g., “If the licensor . . . is about to propose a royalty that’s going to kill the product they’re not going to make any money. And most of the players in this field are sophisticated enough to understand that”, Robert Blackburn,Economic Perspectives on Intellectual Property, Competition, and Innovation, Hearings on Competition and Intellectual Property Law and Policy in the Knowledge-Based Economy, Feb. 26, 2002. 44 Posner (1976) employs the same logic in his criticism of the leverage theory: “[A fatal] weakness of the leverage theory is its inability to explain why a firm with a monopoly of one product would want to monopolize complementary products as well. It may seem obvious…, but since the products are by hypothesis used in conjunction with one another…, it is not obvious at all.” 45 To date, the only case related to the nondiscriminatory aspects of licensing in standards that has been litigated is Broadcom v. Qualcomm, in which Qualcomm was accused of discriminating among licensees of the essential WCDMA technology by charging higher fees to those who did not use Qualcomm’s UMTS chipsets and was charging double royalties to UMTS cell phone manufacturers who use non-Qualcomm UMTS chipsets. Qualcomm’s licensing practice remains puzzling. The main puzzle is why Qualcomm chooses to offer a royalty discount in its CDMA licensing, instead of a lower price in its modem chips. On one hand, if its practice has no anticompetitive intent, then lowering the price of its modem chip while simultaneously eliminating the royalty discount can stop the controversy surrounding its licensing terms without materially affecting its profits; On the other hand, if its practice was indeed to throttle competition in the modem chips

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It is again worth emphasizing that the above discussion does not suggest that antitrust authorities should brush aside any concerns about patent p o ols’ discriminatory licensing practices. After all, results contained in Proposition 6 are derived in a specific model and do not necessarily extend to all economic environments. A more appropriate interpretation of the results is that they support a rule-of-reason approach, such as the one adopted by the Department of Justice:46 . The Agencies will not presume that different royalty payments faced by different licensees (e.g., insiders and outsiders) are anticompetitive. Whether such an arrangement could be anticompetitive would depend upon the specific facts of the case. Finally, it should be noted that the incentive to foreclose does exist in a model of homogenous go o ds, but it is still unclear why discriminatory licensing, instead of high rates, is the best way to exclude. It is well known that, in technology licensing, exclusivity can be implemented without discrimination (Kamien and Tauman, 1986; Katz and Shapiro, 1985). Therefore, a licensor can raise rates in order to foreclose rivals, but the question then becomes whether the rates are reasonable, but not whether they are discriminatory. In other words, even in cases where the incentive to foreclose exists, the value added by the “non-discriminatory” prong of the RAND commitment is dubious. 5. Optimal licensing strategy by a standard owner selling a complementary go o d In many examples mentioned in the introduction, the standard owner also sells directly to consumers a product that is essential to the use of downstream products.47 For example, in order to use iPhone Apps, the iPhone itself must be bought first; the same is true for Microsoft Windows and its applications. In this section, I consider the optimal licensing strategy for such standard owners and focus on its design of the marketplace. For concreteness, I use system (S) to refer to the product that the standard owner sells to consumers directly and applications to refer to the downstream products. To provide more focus, I assume that the standard owner itself does not sell applications, but it is straightforward to extend the results to the opposite case based on the analysis of the last section. I consider a two-p erio d mo del. In the first p erio d, the representative consumer has a unit demand for a system, which is only available from the standard owner; in the market, then price cutting in that very market would be a far more direct and less controversial method. The most plausible rationale appears to be that, being unable to charge different prices among chip customers, Qualcomm chooses to use a roundabout way to implement third-degree price discrimination. Yet it is unclear why its licensees have a greater elasticity of demand or a smaller willingness to pay for modem chips than non-licensees. 46 “Antitrust Analysis Of Portfolio Cross-Licensing Agreements And Patent Pools”, Chapter 3, p. 83, Antitrust Enforcement And Intellectual Property Rights: Promoting Innovation And Competition, U.S. Department of Justice and the Federal Trade Commission (2007) 47 Kende (1998) analyzes the effects of various demand parameters on a system monopolist’s decision to allow competition in the component markets. He also uses a C.E.S. model, but he does not consider the use of licensing in the component markets.

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second p erio d, the standard owner issues licenses to application developers, from which the consumer buys applications. I assume that the standard owner maximizes total profits with a discount factor of δ s ≥ 0, while a consumer maximizes total utility with a discount factor of δ b ≥ 0.48 I denote by PS the system price, VS the intrinsic value of the system for the consumer and CS the unit cost of a system. The consumer’s total discounted utility can be written as:   I − PS + (1 + δb )VS + δb α

n

0

β/ρ xρi di

 −

n

xi pi di .

0

The standard owner’s discounted sum of profits is Π = PS − CS + δs R(f, r, s). It is easy to see that the absolute sizes of VS and CS are immaterial to the analysis, so I normalize both of them to 0 in order to cut down the number of parameters of which we keep track. Thus, the consumer utility can be rewritten as I − PS + δb (V − I ), where V (as in (15) ) is the p erio d 2 indirect utility from applications. It is easy to see that the price of the system will be set such that the standard owner extracts all consumer surplus, i.e., PS = I + δb (V − I ). To complete the model, we need to consider one remaining issue: the amount that the consumer is willing to pay for the system in p erio d 1 depends on the prices as well as the variety of applications available in p erio d 2, which in turn depends on her expectation of the standard owner’s licensing strategy. To put it differently, the standard owner faces a time-consistency problem, its incentive to maximize licensing revenue in p erio d 2 will lower the price of the system in p erio d 1. Clearly, the standard owner would like to promise generous licensing terms to convince the consumer, but such a promise is not always credible.49 Therefore, I analyze two cases, depending on whether the standard owner is able to commit to future licensing terms at the time of the system purchase.50

5.1. Commitment to licensing terms is possible I first analyze the case in which a commitment from the standard owner is possible. The same analysis also applies if consumers purchase both systems and applications at the same time, or if licensing terms and the price of the platform are chosen simultaneously, for there will be no time-consistency problem in these cases.

48 Although I call δ b and δ s discount factors, it is possible for them to be greater than 1 if the flow of utilities the consumer gets from the p erio d where they own both the system and the application greatly outweighs the short p erio d where she owns only the system. 49 For instance, Apple Computer has a “Made for iPod” licensing program aimed at iPod accessories vendors who make products that connect to Apple’s iPod 17-pin Dock connector. Initially, Apple’s licensing fee was 10% of the sales revenue, but in 2006, its fee was changed to a $4 per unit royalty. “Apple Changes iPod License Fee”, David Richards, Smarthouse, October 5, 2006. 50 Elsewhere in the paper, commitment is not an issue because all consumer purchases take place after the licensing game.

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˜ = PS + δs R = I + δb (V − I ) + The standard owner’s total discounted revenue is R ˜ δs R. Plugging (7) and (15) into R, we get    (1 − ρ)f ρr s ˜ R = (1 − δb )I + δb (1 − β) + δs (1 − s)αβ + + F +f c+r 1−s β ⎡ ⎤ ρ−β ⎢ × ⎣

(1 − s)αβ ⎥

ρ

1−ρ ⎦

c+r ρ

.

(20)

F +f 1−ρ

˜ is maximized when It is easy to verify from the first-order conditions of f and r that R f f r r F = c and that any two-part tariff f + rx that satisfy F = c can be replicated by a pure revenue royalty spx, where s = c+r r = F f+f . Therefore, as long as the standard owner’s objective is to maximize licensing revenue, it will be without loss of generality to limit our attention to the use of revenue royalty. Denote by s˜ the optimal rate of revenue royalty. Proposition 7. If a commitment to licensing terms is possible, then the optimal rate of  β+(1−β)δb /δs revenue royalty s˜ = max 1 − , 0 ; (ii) s˜ decreases with δ b /δ s on the interval ρ of [0, s∗ ]; (iii) if δb = 0, then s˜ = s∗ ; (iv ) if δb = δs , then s˜ = 0. Proof. In the appendix.



Proposition 7 shows that the optimal royalty rate depends on the relative patience between the consumer and the standard owner. If consumers do not care much about what is available in the application market, then the standard owner can feel free to maximize licensing revenue, but if consumers are sufficiently patient, then the standard owner may want to commit to a low royalty rate in order to convince consumers of the value of future applications that come with the system. Last, it should be noted that the assumption that consumers do not purchase applications in p erio d 1 is without loss of generality; if the system and applications are purchased at the same time, then there is no discount, equivalent to the case of δb = δs . In such a case, the standard owner offers free licensing. This result is reminiscent of the classic one-monopoly rent argument in the aftermarket theory: if a monopolist can earn profits from two products that are complementary to each other, then it is best to set the price at marginal cost for the product whose demand is more elastic while extracting consumer surplus through the complementary product (Willig, 1978). In my model, consumers have downward-sloping demands for applications but a unit demand for the system, therefore, the standard owner has an incentive to lower the prices of applications while simultaneously raising the system price. 5.2. Gain commitment to fixed-fee licensing by setting up A decentralized marketplace Next I consider the more interesting case, in which the standard owner is unable to commit not to change licensing terms after consumers purchase the system. The first

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observation is immediate. If the standard owner is unable to commit to licensing terms, then its profit is lower than if it could commit. In this case, the standard owner’s ability to replicate the integrated monopoly outcome in the application market becomes a liability, because it lowers a consumer’s willingness to pay for the system. Therefore, paradoxically, the standard owner will have a strong incentive to lose the ability to implement the optimal licensing scheme. Since both optimal licensing strategies, TT and RR, are based on the use of some royalty, the standard owner can credibly “lose” its ability to use them if it is unable to enforce a royalty provision in the licensing agreement. One approach is to design the system such that there will be a decentralized marketplace for applications, as opposed to a centralized marketplace where the standard owner can easily track all transactions and implement royalty-based payment schemes. By making the standard owner more likely use a fixed fee to license its standard,51 a decentralized marketplace serves as a commitment not to maximize licensing revenue, thereby increasing the consumer’s willingness to pay for the system. I modify the game by assuming that in p erio d 1 the standard owner can design its system in such a way that it can commit to either a centralized or a decentralized marketplace. If a decentralized marketplace is chosen, then the standard owner can only use fixed-fee licensing; otherwise, it can also use royalty-based schemes such as revenue royalty (which maximizes licensing revenue according to Proposition 1). Proposition 8. The standard owner restricts sales of applications to a centralized marketplace if and only if δb /δs < (RRR − RF F )/(VF F − VRR ). Proof. A consumer is willing to pay I + δb (V − I ) for a system, so the present value from owning a standard is I + δb (V − I ) + δs R. This means that a centralized marketplace will be chosen if and only if δb VF F + δs RF F < δb VRR + δs RRR ,

(21)

where VFF and RFF (respectively, VRR and RRR ) are obtained when Eqs. (15) and (7) are evaluated at f = fF F , r = 0 and s = 0 (respectively, f = 0, r = 0 and s = s∗ ).  Since VFF > VRR , RFF < RRR and VF F + RF F > VRR + RRR , a necessary condition for the use of a centralized marketplace is δ b < δ s . Empirically, this is plausible because consumers typically face a higher cost of capital than businesses. Thus, Proposition 8 predicts that products targeting businesses are more likely to use a decentralized marketplace, while the reverse is true for products target regular consumers. For example, consider the different approaches adopted by Microsoft and Apple in how their 51 It should be noted that adopting a decentralized marketplace does not necessarily lead to fixed-fee licensing. The main problem associated with a licensor’s inability to track sales when using a royalty-based licensing scheme is the sales leakage mentioned above. If sales leakage is small, the standard owner may still use a royalty-based scheme, but its implementation will be constrained by the leakage and thus fail to maximize licensing revenue.

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customers can buy third-party applications. Many Microsoft Windows users are business customers whose discount factors are comparable to Microsoft’s own, while Apple products are more consumer-oriented.52 Consistent with the above prediction, a Microsoft Windows user can buy any Windows application from any vendor without going through Microsoft, but Apple iPhone owners must use its iTunes online store to install Apps, third-party applications for iPhone.53 6. Conclusion This paper introduces a unified framework that, although highly stylized, is versatile enough to lend itself to the analyses of a number of issues that are important in the literature of standard setting and technology licensing. Several useful results emerge from the analyses. First, the existing literature on the design of patent p o ols has mostly assumed fixed-fee licensing, but this paper shows that revenue royalty is a more appealing licensing strategy and therefore merits more attention from theories of patent p o ol design. Second, the paper argues that the conventional interpretation of non-discriminatory licensing as all licensees receiving the same royalty rate can be misleading, since a patent p o ol member’s royalty payment is partly “rebated” back in the form of a share of the licensing revenue; at the same time, it suggests that standard-setting organizations’ emphasis on non-discriminatory licensing may be misplaced: raising rivals’ costs via discriminatory licensing does not appear to offer benefits to members of the patent pool and it is in their own interest to adopt non-discriminatory licensing. Third, my model shows that it is important, for standard owners as well as consumers, to think about the ramifications of having a system with a centralized marketplace built in the system design. Fourth, the requirement of royalty-free licensing can possibly impede, not facilitate, technology diffusion. To further explore related issues, the model must be extended in a number of directions. The first and foremost is to incorporate network effects, which is central to the standard setting literature. While the omission of network effects does not impose significant limitation to a study of the post-adoption environment, which is the focus of this paper, it severely limits the model’s applicability when the decision to adopt is important. The current representative consumer model is ill-suited for studying network effects. Thus it may be necessary to move away from the representative consumer model in order to gain more insights into the optimal licensing strategy when one considers comp etition b etween standards. Second, one can examine how general the result that revenue royalties can replicate the integrated monopoly outcome is by incorporating more general demand, different market structures and private information. Third, 52 Although I am not aware of any academic research that estimates Apple customers’ discount factors, their eagerness to embrace every latest invention from Apple is legendary. “New Yorkers camp out for iPhone despite summer heat”, Elizabeth Montalbano, IDG News Service, Jun 26, 2007. “iWait: Apple devotees line up in Palo Alto for the iPad launch”, San Jose Mercury News, Apr 3, 2010. 53 It should be noted, however, that there may also be technological reasons for a centralized marketplace. For example, it may help prevent users from inadvertently installing malicious software programs.

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following Melitz (2003) and Hernandez-Murillo and Llobet (2006), one can introduce heterogeneity in the productivities or costs of producers and the resulting asymmetry into the monopolistic competition model and study its implication to the standard owner’s licensing strategy and the use of RAND pricing in standard settings. Last but not least, it will be important to examine how the choice of licensing schemes interacts with R&D investments, standard settings and adoption of competing standards. Many important issues including the hold-up problem, “royalty stacking”, the incentive to integrate among complementary patent holders, etc., still remain unexplored in this paper. Future research that explores these directions will be fruitful.

Appendix. Pro ofs

Pro of of Prop osition 2. If the licensing scheme is restricted to a fixed fee only, i.e., r = 0 ρ

(1−β) β−ρ

ρ ρ(1−β) ρ 1−β β−ρ ρ c β (F + f ) and s = 0, then RF F = (ρβα) ρ−β 1−ρ f ∼ (F + f ) β−ρ f.

ρ(1−β) 1−β) ∂ Hence ∂f RF F ∼ (F + f ) β−ρ 1 + ρ(β−ρ f /(F + f ) . From the first-order condition, we ρ−β obtain that fF F = F β(ρ−β 1−ρ) . Plugging r = 0, s = 0 and fF F = F β(1−ρ) , we obtain pF F = c ρ and

⎡

nF F

ρ β−1 ⎤ ρ−β  −β

c (1 − β)F ρ ⎦ = ⎣αβ . 2 ρ β(1 − ρ)

(22)

Part (i) is immediately from Proposition 1. (ii) From (16) and (22), we can get 1−ρ)   − β(ρ−β  ρ(1 − β) −ρ − β/ρ + 2β WF F = I + K F 1+β β(1 − ρ) 1−β

(23)

and   β   WRR = I + K F ρ−1 β/ρ ρ−β 1 − β 2 /ρ ,

(24)

β −ρ ρ−β β ρ β (1−ρ) ρ−β where K = α ρ−β β ρ−β ρc (1 − ρ) . The exponents in (23) and ( 24) make analytical comparisons exceedingly complicated. In particular, the fact that the exponents of WFF and WRR contain both β and ρ compounds the difficulty. Therefore, I resort to numerical calculations. First, let β = bρ, it is easy to verify that b WF F = WRR = I + K (b/F ) 1−b when ρ = 0; second, I plot z = (WF F − I )/(WRR − I ) in Fig. 2 and find that (WF F − I )/(WRR − I ) > 1 for all b ∈ (0, 1) and ρ ∈ (0, 1). (iii) immediately follows from (i) and (ii). 

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Fig. 2. Welfare under a fixed fee is always greater than welfare under a revenue royalty.

Proof

of

Proposition

3.

From ρ  ρ−β

αβ

/ c (ββ/ρ)F αβ1−β β F ρ 1−β ( ρ ) ( 1−ρ ) ( ρc ) (β(1−β) 2 1−ρ) β−1 x−β −x < 0 when x > β. (1−x)β

(13)

and (22), we

ρ −ρ)1−β ρβ ρ−β = ((11−β) < 1, since 1−β β β 

β  ρ−β

obtain

nF F nRR

=

∂ 1−β β x )= ∂x ((1−x)

−β+βρ+ρ

If f = 0 and s = 0, then ROR = ∼ (r + c) β−ρ r. 1−ρ c+r ρ F ( ρ ) ( 1−ρ )

−β+βρ+ρ βρ+ρ ∂ 1 + −β+ r/(r + c) . From the first-order condiHence ∂r ROR ∼ (r + c) β−ρ β−ρ αβ

αβρ c+r r

ρ−β tion, we obtain that rOR = c ρ−β βρ . Plugging f = 0, s = 0 and rOR = c βρ , we obtain ρ ⎛ ⎞ ρ−β ρ αβ

 ρ−β   1−β c(βρ+ρ−β) β F ( 1−ρ ) βρ2 ⎠

β nOR = c(βρ+ρ−β)αβ . Hence, nOR /nRR = ⎝ = (β/ρ)αβ 1−β F β 1−β ( ) F 1−ρ βρ2 ( ρc ) ( 1−ρ )

−β

) 1/β 1−b 1 + (1−b b 1 + 1−b b1/β |b=1 = 1 , where b = β/ρ. Since and β β

∂ 1−b b1/β = 1 (1β−1) (β + 1) 1β−b  2 > 0, we must have nOR /nRR > 1. ∂b 1 + β bβ

Pro of

of

Prop osition

4. A

licensee’s

profit

is

+r ) ((1 − s) ((1c−s )ρ − c − r)x =

+r ) ((1 − ρ)/ρ)(c + r )x. From a consumer’s utility maximization, αβnβ/ρ−1 xβ−1 = ((1c−s )ρ . 1

β−1 (c + r ) 1−β/ρ Hence x = (1−s . Since licensees earn positive profits, it is opti)αβρ n

1 (c + r ) 1−β/ρ β−1 mal to set a fixed fee f = 1−ρ ( c + r ) n . The revenue per liρ (1−s)αβρ 1





1 r )n1−β/ρ β−1 r )n1−β/ρ β−1 cense is R/n = f + rx + spx = (1 − ρ) c+ρ r (c(+1−s + r (c(+1−s + )αβρ )αβρ 1 1



s(c+r ) (c+r )n1−β/ρ β−1 r )n1−β/ρ β−1 s (c + r ) r (1 − ρ) c+ = (c(+1−s (1−s)ρ (1−s)αβρ )αβρ ρ + r + (1−s)ρ . Thus, the firstorder conditions are   (c+r ) r 1 (1−ρ)( c+ ∂ ρ )+r+s (1−s)ρ 1 R ∼ (c + r ) β−1 + (25) = 0, (β−1)(c+r ) (1−s)ρ ∂r 1

β−1 ∂ −ρc+ρcs+cβ+rβ 1 R ∼ 1−s = 0. (26) (β−1)(−1+s)2 ρ ∂s

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It is easy to verify that (25) and ( 26)are identical. This means that the optimal licensing strategy can be implemented by a two-part tariff containing a fixed fee and either an output royalty or a revenue royalty. Consider a two-part tariff in which s = 0, then β

β−1 1  1−β/ρ  β−1 n the solution is: r = c βρ − 1 and f = (1 − ρ) βc /α ; alternatively, for a 1

β−1 tariff in which r = 0, then s = 1 − β/ρ and f = (1 − ρ) ρc αβc 2 n1−β/ρ .  Pro of of Prop osition 5. I prove this result by first solving for the integrated monopoly outcome and then show that a two-part tariff (t, 0, s∗ ) can replicate the integrated monopoly outcome. An integrated monopolist’s profit is the industry revenue minus the total fixed costs of developing products: max (p − c)xn − n(F + t), where p = αβnβ/ρ−1 xβ−1 . n,x

(27)

ρ F +t c Solving the monopolist’s problem, we can obtain that x = 1−ρ c , p = β and n = ρ   ρ−β (β/ρ)αβ . Now consider the two-part tariff (t, 0, s∗ ). Compared with a pure β +t 1−β ( ρc ) ( F1−ρ ) revenue royalty, the tariff has an additional fixed fee t, which is equivalent to an increase in F. By a change of variable and using (11)−(13), we can easily verify that the two-part tariff replicates the integrated monopoly outcome. 

Proof of Proposition 7. (i) In order to obtain the exact optimal licensing strategy, we separate the parameter values into two cases (let γ = δb /δs ) : (1) : ρ ≥ β + γ(1 − β). If s is set to be 0, then solving the first-order conditions



with respect to f and r gives us f ∗ = F β+γ(ρ1−β) − 1 and r ∗ = c β+γ(ρ1−β) − 1 ; if both f and r are set to be 0, then solving the first-order condition with respect to s gives us s∗ = 1 − β+γ(ρ1−β) . ∂ ˜ ∂ ˜ (2) : ρ < β + γ(1 − β). It is easy to verify that ∂f R|r=0,s=0 < 0, ∂r R|f =0,s=0 < 0 and ∂ ˜ ˜ R | < 0 . Hence, R is maximized at (0, 0, 0). In a sum, the total discounted f =0,r=0 ∂s   revenue can be maximized by setting (f, r, s) to either 0, 0, max 1 − β+γ(ρ1−β) , 0 

 

 F max β+γ(ρ1−β) − 1 , 0 , c max β+γ(ρ1−β) − 1 , 0 , 0 , where γ = δb /δs . (ii), (iii) and (iv ) follow immediately from (i). 

or

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