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Licensing policy and technology adoption in standard setting organizations.

I. INTRODUCTION

Standard setting organizations (SSOs) bring together multiple firms to decide on the design of a final product or process (Farrell and Saloner 1988). Scholars in the fields of law and economics have devoted a considerable amount of attention to standard setting bodies (Swanson and Baumol 2005; Lemer and Tirole 2006; Gilbert 2011). The reason is that the importance of technological standards has grown tremendously in the past decades. For example, in the information and communications technology industries the process of standard setting has led to the adoption of technologies that are as valuable as the ADSL, Wi-Fi protocol, and MPEG. Scotchmer (2004) corroborates the importance of SSOs by showing that they facilitate products' interoperability and avoid mis-coordination among producers, and Rysman and Simcoe (2008) document the impact of SSOs on technology diffusion.

As the commercial stakes attached to standards have become very important, strategic tensions often undermine the work in standard-setting committees. A major source of disagreement stems from the conflicting interests that operators with different business structures put forward in the process of standard definition (e.g., DeLacey et al. 2006; Feldman, Graham, and Simcoe 2009; Sherry and Teece 2003), particularly when firms are competitors and patent-protected technologies are involved (Chiao, Lerner, and Tirole 2007; Ganglmair and Tarantino 2012; Ganglmair and Tarantino 2014). In this paper, it is proposed a model that studies the impact of these conflicts on the SSO's participant's decisions regarding (1) the technological specification of the standard and (2) the licensing rule of the organization.

The process of standard setting begins when an SSO member proposes to work on a standard and, upon the manifestation of interest of other members, a working group is formed. Updegrove (1993) shows that, to avoid mis-coordination among vendors, manufacturers push for the formation of working groups. Motivated by this evidence, assume that in the SSO of the model manufacturers decide on the composition of the standard by comparing respective profits under all possible specifications, and the final choice is dictated by the majority of votes. (1) In the model, manufacturers can choose between a configuration of the standard that incorporates the technology of a vertically integrated firm and a configuration that incorporates the technology of a pure licensor. In this way, the standard choice is shaped by the conflict between a vertically integrated operator (like IBM and Nokia) and a pure developer of new technologies (like Rambus and Qualcomm), thus rendering pivotal the decision of the other integrated organization. This conflict is at the core of high profile Antitrust cases and in particular of the FTC v. Rambus case (hereafter, the Rambus case) and the EC v. Qualcomm case (hereafter, the Qualcomm case). In both, vertically integrated firms were among the plaintiffs and accused upstream developers of keeping a misleading conduct during the phase of standard definition. To make this conflict more interesting, let us assume that the pure innovator is more efficient and study under which conditions its technology is included in the standard.

The choice of SSOs' licensing policy is generally taken by the board of directors, which represents all the members who participate to the organization. (2) Hence, in the SSO of the model all firms vote on the licensing policy. More specifically, assume that two licensing policies are possible, ex-ante or ex-post licensing, depending on whether the licensing stage takes place, respectively, before or after the adoption of the standard by manufacturers. Indeed, although most SSOs employ an ex-post licensing rule, few of them (e.g., VITA and IEEE) recently switched to a policy of ex-ante licensing. (3)

The negotiation environment in the exante licensing regime is consistent with the implementation of RAND agreements' reasonableness requirement (Layne-Farrar, Padilla, and Schmalensee 2007; Swanson and Baumol 2005) (4): licensors who own substitute patented technologies compete for the inclusion in the standard and set royalty fees before manufacturers commit to the adoption of a specific technology. Instead, the ex-post licensing regime is consistent with a negotiation environment in which parties are not required to comply with RAND commitments.

The manufacturers' equilibrium decision on the technological composition of the standard depends on the licensing policy chosen by the SSO. In the ex-ante licensing policy, firms set their royalty rates competing for the adoption in the standard. Consequently, at the equilibrium the standard configuration taken under ex-ante licensing features the adoption of the inputs of the efficient firms. In the ex-post licensing regime firms whose technology has been employed have full monopoly power on the determination of the royalty rates. To fix this source of contractual inefficiency, under ex-post licensing vertically integrated firms sign cross-licensing agreements. Pure upstream firms cannot cross-license, because they are not active in the product market. Therefore, the trade-off that determines manufacturers' standard choice under ex-post licensing is as follows. On the one hand, the employment of the independent upstream firm's input allows integrated companies to use a more efficient technology for the production of the final good. On the other hand, it allows the efficient stand-alone licensor to exploit monopoly bargaining power over its patented technology.

The standard configuration under ex-post licensing features the adoption of the technology of the efficient stand-alone upstream firm if the marginal cost of the pivotal integrated firm ([V.sub.1] in the model) increases above a threshold. Instead, the standard comprises the technology produced by the inefficient integrated firm if the marginal cost of production of [V.sub.1] is sufficiently small (Proposition 1). The intuition is clear: as long as the integrated pivotal firm is efficient enough it prefers entering a cross-licensing agreement with the second vertically integrated firm to dealing with the efficient stand-alone upstream firm. As the marginal cost of production of [V.sub.1] rises, the benefits of cross-licensing reduce, rendering the employment of the efficient firm's technology in the standard more appealing. By comparing the total surplus (TS) generated by the two alternative specifications of the standard under ex-post licensing, we find that there is a wedge between the decision of the standard specification as taken by manufacturers and the one that would be taken by a benevolent planner. In this wedge, the planner would choose the standard with the efficient firm's technology, whereas manufacturers choose the standard with the technology of the inefficient firm.

For given equilibrium standard composition under ex-post and ex-ante licensing, which licensing policy is chosen by all SSO members is determined. (5) This allows us to determine whether the inefficient exclusion of the standalone upstream firm technology taken under ex-post licensing arises even after SSO members choose the licensing policy. We find that for ex-post licensing to arise at equilibrium it is necessary that the rents that the pivotal integrated firm (V!) can extract under ex-ante licensing are small enough. If this is the case, ex-post licensing is adopted and the standard with the inefficient technology is employed for low values of [V.sub.1]'s marginal cost of production.

Finally, which between ex-ante and ex-post licensing is the more efficient policy is assessed. We find that ex-ante licensing is more efficient than ex-post licensing for small and intermediate values of the marginal cost of production of [V.sub.1]. However, when this parameter is particularly large, the TS generated by ex-post licensing increases up to render the adoption of ex-ante licensing inefficient. The reason is that, as the marginal cost of production of [V.sub.1] increases, the larger rents that licensors can extract under ex-post licensing render the TS generated under this regime larger than the one produced under ex-ante licensing. This result is analogous to the finding in Froeb, Ganglmair, and Werden (2012) that an incremental value licensing policy discourages licensors to invest in innovation and might therefore be inefficient, even though the theoretical underpinnings in this model are different. Summarizing, two sorts of inefficiencies can arise in the ideal SSO of the model. The first regards the adoption of an inefficient licensing policy. The second is that, if ex-post licensing is chosen, the efficient technology produced by a pure licensor might be excluded from the standard specification at equilibrium.

The main model is solved under the assumption that active licensors sell their technologies by means of royalty rates. Layne-Farrar and Lerner (2011) document that linear royalties are used by a vast majority of patent pools' members to license out their technology. Note that under linear pricing and the ex-post licensing regime, contracts are influenced by two strategic effects, the Cournot effect and the raising rival's costs effect. The former effect is caused by the complementarity between the technologies required to produce the final good. Indeed, when pricing their technology independently and as monopolists, licensors do not take into account the negative externality they exert on downstream firms (Cournot 1838). The latter effect is related to the incentive that the vertically integrated firms have to increase rivals' costs and foreclose the downstream market (Salop and Scheffman 1983, 1987).

To assess the robustness of the main results to the assumption on the contractual form, the model is solved using two-part tariffs. Twopart tariff contracts are not affected by double marginalization (implying that they are more efficient than royalty rates). (6) The results obtained with two-part tariffs are analogous to the ones that were obtained with linear pricing: with expost licensing the technology of the stand-alone upstream firm is excluded from the standard, and for ex-post licensing to be preferred by SSO members to ex-ante licensing it is necessary that the rents that the vertically integrated firm [V.sub.1] can extract in the ex-ante licensing regime are sufficiently small. Differently from the model with linear pricing, though, with two-part tariffs exante licensing is always more efficient than expost licensing.

The model contributes to the literature on SSOs by proposing a simple setup to analyze both the decision on standard specification and the decision on the licensing policy. Lately, the U.S. Department of Justice and the Federal Trade Commission have provided guidance to SSOs like VITA and IEEE on the design of respective licensing rules. (7) Moreover, the European Commission has recently issued new draft guidelines on horizontal cooperation to set up the legal framework for the analysis of the horizontal agreements that can be exempted from the application of the legislation against collusive agreements. (8) Froeb, Ganglmair, and Werden (2012) and Layne-Farrar, Padilla, and Schmalensee (2007) analyze the impact of licensing rules' design on, respectively, upstream firms' incentives to invest in innovation and participation in a standardization consortia. Llanes and Poblete (2014) analyze the impact of ex-ante licensing agreements on patent pools' formation. Ganglmair and Tarantino (2014) analyze the role of ex-ante licensing commitments on strategic disclosure of essential intellectual property rights. Finally, Gilbert (2011) studies the impact of the enforcement of the nondiscriminatory requirement in RAND agreements. In this paper, the relationship between licensing rules and standard's technological specification is studied. To do so, first we determine manufacturers' decision on standard specification for a given licensing policy, then determine the SSO members' decision on the licensing rule, and finally assess the efficiency of SSO members' decisions at equilibrium.

Part of the theoretical literature has highlighted the tensions arising from the presence of competing interests and strategic motives in standard setting (e.g., Chiao, Lerner, and Tirole 2007; Farrell and Simcoe 2012; Ganglmair and Tarantino 2012). In this article, it is shown that "exclusionary effects" may influence the choice of a technology standard by looking at how technology adoption interacts with licensing decisions and product-market competition. Schmalensee (2009) and Schmidt (2014) investigate the interdependence between the pricing decisions taken by upstream innovators, downstream producers, and integrated entities; however, they do not analyze technology adoption and do not study the extent to which cross-licensing can lead to upstream exclusion. (9)

The mechanism for which the stand-alone firm is excluded from the standard shares some analogies with the one in Bernheim and Whinston (2000) and Segal and Whinston (2000), where contracting externalities can give rise to anticompetitive outcomes. Indeed, the independent firm's technology might be excluded from the standard because of the externality exerted on the pivotal voter (the integrated firm [V.sub.1]) in the decision on standard composition by the other integrated firm's ([V.sub.2]) bias in favor of cross-licensing, and by the fact that the efficient upstream firm does not participate to the decision on standard adoption. (10)

The article is also related to the literature on patent pools' formation (e.g., Lerner and Tirole 2004) and coalitions' formation in SSOs (e.g., Bloch 1995). Lerner and Tirole (2004) study an all-or-nothing patent pool formation problem. In Lerner and Tirole (2004) the degree of patents' complementarity is the equilibrium outcome of a game in which licensing decisions are constrained by either demand forces or strategic forces. Instead, in this article, the author is interested in the analysis of the conflicts between holders of competing technologies for a given degree of complementarity, to understand whether inefficient holdouts may arise at equilibrium. Bloch (1995) studies a problem of coalition formation by using a model in which the initiator of an association proposes a cooperative agreement to its product-market competitors. The equilibrium of the model is one where coordination efforts fail, because competing associations always form. This model differs from Bloch (1995) insofar as it provides an analysis of the standard configuration choice adopted by a given organization and its consequences on welfare.

Finally, the contribution of the article to the literature on vertical integration and restraints is twofold. First, we analyze the incentives that vertically integrated firms have to exclude an independent firm that operates on the upstream market if inputs are complementary. Instead the received literature has typically focused on settings with substitute intermediate goods (Rey and Tirole 2007). (11) Second, we investigate whether cross-licensing can cause the inefficient exclusion in the upstream market. (12)

The article proceeds as follows. Section II presents the model and Section III solves it under the assumption of linear pricing. Section IV discusses the model's main assumptions. In Section V, the robustness of the results is tested by employing two-part tariffs and Section VI concludes.

II. THE MODEL

Production technology. There are five firms: [V.sub.1] and [V.sub.2] are vertically integrated, [U.sub.1] and [U.sub.2] are stand-alone upstream firms, [D.sub.3] is a pure downstream firm. Downstream firms (or manufacturers) compete in quantities and produce a homogeneous good at zero marginal cost. Moreover, they face consumers with inverse demand P(Q), where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]is the total industry output, and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are the quantities produced by [V.sub.1], [V.sub.2], and [D.sub.3], respectively. Throughout the analysis, P(Q) is assumed to be linear and equal to max{0,1 -- Q). Demand linearity implies that the Coumot-Nash equilibrium of the game exists and is unique.

To produce one unit of the final good, each manufacturer needs one unit of two input goods. In other words, the two input goods are perfect complements and used in fixed proportions for the production of the final good. The first input can be acquired from [V.sub.1] or [U.sub.1], the second input from [V.sub.2] or [U.sub.2]. Denote by [[tau].sub.i], and [[??].sub.i], the two substitute patented technologies supplied by [V.sub.1] and [U.sub.i], respectively, with i= 1, 2. (13) The upstream units of [V.sub.1] and [V.sub.2] bear a marginal cost equal to c [member] (0,[??]) to produce respective input goods under their patented technology, instead firm [U.sub.2]'s marginal cost of production is nil and [U.sub.1]'s marginal cost of production is [??] > c, with [??] [member of] (c, 1/2), implying that c < 1/2. Therefore, firm [U.sub.1] is less efficient than firm [V.sub.1], instead firm [U.sub.2] is more efficient than [V.sub.2].

The framework of the model is given in Figure 1.

Contractual environment. Upstream firms license out their technologies by means of public contracts with linear prices or two-part tariffs. First analyze the case with linear pricing and then consider two-part tariffs. Moreover, licensors can choose among two pricing schemes to sell their technologies: independent licensing or cross-licensing. As in Schmidt (2006), cross-licensing is designed so that active licensors maximize joint profits and can only take place between vertically integrated firms.

In the section with linear pricing, side payments are not allowed. Side payments would take the form of conditional contracts in which parties specify before the adoption of a standard the transfers they would carry out depending on standard configuration. Agreements of this sort can be ruled out invoking two main arguments. First, having a contingent nature the parties may be tempted to renegotiate them ex-post. Second, rational agents may design them to collude on the product market, so that, like other forms of horizontal agreements, they are typically treated as per se unlawful by antitrust authorities. In Section V, it is shown that introducing side payments between contracting parties does not change the results.

Finally, consistently with the nondiscriminatory requirement that firms in SSOs must comply with when agreeing on RAND commitments, upstream suppliers cannot discriminate among downstream manufacturers.

Decision on standard configuration and on licensing rule. The decision on which technology to include in the standard is taken by manufacturers by comparing own profits under different configurations. More specifically, the decision rule at the standard choice stage requires that a majority of manufacturers agree for a technology standard to be adopted by the SSO. Note that, if a manufacturer is indifferent, then assume that it votes for the inclusion of the technology produced by the efficient source. Moreover, the model's working assumption is that the standard adopted by manufacturers is compulsory for all SSO members ("compulsory standard" assumption). That is, rule out the cases in which alternative technologies are employed by downstream firms for the production of the final good. (14)

We consider two different licensing policies, namely ex-post licensing and ex-ante licensing. In the former, licensing contracts are signed after manufacturers have chosen and adopted a certain standard. In the latter, licensing takes place before standard choice and adoption. The analysis of the ex-ante licensing case allows us to determine the consequences of the implementation of a policy of early licensing commitments on the choice of the technologies in the standard, so to replicate the effects of RAND agreements' reasonableness requirement. (15)

In the ex-post licensing regime the assumptions on upstream firms' efficiency limit the scope of the analysis to two alternative standards, S ([[tau].sub.1];[[tau].sub.2]) and [delta] ([[tau].sub.1],[[??].sub.2]). The reason is that at the licensing stage the firm whose technology has been adopted by manufacturers holds all the bargaining power, thus no manufacturer would prefer [[??].sub.1] to [[tau].sub.1] ([U.sub.1] is less efficient than [V.sub.1]). Instead, the presence of [[??].sub.1] plays a crucial role under the ex-ante licensing rule, as it constrains the market power of [V.sub.1].

After solving for manufacturers' standard decision under ex-post and ex-ante licensing, let all SSO members vote on the licensing rule. The approach is analogous to the one used to pin down the manufacturers' decision on standard configuration: all firms vote on the licensing policy they prefer, and the final decision is dictated by the majority of votes.

Welfare. We analyze the consequences of manufacturers' standard configuration and licensing rule decisions on welfare. In particular, compare the choice taken by manufacturers on standard configuration for given licensing rule with the choice that a benevolent planner (planner, she) would take. Then, compare the choice of the licensing rule taken by SSO members with the choice of the planner.

The planner decides by comparing the TS generated by each scenario considered. Note that the planner delivers the constrained efficient choice of standard configuration and licensing rule. This is because she disregards the strategic interactions that determine manufacturers' equilibrium standard specification and SSO members' licensing rule decisions, but takes into account the impact that the employment of a particular technology has on firms' choices at the licensing and product-market stages.

III. LINEAR PRICING

In this section, the results of the analysis carried out under the assumption that firms set licensing agreements by means of public and nondiscriminatory contracts with linear prices are presented. Denote by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] the royalty rates set by the two vertically integrated firms and by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] the royalty rates set by the two stand-alone upstream firms. Moreover, assume that [V.sub.1] and [V.sub.2] internalize the cost of using their own technology (i.e., [[tau].sub.1] or [[tau].sub.2]) in the production process.

A. Ex-Post Licensing

Let us start by considering the equilibrium of the standard adoption game in the ex-post licensing regime. The timing of the game is as follows.

1. Standard Choice Stage: downstream firms choose the technology standard and sink a fixed investment cost equal to I.

2. Pricing Scheme and Royalty Setting Stage: upstream firms whose technology is adopted downstream first choose the pricing scheme (independent licensing/cross-licensing) and then the royalty rate. Finally, each downstream firm decides whether to pay the royalty rate (and produce) or give up production.

3. Product-Market Competition Stage: active firms set quantities.

By sinking I, the manufacturers commit to technology-specific investments and set up the equipment necessary to carry out final good's production. In what follows, it is assumed that the fixed cost I is large enough to make the standard choice irreversible once the licensing stage is reached. Consequently, the firms whose technologies are in the standard behave as if they were monopolists at the licensing stage.

The model is solved by backward induction and the equilibrium concept employed is the subgame perfect Nash equilibrium (SPE). First the case featuring the adoption of S ([[tau].sub.1], [[tau].sub.2]) is presented, then the one featuring the adoption of S([[tau].sub.1], [[??].sub.2]). Finally, the standard choice game and the welfare analysis is studied.

Adoption of S([[tau].sub.1], [[tau].sub.2]) as the Technology Standard. To start with, derive the optimal quantities set by [V.sub.1] and [V.sub.2] for given royalties, then compute the equilibrium royalty rates chosen by [V.sub.1] and [V.sub.2]. At the competition stage, each downstream firm maximizes:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

With i, k = 1,2 and i [not equal to] k. Firm [D.sub.3] solves:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Firms' reaction functions are given by:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

leading to

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Two subcases must be distinguished: the one in which [V.sub.1] and [V.sub.2] license their technologies independently (independent licensing) and the one in which licensing decisions are taken cooperatively (cross-licensing).

Independent licensing. At the royalty setting stage of the game with independent licensing vertically integrated firms maximize:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

With i,k= 1,2 and i [not equal to] k. Dropping functional notation, the relative first-order conditions can be written as:

(7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

When [V.sub.i] sets [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] it trades off the higher revenue generated downstream (partly due to the raising rival's costs effect) with the lower revenue raised on the upstream market because of rival firms' output contraction downstream. Linearity leads to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. At these royalty rates, firm [D.sub.3] is excluded from the downstream market, so that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] at equilibrium. Therefore, Equations (1) and (2) are solved for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and obtain the following product-market equilibrium quantities and price:

(8) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(10)[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The royalty rate set by [V.sub.1] and [V.sub.2] is equal to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Plugging [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] into the product-market equilibrium expressions above implies that, under the joint employment of [delta] ([[tau].sub.1], [[tau].sub.2]) and independent licensing, the results in Table 1 are obtained. Active firms' profits are [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and consumer surplus (CS) is CS = [Q.sup.2]I2 = 8[(1 - 2c).sup.2]/121.

The equilibrium royalty rates of the licensing game in which vertically integrated firms price their technologies noncooperatively are determined by two effects: the Cournot effect and the raising rival's costs effect. The former is due to the relationship of complementarity between the technologies in the standard. The latter reflects the fact that each vertically integrated firm is a monopolist input provider of its product-market rival. In the following, it is shown that cross-licensing fixes these inefficiencies and is preferred to a noncooperative pricing scheme.

Cross-licensing. Cross-licensing is modeled as in Schmidt (2006). Vertically integrated firms maximize joint profits by setting a royalty rate [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], that implements the monopoly outcome on the product market. Using the definition of [w.sup.cl] in the expression for Q in Equation (9), upstream firms solve:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Symmetry implies that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Cross-licensing allows firms to fix the inefficiencies related to the raising rival's costs and double marginalization effects, and brings royalties down to the monopoly level ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]).

Under cross-licensing, vertically integrated firms split the monopoly profit and obtain [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] each. Moreover, CS is CS = [Q.sup.2]/2 = [(1 - 2c).sup.2]/8 > 8[(1- 2c).sup.2]/121, implying that cross-licensing is beneficial for consumers, also.

It is clear from Table I that cross-licensing is the equilibrium licensing scheme when manufacturers adopt S ([[tau].sub.1], [[tau].sub.2]). Indeed, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Moreover, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Finally, the TS generated by S, ([[tau].sub.1], [[tau].sub.2]) and ex-post licensing is [TS.sup.p] ([[tau].sub.1], [[tau].sub.2]) = [3(1 - 2c).sup.2]/8.

Adoption of S ([tau].sub.1] = [[??].sub.2]) as the Technology Standard. Let manufacturing firms adopt a standard that includes technologies [[tau].sub.1] and [[??].sub.2]. This implies that integrated firms are asymmetric at the upstream level, because [V.sub.2] does not license its technology downstream and needs to acquire externally both [[tau].sub.1] and [[??].sub.2]. Moreover, [V.sub.1] and [U.sub.2] cannot cross-license respective technologies, because [U.sub.2] is not active on the downstream market.

At the product-market competition stage, firm [V.sub.1] solves:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

[V.sub.2] and [D.sub.3], solve, respectively,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Manufacturers' reaction functions are equal to:

(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(13) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Thus, if all three downstream firms are active at equilibrium then the following holds:

(14) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(15) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(16) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(17) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(18) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

At the royalty setting stage, V, solves the following problem:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The associated first-order condition is equal to:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The optimal value of [w.sub.1] solves the trade-off triggered by the impact of a larger royalty rate on downstream and upstream revenues. More specifically, the first term of the first-order condition is related to the raising rival's costs effect, it is positive and acts at the expense of firms [V.sub.2] and [D.sub.3].

Firm [U.sub.2] solves the following problem:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The resulting first-order condition is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Clearly, the decision of [U.sub.2] is not influenced by the raising rival's costs effect, because [U.sub.2] does not operate on the product market. Invoking linearity and solving for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], we find that

(19) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(20) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Plugging these royalties into Equations (14), (15), and (16) it turns out that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], that is, [V.sub.1] is the only active firm. Therefore, impose [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and use Equation (11) to compute [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. This leads to the following product-market equilibrium values:

(21) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(22) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Finally, solving for the royalty rate set by [U.sub.2] we find that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Table 2 summarizes the results of this section. More specifically [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Finally, the TS generated by S ([[tau].sub.1], [[??].sub.1]) and ex-post licensing is [TS.sup.p] ([[tau].sub.1], [[??].sub.2]) = 7[(1 - c).sup.2] /32.

The equilibrium of the game in which firms [V.sub.1] and [U.sub.2] price their technologies noncooperatively features a monopoly of [V.sub.1] downstream. This is because, with respect to the case featuring the adoption of S([[tau].sub.1], [[tau].sub.2]), firm [V.sub.2] loses a device to deal with firm [V.sub.1], competition on the product market (namely, the possibility to price an input of [V.sub.1]).

Standard Choice with Ex-Post Licensing. In the first stage of the game, manufacturers choose which between S([[tau].sub.1], [[tau].sub.2]) and S([[tau].sub.1], [[??].sub.2]) they employ as the technology standard for the production of the final good. The decision rule requires that a majority of manufacturers agree for a standard to be adopted by the SSO.

PROPOSITION 1. (Standard adoption with expost licensing) Assume that the choice of the technology is taken by manufacturers and side payments are not allowed. The unique Nash equilibrium of the adoption game features the employment of standard S([[tau].sub.1], [[tau].sub.2]) under cross-licensing if c [member of] (0, [c.sup.-j]], and the employment of standards S([[tau].sub.1], [[??].sub.2]) under independent licensing if c [member of] ([c.sup.-p], 1/2).

Proposition 1 shows that the adoption of S([[tau].sub.1], [[??].sub.2]) as the technology standard is not an equilibrium of the technology adoption game if c is smaller than [c.sup.-p], with [c.sup.-p] = (3 - [square root of 2]) /7 < 1/2. This outcome is determined by the basic trade-off outlined in Section I: from the point of view of [V.sub.1], cross-licensing preserves rents, instead contracting with a pure developer, like [U.sub.2], is efficient but leads to rent dissipation. If c is small the former effect prevails, whereas if c is large the latter effect prevails.

The proof of the result in the proposition directly follows from the comparison of the manufacturing firms' profits given in Tables 1 and 2. First note that firm [D.sub.3] is excluded from the downstream market independently of the specification of the standard. This means, it is indifferent between S ([[tau].sub.1], [[tau].sub.2]) and S[[tau].sub.1], [[??].sub.2], and, given our tie-break rule, it will vote for S ([[tau].sub.1], [[??].sub.2]) (i.e., for the inclusion of the efficient firm's technology). [V.sub.2] strictly prefers S ([[tau].sub.1], [[tau].sub.2]) to S ([[tau].sub.1], [[??].sub.2]), because its profits are nil if the latter is adopted. Thus, [V.sub.1] is pivotal. [V.sub.1] prefers S ([[tau].sub.1], [[tau].sub.2]) to S ([[tau].sub.1], [[??].sub.2]) if, and only if, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Therefore, [V.sub.1] votes with [V.sub.2] for the adoption of S ([[tau].sub.1], [[tau].sub.2]) as the technology standard when c [member of] (0,[c.sup.-p]]. Instead, [V.sub.1] votes with [D.sub.3] for the adoption of S ([[tau].sub.1], [[??].sub.2] as the technology standard when c [member of] ([c.sup.-p] 1/2).

Welfare Analysis with Ex-Post Licensing. The welfare analysis is conducted by assuming that a social planner decides by comparing the value of TS generated by the two competing configurations of the standard (S[[tau].sub.1], [[tau].sub.2] and S[[tau].sub.1], [[??].sub.2]). The planner solves the following game.

1. Standard Choice Stage: the planner chooses the technology standard.

2. Pricing Scheme and Royalty Setting Stage: upstream firms whose technology is adopted downstream choose the pricing scheme (independent licensing/cross-licensing) and then the royalty rate. Consequently, each downstream firm decides whether to pay the royalty rate (and produce) or give up production.

3. Product-Market Competition Stage: active firms set quantities.

The planner chooses the standard configuration disregarding the strategic interactions that determine the equilibrium in Proposition 1; however, she takes into account the impact that the employment of a particular technology has on firms' choices at the licensing and product-market stages. Therefore, the planner delivers the constrained efficient standard configuration. The result of the game above is in what follows.

LEMMA 1. Assume that the choice of the technology is taken by a social planner, then the technology standard she would employ is S ([[tau].sub.1], [[tau].sub.2]) if c [member of] (0, [c.sup.E]] and S ([[tau].sub.1], [[??].sub.2]) if c [member of] ([c.sup.E], 1/2), with 0 < [c.sup.E] = (17-2 [square root of 21]) /41 < 1/2.

Using Proposition 1 and Lemma 1 we obtain the result in the following proposition.

PROPOSITION 2. (Inefficient exclusion under ex-post licensing) There is a wedge between the manufacturers' and the planner's technology standard choice. If c [member of] [[c.sup.E], [c.sup.-p]] the adoption of S ([[tau].sub.1], [[??].sub.2]) would be constrained efficient at equilibrium. Instead, manufacturers adopt S([[tau].sub.1], [[tau].sub.2]).

Proposition 2 shows that the conflict between the technological efficiency of the [U.sub.2]'s input and the contractual efficiency of cross-licensing can lead to a standard choice that is suboptimal from the total welfare point of view. This is because, if the marginal cost of production (c) is sufficiently large, the SSO sponsors S ([[tau].sub.1], [[tau].sub.2]) and vertically integrated firms cross-license respective technologies, whereas the planner would adopt S ([[tau].sub.1], [[??].sub.2]).

Figure 2 illustrates the results in Propositions 1 and 2. In particular, it shows that there is a wedge between manufacturers' and the planner's adoption choices.

B. Ex-Ante Licensing

Under the ex-post licensing policy, active licensors set royalty rates after their technology has been adopted by manufacturers; this grants monopoly power to the licensors whose technology is employed for downstream production. In this section, the SPE of a game in which the royalty rate stage precedes technology choice and adoption is derived, and let [V.sub.i] and [U.sub.i] compete for the employment of respective technologies by downstream firms.

The new timeline reproduces the results of an auction carried out between substitute technologies at the competitive conditions prevailing before the adoption phase:

1. Royalty Setting Stage: upstream firms decide the royalty rate.

2. Technology Choice Stage: downstream firms choose the technology.

3. Product-Market Competition Stage: active firms set quantities.

The equilibrium of this game directly follows from the assumptions on upstream firms' efficiency. At the licensing stage, [V.sub.1], offers [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [U.sub.2] Offers [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], thus manufacturers choose S ([[tau].sub.1], [[??].sub.2]) (inefficient sources stay inactive), (16) and produce

(23) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(24) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(25) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Moreover, Q = (3 - 4c - 2[??]) /4 and P(Q) = (1 + 4c + 2[??]) /4.

Firms' profits are

(26) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(27) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(28) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(29) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Finally, CS = [(3 - 4c - 2[??]).sup.2] /32 and T[S.sup.a] ([[tau].sub.1], [[??].sub.2]) is as follows:

(5 - 4c + 2[??]) (3 - 4c - 2[??]) /32

Proposition 3 summarizes the results of the game with ex-ante licensing.

PROPOSITION 3. (Standard adoption with ex-ante licensing) Assume that active licensors set royalty rates before their technologies have been employed by manufacturers, then at the licensing stage [V.sub.1] licenses out its technology at [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [U.sub.2] at [[tau].sub.1], [[tau].sub.2]. Consequently, manufacturers choose S ([[tau].sub.1], [[??].sub.2]) as the technology standard.

In this setup, firm [U.sub.2], being more efficient than [V.sub.2], can match the best offer of [V.sub.2] and convince manufacturers to employ [[??].sub.2]. This shows that it is the monopoly power granted by expost licensing that tilts the licensing negotiations between firm [V.sub.1] and [U.sub.2] in the ex-post licensing case.

C. Licensing Rule Decision with Linear Pricing

In this section, SSO's member's choice of the licensing policy under linear pricing is analyzed. The aim is to determine the conditions under which a given licensing policy is employed and the consequences on the configuration of the standard.

For a licensing policy to be adopted by the SSO a majority of firms' votes is required. In particular, firms decide by comparing own profits in the ex-ante and ex-post licensing policy, and given the consequent standard configuration at equilibrium. Equilibrium results are in Proposition 4, the proof is relegated to the Appendix. Note that [DELTA] = [??] - c > 0 denotes the degree of efficiency of [V.sub.1] with respect to [U.sub.1]. Moreover, assume that [DELTA] < [bar.[DELTA]] (c) [equivalent to] (1 - 2c) /2, so that manufacturers are all active under ex-ante licensing.

PROPOSITION 4. (Licensing policy with linear pricing) Assume that the licensing policy is chosen by all SSO's members and let [DELTA] = [??] - c > 0 c > 0, with [DELTA] < [bar.[DELTA]] (c). If c [member of] (0, [c.sup.-p]], the ex-ante licensing policy is adopted if, and only if, [DELTA] [member of] {[DELTA].sup.*] (c), [[bar.[DELTA]] (c) J. Ex-post licensing is adopted if, and only if [DELTA] [member of] (0, [DELTA] *(c)]. If c [member of] {[c.sup.-p], 1/2), exante licensing is adopted if [DELTA] [member of] ([[DELTA].sup.**] (c), [[bar].sup.[DELTA] (c) J or [DELTA] [member of] (0, [[DELTA].sup.***] (c)]. Ex-post licensing is adopted if [DELTA] [member of] (0, [[DELTA].sup.**] (c)] and [DELTA[ [member of] ([[DELTA].sup.**] (c), [[bar].[DELTA]](c)).

Proposition 4 provides the conditions that determine the choice of the licensing rule by the SSO members. In what follows, to begin with the details of the choice of the licensing rule are discussed and then their intuitions are presented.

Recall that for a licensing regime to be adopted it is necessary that three SSO members vote for it. [U.sub.1] is indifferent between ex-post and ex-ante licensing, thus, for the sake of simplicity, it is assumed that it votes for expost licensing. (17) [D.sub.3] prefers ex-ante licensing to ex-post licensing independently of the value of c, because it is excluded from the product market under ex-post licensing. The vote of [V.sub.2] depends on whether c lies above or below [c.sup.-p]. Below [c.sup.-p], [V.sub.2] votes for ex-post licensing [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The position of [V.sub.1] depends on the value of [DELTA], which measures [V.sub.1]'s degree of efficiency vis-a-vis [U.sub.1]. If [DELTA] is lower than [DELTA]*(c), with [DELTA]* (c) = (3 - [square root of 6])(1 -2c)/6 [member of] (0, [[bar.[DELTA]] (c)), then [V.sub.1] votes for ex-post licensing. Conversely, as [DELTA] increases above [[DELTA].sup.*](c), [V.sub.1] prefers ex-ante to ex-post licensing. This implies that if c < [c.sup.-p] and [DELTA] lies below [[DELTA].sup.*](c) the ex-post licensing regime is chosen at equilibrium. Instead, if c < cJ> and A lies above A*(c) the ex-ante licensing regime is chosen at equilibrium.

Above [c.sup.-p], [V.sub.2] votes for ex-ante licensing, because under ex-post licensing manufacturers would employ S ([[tau].sub.2][[??].sub.1]) and [V.sub.2] would be inactive. Given that [U.sub.1] votes for ex-post licensing, this regime is employed if [V.sub.1] votes for it, that is, if [DELTA] [member of] (0, [[DELTA].sup.**](c)], with [[DELTA].sup.**] (c) = (3 - 6c - [square root of (9 -42c - 45[c.sup.2])])/6, and [U.sub.2] votes for it, that is, if [DELTA] [member of] ([[DELTA].sup.***] (c), [[bar.[DELTA] (c)), with [[DELTA].sup.***] (c) = (8c- 13[c.sup.2]-1)/4c. Instead, if either [DELTA] [member of]([[DELTA].sup.**] (c), [[bar.[DELTA]](c)) or [DELTA] [member of](0, [[DELTA].sup.***] (c)] ex-ante licensing is chosen at equilibrium.

The condition that [V.sub.1] favors ex-post licensing only for small values of [DELTA] has a clear intuition. Although under ex-post licensing [V.sub.1] is the downstream market monopolist, it is also subject to the monopoly power of [U.sub.2]. Instead, with ex-ante licensing [U.sub.2] sells its technology at the competitive price. Given this, the larger is [V.sub.1]'s degree of efficiency with respect to [U.sub.1], the more it can extract of the rivals' downstream rents under exante licensing. In turn, above [c.sup.-p] [U.sub.2] votes for expost licensing only if [DELTA] is relatively large. The reason is that as [DELTA] increases, the profits that [U.sub.2] obtain under ex-ante licensing decrease (because industry quantity decreases with [DELTA]). (18)

Figure 3 illustrates the SSO decision on the licensing policy (Proposition 4), and the associated specification of the standard (as resulting from Propositions 1 and 3). Note that, in the figure, EP denotes ex-post licensing and EA denotes ex-ante licensing. Two questions arise: Is technology [[??].sub.2] still inefficiently excluded from the standard? Is manufacturers' decision on the licensing rule in Proposition 4 efficient? The first question is addressed in Corollary 1.

COROLLARY 1. (Inefficient exclusion of [[??].sub.2]) If c [member of] [[c.sup.E], [c.sup.-p]] and the conditions for ex-post licensing to be chosen are met, [[??].sub.2]) is inefficiently excluded from the technology standard.

This result follows immediately from Propositions 2 and 4, and shows that the inefficient exclusion of the pure upstream firm [U.sub.2] arises as an outcome of manufacturers' technology choice and SSO members' decision on the licensing rule. Finally, the efficiency of the licensing policy is assessed by considering the decision that the planner would take by comparing the TS generated by the two alternative licensing policies (ex ante and ex post). The results are summarized in Proposition 5, the relative proof is in the Appendix.

PROPOSITION 5. Let 0 < [DELTA] < [bar.[DELTA]] (c). If c [less than or equal to] [c.sup.p] total welfare is lower under ex-post licensing than under ex-ante licensing. If c > [c.sup.-p], total welfare is larger under ex-ante licensing if c [member of] ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), lower otherwise.

Proposition 5 has two main take-aways. The first is that below [c.sup.-p] the adoption of ex-ante licensing is constrained efficient. The second is that, above [c.sup.-p], the adoption of ex-ante licensing is constrained inefficient if[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), with [??]([DELTA]) = 2(l - [DELTA])/5 [member of] ([c.sup.-p], 1/2). The reason is that, as the marginal cost of production c increases, the larger rents that licensors can extract under ex-post licensing render the TS generated by this regime larger than the one produced by ex-ante licensing, more than compensating the lower CS with ex-post licensing.

A comparison with the results in Proposition 4 is helpful to clarify that below [c.sup.-p] the planner would always adopt ex-ante licensing and standard S' ([[tau].sub.1], [[??].sub.2]), whereas manufacturers might choose ex-post licensing and standard S ([[tau].sub.1], [[??].sub.2]) if [DELTA] [member of](0, [[DELTA].sup.*] (c)]. Above [c.sup.-p] the choice of the planner and the choice of manufacturers do not coincide to the extent that c [member of] ([??](A), 1 /2) and manufacturing firms choose ex-ante licensing.

IV. DISCUSSION OF MODEL'S ASSUMPTIONS

The model builds upon three major assumptions, namely on (1) the composition of the SSO, (2) the contracting environment, and (3) the decision rule on standard configuration.

As remarked in Section I, the framework in Figure 1 is chosen to represent the variety of firms that populate SSOs. In particular, the presence of a majority of manufacturers is consistent with the evidence in Blind and Thumm (2004). Although the inefficient source to input 1 ,[U.sub.1], and the pure manufacturer, [D.sub.3], are never active under ex-post licensing, their role becomes important with exante licensing. Indeed, the presence of [U.sub.1] limits the market power that [V.sub.1] can exercise under exante licensing, and the presence of [D.sub.3] shows that the exclusion of the efficient upstream firm arises independently of whether only the downstream affiliates of the integrated companies operate on the product-market.

Vertically integrated firms [V.sub.1] and [V.sub.2] are asymmetric in their degree of efficiency; while [U.sub.2] is more efficient than [V.sub.2], [U.sub.1] is less efficient than [V.sub.1]. This assumption is introduced to let the conflict between the productive efficiency of the upstream firm technology and the contractual efficiency of cross-licensing arise and study how the competing interests that characterize integrated operators and stand-alone upstream firms affect standard's specification. (19) Indeed, if [V.sub.2] was more efficient than [U.sub.2], then the only equilibrium would feature the efficient adoption of S([[tau].sub.1], [[??].sub.2]) as the technology standard.

In Section [V.sub.1] it is shown that the employment of two-part tariffs leads to results that are qualitatively analogous to the ones obtained using linear pricing. Here it is worth emphasizing that the model captures the impact of post- versus prestandard pricing decisions on standard's specification, but not collusion. Specifically, the setup does not capture the effects of collusion within ex-ante licensing negotiations. For instance, suppose that [V.sub.1] and [V.sub.2] would be allowed to make a take-it-or-leave-it license price offer to [U.sub.2] during the licensing discussion, then [U.sub.2] would be stuck with a low price that might negatively affect its incentives to innovate in the future.

Finally, in the model the decision on standard specification is taken by manufacturers. This assumption is motivated by the evidence in Updegrove (1993) that standardization bodies, especially in the information and communications technology industries, are commonly founded by manufacturers with the intent of controlling the development of a particular technology and avoid mis-coordination among vendors.

V. TWO-PART TARIFFS

In this extension, upstream firms use two-part tariffs to license out their technology to downstream firms. Two-part tariffs are more efficient than linear pricing because they are not affected by double marginalization. Therefore, if the exclusionary result arises in this setting it is entirely caused by the monopoly power granted to upstream licensors whose technology is in the standard under ex-post licensing. As in Section III, first the standard adoption decision under expost licensing is considered and then the case with ex-ante licensing is analyzed.

A. Ex-Post Licensing

The timing of the game is as follows.

1. Standard Choice Stage: downstream firms choose the technology standard and sink a fixed investment cost equal to I.

2. Licensing Scheme and Royalty Setting Stage: upstream firms whose technology is adopted by manufacturers first choose the pricing scheme (independent licensing/cross-licensing) and then make public and nondiscriminatory take-it-or-leave-it offers to downstream firms. We denote by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (respectively, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) the tariff offered by integrated upstream firms (respectively, pure upstream firms).

3. Product-Market Competition Stage: the downstream firms that decide to pay the tariff(s) set product-market quantities.

Manufacturers pay the due tariff after the product-market competition stage and under the protection of a limited liability constraint for which they cannot pay more than the profits they raise on the downstream market. Therefore, first firms negotiate over the licensing contracts, then they decide to produce and carry out the payment of the tariffs they agreed upon initially. Like in the setup with linear pricing, the fixed cost I is large enough to make the standard choice irreversible once the licensing stage is reached under ex-post licensing. Consequently, the firms whose technologies are in the standard behave as monopolists at the licensing stage.

Remember that firms [V.sub.1] and [V.sub.2] bear a marginal cost equal to c [member of] (0, [??]) to produce respective input goods under their patented technology, instead firm [U.sub.2]'s marginal cost of production is nil and [U.sub.1]'s marginal cost of production is [??] > c, with [??] < (1 - c) /4. In contrast to the the model with linear prices, in this extension, payments between contracting firms are allowed through the tariff's fixed component. Finally, note that we use [pi] to denote the rent generated by the product market, as opposed to [PI], which indicates total profits (i.e., net of the tariff(s) paid by manufacturers).

Adoption of S ([[tau].sub.1], [[tau].sub.2]) as the Technology Standard. If manufacturers choose S ([[tau].sub.1], [[tau].sub.2]) as the technology standard, at the product-market competition stage the equilibrium values are the same as in Equations (3) and (4). Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (respectively, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (respectively, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denote the Cournot (respectively, monopoly) downstream profits and quantity when manufacturers bear as marginal costs [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] on inputs 1 and 2, respectively. Specifically, when[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the per-firm quantity produced under Cournot is [q.sup.c](c,c) = (I - 2c)/4 and the associated profits are equal to [[pi].sup.c] (c,c) = [(1 -2c).sup.2]/16. In turn, if monopolist, a firm produces [q.sup.m](c, c) = (1 - 2c)/2 and raises profits given by [[pi].sup.m] (c, c) = [(1 - 2c).sup.2]/4.

Independent licensing. Lemma 2 presents the equilibria of the licensing game when [V.sub.1] and [V.sub.2] set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] noncooperatively.

LEMMA 2. Under independent licensing and technologies [[tau].sub.1] and [[tau].sub.2] in the standard, the Nash equilibria of the licensing game feature [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. At these equilibria firm [V.sub.i] is active as monopolist, whereas firms [V.sub.k] and [D.sub.3] are excluded from the product market.

At a Nash equilibrium of the noncooperative licensing game, one of the two licensing firms stays out of the downstream market with [D.sub.3], but extracts rival's downstream profits through the fixed fee. These results stem from the consideration that each upstream firm whose technology is in the standard tries to exploit its bargaining position, imparted by the timing of negotiations, and extract the monopoly profit from downstream manufacturers. From the proposition it is clear that, due to multiple equilibria, it cannot be determined whether it is firm [V.sub.1] or firm [V.sub.2] that obtains the full monopoly profit in a simultaneous offer game.

Cross-licensing. Under cross-licensing, [V.sub.1] and [V.sub.2] set their tariffs cooperatively, but behave noncooperatively at the production stage. The best deal that vertically integrated firms can negotiate upon is the one at which they equally share the monopoly rent.

LEMMA 3. Under cross-licensing and technologies [[tau].sub.1] and [tau].sub.2] in the standard, at an equilibrium [V.sub.1] and [V.sub.2] write the following contract: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

At a cooperative equilibrium, [V.sub.1] and [V.sub.2] enter the same agreement as in the linear pricing case and in this way they share the monopoly profits. This means, cross-licensing and independent licensing deliver the same industry profits under two-part tariffs. However, cross-licensing eliminates the uncertainty regarding which firm is active downstream and this renders it preferable to independent licensing. Therefore, at an equilibrium with standard S ([[tau].sub.1], [[tau].sub.2]) and ex-post licensing, firms' payoffs are [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Adoption of S (([[tau].sub.1], [[??].sub.2])) as the Technology Standard. If manufacturers choose S (([[tau].sub.1], [[??].sub.2])) as the technology standard, at the product-market competition stage the equilibrium values are the same as in Equations (14), (15), and (16). Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) (respectively, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) (respectively, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII])) denote the Cournot (respectively, monopoly) profits and quantity when manufacturers bear as marginal costs [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] on inputs 1 and 2, respectively. Specifically, when [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and all manufacturers are active, each produces [q.sup.c](c, 0) = (1 -c)/4 and obtains [[pi].sup.c] (c, 0) = [(1 - c).sup.2]/16. Instead, a downstream monopolist would produce [q.sup.m](c, 0) = (1 - c)/2 and gain profits equal to [[pi].sup.m] (c, 0) = [(1 - c).sup.2]/4.

Lemma 4 presents the tariffs at equilibrium in this case.

LEMMA 4. At a Nash equilibrium firm [U.sub.2] offers [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Under the adoption of S(([[tau].sub.1], [[??].sub.2])) as the technology standard, if licensors sell their technologies by means of two-part tariffs then the stand-alone upstream firm [U.sub.2] is able to fully squeeze manufacturer's profits. At equilibrium, independently of which firm among [V.sub.1], [D.sub.3], and [V.sub.2] is the downstream monopolist, all the downstream rents are extracted by [U.sub.2] via the fixed fee. Hence, with ex-post licensing and standard S (([[tau].sub.1], [[??].sub.2])) firms payoffs at equilibrium are equal to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Standard Choice and Welfare Analysis with ExPost Licensing. Proposition 6 presents the Nash equilibrium of the adoption game and the results of the welfare analysis under public and nondiscriminatory licensing contracts featuring two-part tariffs. The proof directly follows from the comparison between manufacturers' payoffs and TSs above.

PROPOSITION 6. (Standard adoption with expost licensing and two-part tariffs) Assume that the choice of the technology is taken by manufacturers, then the unique Nash equilibrium of the adoption game features the choice of S (([[tau].sub.1], [[tau].sub.2])) as the technology standard. If the choice would be taken by the planner she would employ S(([[tau].sub.1], [[??].sub.2])) as the technology standard.

With two-part tariffs and ex-post licensing, [V.sub.1] and [V.sub.2] strictly prefer standard S (([[tau].sub.1], [[tau].sub.2])) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], while D3 is indifferent between S (([[tau].sub.1], [[tau].sub.2])) and S (([[tau].sub.1], [[tau].sub.2])). Given the majority rule assumption, S (xj,x2) is chosen at equilibrium. However, comparing [bar.T][S.sup.p](([[tau].sub.1], [[tau].sub.2])) with [bar.T][S.sup.p](([[tau].sub.1], [[??].sub.2])) it is clear that the employment of S ([[tau].sub.1], [[??].sub.2]) would be (constrained) efficient. Therefore, the decision on the configuration of the standard is always inefficient under ex-post licensing and two-part tariffs.

B. Ex-Ante Licensing

As in Section III.B, we study the SPE of a game in which the licensing stage precedes technology choice and adoption, so to let [V.sub.1] and [U.sub.i] compete for the employment of respective technologies by downstream firms. The timeline follows.

1. Royalty Setting Stage: upstream firms whose technology is adopted by manufacturers first choose the pricing scheme (independent licensing/cross-licensing) and then make public and nondiscriminatory takeit-or-leave-it offers to downstream firms. We denote by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (respectively, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] the tariff offered by integrated upstream firms (respectively, pure upstream firms).

2. Technology Choice Stage: manufacturers choose the technology standard.

3. Product-Market Competition Stage: the manufacturers that decide to pay the tariff(s) set product-market quantities.

At equilibrium, direct competition between [V.sub.1] and [U.sub.1] implies that the linear component of the efficient sources' tariff is equal to respective marginal costs (i.e., [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]). Thus, all downstream firms are active and the fixed fees set by [V.sub.1] and [U.sub.2] are given by each licensor's contribution to manufacturers' Cournot profits, that is

(30) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(31) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

implying that the inefficient sources ([U.sub.1] and [V.sub.2]) remain inactive on the upstream market. The results in Proposition 7 follow.

PROPOSITION 7. (Standard adoption with ex-ante licensing and two-part tariffs) Assume that active licensors set their tariffs before their technologies have been employed by manufacturers, then at the licensing stage [V.sub.1] offers [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [U.sub.2] offers[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Consequently, manufacturers employ S (([[tau].sub.1], [[??].sub.2]) as the technology standard.

To summarize, with ex-ante licensing S (([[tau].sub.1], [[??].sub.2])) is chosen as the technology standard and downstream firms produce [q.sup.c](c, 0) = (1 - c)/4. All this leads to the following payoffs:

(32) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(33) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(34) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (the working assumption in this section). Finally, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

C. Licensing Rule Decision with Two-Part Tariffs

In this section, the choice of the SSO licensing policy with two-part tariffs is analyzed. For a licensing rule to be adopted, a majority of SSO's members must vote in favor of either ex-post or ex-ante licensing. The choice of the licensing policy at equilibrium is given in Proposition 8, the proof is relegated to the Appendix. We assume that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], so that manufacturers' profits are all positive under ex-ante licensing.

PROPOSITION 8. (Licensing rule choice with two-part tariffs) Let the choice of the licensing rule be taken by all SSO's members and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The policy of ex-ante licensing is adopted if, and only if[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Ex-post licensing is adopted if, and only if, [DELTA] [member of] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Finally, if the licensing rule would be chosen by the planner, she would always adopt ex-ante licensing.

In analogy to Proposition 4, Proposition 8 provides the conditions for the choice between ex-ante and ex-post licensing in a framework with two-part tariffs. Moreover, the proposition shows that ex-ante licensing is constrained efficient.

Note that [U.sub.1] is indifferent between ex-post and ex-ante licensing, thus, as for Proposition 4, it is assumed that it votes for ex-post licensing. [D.sub.3] prefers ex-ante licensing to expost licensing because it is excluded from the downstream market under ex-post licensing. Moreover, [V.sub.2] votes for ex-post licensing because [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The position of [V.sub.1] depends on the value of [DELTA]. If [DELTA] is lower than min [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], then [V.sub.1] votes for ex-post licensing. Conversely, as [DELTA] increases above min [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], [V.sub.1] votes for ex-ante licensing. This implies that if [DELTA] lies below min [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] ex-post licensing is chosen at equilibrium.

The intuition to the results in Proposition 8 follows the same insights developed below Proposition 4: as [DELTA] increases, the rents that [V.sub.1] can extract under an ex-ante licensing policy increase to the point that [V.sub.1] prefers ex-ante to ex-post licensing. In Proposition 8, we also find that with twopart tariffs ex-ante licensing generates a larger TS than ex-post licensing. This means, ex-ante licensing is constrained efficient. To conclude, we remark that if ex-post licensing is chosen at equilibrium, it implies the inefficient exclusion of firm [U.sub.2] from the standard.

REMARK 1. (Inefficient exclusion of [[??].sub.2]) If the conditions for the choice of ex-post licensing are met, [[??].sub.2] is inefficiently excluded from the technology standard.

Remark 1 stresses that the inefficient exclusion of the pure upstream firm [U.sub.2] can arise as an outcome of manufacturers' technology choice and SSO members' decision on the licensing rule even in a setting with two-part tariffs.

VI. CONCLUSION

Motivated by the intense debate in the literature on law and economics (e.g., Gilbert 2011; Lerner and Tirole 2006; Swanson and Baumol 2005) and by a number of high-profile Antitrust cases (e.g., the Rambus and Qualcomm cases, among others), we study how the conflicts between firms with different business structure affect an ideal SSO participant's decisions regarding the technological specification of the standard and the licensing rule of the organization. We provide the conditions under which a licensing regime that grants monopoly power to the licensors whose technology is in the standard (ex-post licensing) is employed by the SSO. Importantly, we find that the adoption of ex-post licensing might lead to the exclusion of the technology developed by an efficient pure licensor. Finally, it is shown that a policy of ex-ante licensing, whereby firms compete for the adoption in the standard, is generally more efficient than ex-post licensing.

These results, and in particular the one on the efficiency of ex-ante licensing, are derived in a model that captures the impact of post- versus pre-standard pricing decisions on standard's specification, but not the effects of collusion within ex-ante licensing negotiations. The analysis of collusion in standard setting and its impact on standard's technological composition are left for future research.

ABBREVIATIONS

CS: Consumer Surplus

RAND: Reasonable and Nondiscriminatory

SPE: Subgame Perfect Nash Equilibrium

SSOs: Standard Setting Organizations

TS: Total Surplus

doi: 10.1111/ecin.12112

APPENDIX

Proof of Proposition 4

Proof. Denote [DELTA] = [??] - c > 0. First note that Equations (23), (24), and (25) are positive if [DELTA] < [DELTA] (c) = (1 -2c)/2. Therefore, assume c [member of] (0,1/2) and [DELTA] < [bar.[DELTA]] (c). Given the results in Propositions 1 and 2, it is clear that, independently from the value of c, [D.sub.3] votes for an ex-ante licensing policy ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) and [U.sub.1] is indifferent between ex-ante and ex-post licensing. In what follows, it is assumed that [U.sub.1] votes for ex-post licensing.

If c [less than or equal to] [c.sup.-P], [V.sub.2] votes for ex-post licensing, because [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Moreover, [U.sub.2] votes for ex-ante licensing," because it would be inactive under ex-post licensing. Finally, [V.sub.1] prefers ex-post licensing if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] can be rewritten as

(A1) [1 + 4[c.sup.2] - 12(1 - [DELTA]) [DELTA] - 4c (1 - 6[DELTA])] /16.

Equation (A1) is weakly positive if [DELTA[ [member of] (0, [[DELTA].sup.*] (c)] with [[DELTA].sup.*] (c) = (3 - [square root of 6] (1 - 2c)/6 < [bar.[DELTA]] (c). Therefore, for ex ante licensing to be adopted by the SSO it is sufficient that [DELTA] > [[DELTA].sup.*] (c) ([V.sub.1], [U.sub.2], and [D.sub.3] have the majority of votes). Instead, ex-post licensing is adopted if [DELTA] [less than or equal to] [[DELTA].sup.*] (c), so that [V.sub.1], [V.sub.2], and [U.sub.1] have the majority of votes.

If c > [c.sup.-p], [V.sub.2] votes for ex-ante licensing, because it is inactive under ex-post licensing ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]). Therefore, for ex-post licensing to prevail the necessary and sufficient condition requires that [V.sub.1] and [U.sub.2] vote for it. [V.sub.1] votes for ex-post licensing if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

In turn, [U.sub.2] votes for ex-post licensing if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], that is, if

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

It follows that for ex-post licensing to prevail it must be that [U.sub.2] votes for it ([DELTA] [member of] [[DELTA].sup.***] (c), [bar.[DELTA]] (c)) and [V.sub.1] votes for it ([DELTA] [member of](0, [[DELTA].sup.**] (c)]). In turn, ex-ante licensing is adopted if [DELTA] [member of] ([[DELTA].sup.**] (c), [bar.[DELTA]](c)) or [DELTA] [member of] (0, [[DELTA].sup.***] (c).

Proof of Proposition 5

Proof. We first show that ex-post licensing is always less efficient than ex-ante licensing below [c.sup.-p]. For c [greater than or equal to] [c.sup.-p], the difference between the TS generated by ex-post licensing and the TS associated to ex-ante licensing is equal to

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

and takes a negative value for all 0 < c < 1/2 and [DELTA] [member of] (0, [bar.[DELTA]](c)). This proves the first part of the claim in the proposition.

In the following, we compare the TS associated to expost licensing and the TS generated by ex-ante licensing for c > [c.sup.-p]. It is found that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

This difference is negative if c [member of] ([c.sup.-p], [??] ([DELTA])), with

[??]([DELTA]) = 2(1-[DELTA])/5 [member of](?,l/2),

positive otherwise. This completes the proof.

Proof of Lemma 2

Proof. To start with, notice that if firm [V.sub.i] to set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], then it would raise the royalty rate up to push [D.sub.3] and [V.sub.k], with i,k = 1,2 and i [not equal to] k. out of the market and be the downstream monopolist. Then, the best reply by [V.sub.k] would be to set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and extract [V.sub.i]'s downstream rent.

If[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], in order to determine the equilibria of the licensing game we analyze firm [V.sub.k]'s best response to the fixed fee set by[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (20) There are two relevant thresholds: the Cournot profit ([[pi].sup.c] (c, c)) and the monopoly profit ([[pi].sup.m] (c, c)). Consequently, three cases must be considered.

1. Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. If [V.sub.k] to reply with[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], then it would be a monopolist and attain profits equal to[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Instead, if [V.sub.k] were to set[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], then it would obtain profits equal to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Therefore, the best response by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is to set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and obtain [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. This is indeed optimal because [[pi].sup.m](c, c) > 3[[pi].sup.c](c, c). At [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], [V.sub.i] and [D.sub.3] would stay out of the downstream market and gain, respectively, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

2. Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Given [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], firm [V.sub.k] would be active only if monopolist, instead it would not find it profitable to produce if oligopolist. In particular, if firm [V.sub.k] were to reply with[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], then it would be a monopolist and gain[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. If [V.sub.k] would set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], it would stay out of the market and fully extract [V.sub.i]'s monopoly profit ([[pi].sup.m](c, c)). Finally, [V.sub.k] might set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], at which it would be inactive and have incentive to raise its fee further. Therefore, the best response by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is to set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], at which [V.sub.i] would be the downstream monopolist and [V.sub.k] would squeeze all [V.sub.i]'s profits, thus [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Finally, [D.sub.3] would be inactive ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]).

3. Let[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Firm [V.sub.k] is out of the market independently from the fee it sets. Therefore, [V.sub.k]'s optimal response prescribes to set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], stay out of the product market and extract all [V.sub.i]'s downstream revenue.

It follows that, under independent licensing and technologies [[tau].sub.1] and [[tau].sub.2] in the standard, the Nash equilibria of the licensing game feature is as follows:

* [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]: at these equilibria firm [V.sub.i] is active as monopolist. whereas firms [V.sub.k] and [D.sub.3] are excluded. However, [V.sub.k] extracts all firm [V.sub.i]'s downstream profits. Hence, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Note that there does not exist any equilibrium where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], because the best reply by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] would be to set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Proof of Lemma 4

Proof. First, firm [U.sub.2] sets [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to avoid double marginalization, which would distort downstream firms' production decisions and tamper industry profits. Moreover, note that if [V.sub.1] would sets [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] it would raise the linear component so as to monopolize the downstream market. In turn, it would have all its downstream rent extracted by [U.sub.2] through the fixed fee.

Now, let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. In the following, the best response of [V.sub.1] to the fee set by [U.sub.2] is analyzed.

1. Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] can reply in two possible ways: the first would be to set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the second would be to set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], [V.sub.2] and [D.sub.3] would not operate. More specifically, [V.sub.1] would gain [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], whereas the payoffs of [V.sub.2] and [D.sub.3] would be nil. Finally, [U.sub.2] would extract [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] from [V.sub.1]. If [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the profit of [V.sub.1] would be equal to it [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], firms [V.sub.2] and [D.sub.3] would gain [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] would extract [[pi].sup.2](c, 0) from [V.sub.1]. (21) Clearly, [V.sub.1]'s best response is to set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], operate as monopolist and obtain [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

2. If [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], a downstream firm would be active only if monopolist. By setting [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], [V.sub.1] would force [V.sub.2] and [D.sub.3] to stay out of the market so to gain it [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], instead [U.sub.2] would extract [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] from [V.sub.1]. Otherwise, by setting [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] would stay out and extract the profits of the active downstream firm, which, although monopolist, would be left with zero profits because [U.sub.2] would extract [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] from the downstream market. [V.sub.1] optimal response is to set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], at which, independently from whether it would be the downstream monopolist or not, it would raise zero profits. At the same time, [V.sub.2] and [D.sub.3] would gain zero profits, whereas [U.sub.2] would obtain [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

3. If [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], all manufacturers stay out of the market. Therefore, all firms would earn zero profits.

First note that it is a dominant strategy for firm [U.sub.2] to set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], with [eta] arbitrarily close to zero. Consequently, it is an equilibrium for firm [V.sub.1] to set a tariff equal to[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], at which one between [D.sub.3] or [V.sub.1] is active as monopolist, or one tariff between [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], at which [V.sub.1] is active as monopolist. In either case, the profits of the downstream monopolist would be extracted by [U.sub.2]. Thus, at the unique equilibrium the payoffs of [V.sub.1], [D.sub.3], and [V.sub.2] are nil [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

One may find counterintuitive that firm [U.sub.2] takes all the industry profit and firm [V.sub.1], which has a complementary technology, takes none, and also wonder whether there exist other equilibria where [V.sub.1] is able to extract a part of the industry surplus. In fact, this never occurs. Suppose there is a candidate equilibrium where [V.sub.1] sets [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [U.sub.2] sets [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], with k [member of] (0,1 ], (22) At this equilibrium, [U.sub.2] would obtain a payoff equal to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], but it would have an incentive to deviate and set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. If [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], [V.sub.2] and [D.sub.3] would never produce because they would not be able to recover the cost of the fees, even if [V.sub.1] does not produce. Instead, if [V.sub.1] produces it will not have to pay the fee for the use of technology [[tau].sub.1], so there is a continuation equilibrium where [V.sub.1] sells, [V.sub.2] and [D.sub.3] do not, and [V.sub.1] transfers all the monopoly profit to [U.sub.2] through the fee. This shows that the unique equilibrium consists in the one identified above, where firm [U.sub.2] extracts all the monopolistic rents from the industry.

Proof of Proposition 8

Proof. Given the results in Propositions 6, 7, and 8, it is clear that [D.sub.3] votes for an ex-ante licensing policy [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) and [U.sub.1] is indifferent between ex-ante and ex-post licensing (thus, as in Proposition 4, in what follows assume that [U.sub.1] votes for ex-post licensing).

[U.sub.2] votes for ex-ante licensing, because it would be inactive under ex-post licensing. Instead, [V.sub.2] votes for expost licensing, because [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Finally, [V.sub.1] prefers ex-post licensing if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] can be rewritten as

(A2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Equation (A2) is weakly positive if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Therefore, for ex-ante licensing to be adopted it is sufficient that [DELTA] > min[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], so that [V.sub.1], [U.sub.2], and [D.sub.3] would have the majority of votes. Instead, ex-post licensing is adopted if [DELTA] [less than or equal to] min [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], so that [V.sub.1], [V.sub.2]. and [U.sub.1] would have the majority of votes.

Finally, by comparing [bar.T][S.sup.p] ([[tau].sub.1], [[tau].sub.2]) = 3[(1- 2c).sup.2]/8 with [bar.T][S.sup.a] ([[tau].sub.1], [[??].sub.2]) = 15[(1- 2c).sup.2]/32, it turns out that the planner would choose ex-ante licensing.

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(1.) Gandal. Salant, and Waverman (2003) documents that in ETSI the voting rule allowed even a small minority of manufacturers to impose their favorite standard configuration. Moreover, the evidence collected by the FTC in the FTC v. Rambus case shows that JEDEC, the SSO that was deciding on the SDRAM standard, was mostly composed by vertically integrated manufacturers.

(2.) For instance, the board of directors of JEDEC (the SSO of the Rambus case) includes representatives of pure developers (e.g., Micron and Qualcomm) and integrated companies (e.g., IBM and Nokia), see http://www.jedec.org/about-jedec/board-directors.

(3.) In particular, VITA has adopted a policy that requires patent holders to disclose the maximum royalty rates they will demand for essential rights. Instead, IEEE patent policy permits (but does not require) a holder to provide a maximum license rate.

(4.) The licensors who participate to SSOs are often required to commit to license their technologies on reasonable and non-discriminatory (RAND) terms in the case of adoption by manufacturers. A patent holder commitment to license to any interested party on RAND terms implies that each licensee can obtain a license at the royalty rate established by the patent holder and is not put in comparative disadvantage with respect to other licensees.

(5.) SSOs adopt licensing policies that are general, not standard specific. This means that, in real SSOs the choice of the licensing policy is likely to be determined by expectations of the parameter values over families of standards.

(6.) Wang (1998) compares the profitability of licensing contracts with linear royalties and fixed fees for a monopolist licensor that also competes in a downstream duopoly. Although this work shares some analogies with Wang (1998), the author is not interested in the analysis of the optimality of the type of licensing contract but rather in whether producers' optimal technology choice changes with the type of licensing contract.

(7.) As far as VITA is concerned, see http://www. justice.gov/atr/public/busreview/219380.pdf. The guidelines to IEEE licensing policy are at http://www. justice.gov/atr/public/busreview/222978.pdf.

(8.) Guidelines on the applicability of Article 101 of the Treaty on the Functioning of the European Union to horizontal co-operation agreement.

(9.) Schmalensee (2009) focuses on the analysis of the strategic pricing decisions taken by integrated firms and vertically-specialized operators, and then on the pricing schemes that may solve the holdup problem. Schmidt (2014) finds that, compared to a situation in which only vertically integrated firms are active, the presence of pure upstream innovators triggers royalty rates' and final output's decrease: this result is driven by the incentive that vertically integrated firms have to raise the cost of the inputs sold to downstream rivals (the raising rival's cots problem).

(10.) Indeed, could the upstream firm compensate [V.sub.2] for the profit loss suffered when the latter does not cross-license with [V.sub.1], then the standard would always incorporate the technology of the stand-alone upstream firm.

(11.) An exception is provided by Reisinger and Tarantino (2011), who investigate the welfare consequences and the profitability of vertical integration in a setting with complementary inputs and secret offers.

(12.) Most of the economic literature on licensing has studied the anticompetitive effects imparted by upstream pricing decisions on the downstream market. More specifically. Rey and Salant (2012) analyze the impact of alternative licensing policies by owners of essential intellectual property on downstream competition. Lin (1996) shows that firms can use licensing agreements to collude on the product market. Analogously, Eswaran (1994) proves that cross-licensing constitutes a device that facilitates collusion among downstream horizontal competitors.

(13.) These assumptions imply that all technologies have been disclosed by the SSO's licensors. For an analysis of the impact of patent disclosure on firms' incentives to participate in that standardization process, see Ganglmair and Tarantino (2012) and Ganglmair and Tarantino (2014).

(14.) The "compulsory standard" assumption can be relaxed to show that analogous results would arise if at the technology choice stage manufacturers are allowed to adopt competing technologies.

(15.) Reasonableness requires that licensing decisions taken before technology adoption must be consistent with those decided after technology's employment by manufacturers, so to avoid excessive royalties due to the lack of competitive alternatives.

(16.) Note that the tie-break rule is that, if indifferent, a manufacturer chooses the technologies of the efficient sources ([[tau].sub.1], and [[??].sub.2]).

(17.) Were [U.sub.1] to vote by randomizing between the two policies the crucial results of the paper would not change, but their exposition would be more tedious.

(18.) If only manufacturers were to decide on the licensing rule, ex-post licensing would always be employed below c. In other words, in this case ex-post licensing would be even more likely to emerge as the SSO licensing policy.

(19.) Integrated organizations participate in SSOs striving for the achievement of coordination among industry participants on the adoption of a technology standard, so to secure the ensuing economic benefits (due, e.g., to network effects or economies of scale). Consequently, they have a clear interest in paying low rates for standard's technologies and being competitive on the product market. In turn, pure developers of new technologies raise their revenue from the technology licensing market. They are primarily interested in having a patented technology into a new standard, because this would insure a long stream of licensing revenue.

(20.) Due to symmetry, [V.sub.i]'s best response will be analogous.

(21.) Indeed, if [U.sub.2] to set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] then it would have the incentive to raise it further.

(22.) In the continuation equilibria, either [V.sub.1] is the monopolistic supplier, gaining [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], or one between [V.sub.2] and [D.sub.3] is the monopolistic supplier, with [V.sub.1] gaining k[[pi].sup.c] (c, 0). In both cases, the payoff of [U.sub.2] would be(1 -k) [[pi].sup.m](c, 0).

EMANUELE TARANTINO , The support of TILEC (Tilburg University), where the first draft of this paper was completed, is gratefully acknowledged.

Disclaimer: This paper is a revised version of Chapter 2 of Tarantino's Ph.D. Thesis (European University Institute, 2010). He benefited from comments by Vincenzo Denicolo, Bernhard Ganglmair, Renato Gomes. Massimo Motta, Patrick Rey, David Salant, Klaus Schmidt and the participants in various conferences and seminars. The usual disclaimer applies. Tarantino: "Franco Modigliani" Research Fellow, Department of Economics, University of Bologna, Bologna 1-40126, Italy. Phone +390512098885, Email Emanuele.Tarantino@unibo.it; TILEC, Tilburg University, Tilburg 5037 AB, the Netherlands

TABLE 1
Adoption of S ([[tau.sub.1], [[tau.sub.1])

                       Independent                Cross-Licensing
                       Licensing

[MATHEMATICAL          (5 + c)/11,                (1 + 2c)/4,
EXPRESSION NOT         (5 + c)/11                 (1 + 2c)/4
REPRODUCIBLE IN
ASCII]
                       2(1-2c)/l 1,
[MATHEMATICAL                                     (1 - 2c)/4,
EXPRESSION NOT         2(1-2c)/11,0               (1 - 2c)/4, 0
REPRODUCIBLE IN
ASCII]

Q, P(Q)                4 (1 - 2c)/11,             (1 - 2c)/2,
                       (7 + 8c)/11                (1 + 2c)/2

CS                     8[(1 - 2c)                 [(1 - 2c).sup.2]/8
                       .sup.2]/121

[MATHEMATICAL          14 [(1 - 2c).sup.2]/121,   [(1 - 2c).sup.2]/8,
EXPRESSION NOT         14 [(1 - 2c).sup.2]/       [(1 -2c).sup.2]/8,
REPRODUCIBLE IN        121, 0, 0, 0               0,0,0
ASCII]

TS                     36[(1 -2c)                 3[(1 -2c).sup.2]/8
                       .sup.2]/121

TABLE 2
Adoption of S ([[tau].sub.1], [[??].sub.2])

[MATHEMATICAL EXPRESSION          (1 - c)/2
NOT REPRODUCIBLE IN ASCII]

[MATHEMATICAL EXPRESSION       (1 - c)/4. 0, 0
NOT REPRODUCIBLE IN ASCII]
Q, P(Q)                      (1 - c)/4, (3 + c)/4

CS                             [(1 - c).sup.2]/32

[MATHEMATICAL EXPRESSION     [(1 - c).sup.2]/l6. 0,0.0.
NOT REPRODUCIBLE IN ASCII]     [(1-c).sup.2]/8

TS                           7[(1 - c).sup.2]/32
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Author:Tarantino, Emanuele
Publication:Economic Inquiry
Date:Jan 1, 2015
Words:14823
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