International Journal of Industrial 28 (2010) 244–253 Int. J. Ind. Organ. 28Organization (2010) 244–253

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International Journal of Industrial Organization j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j i o

Complements and potential competition Mikko Packalen Department of Economics, University of Waterloo, Ontario Canada N2L 3G1

a r t i c l e

i n f o

Article history: Received 5 January 2008 Received in revised form 27 August 2009 Accepted 31 August 2009 Available online 6 September 2009 JEL classification: K11 K21 L24 L41 Keywords: Complements Monopoly Entry inducement Cooperation Double marginalization Double monopoly

a b s t r a c t In this paper we examine the effect of cooperation between complementary incumbent monopolists on consumer welfare. While divided technical leadership makes it difficult for firms to integrate into complementary markets, firms induce entry in complementary markets by reducing the cost of entry in those markets. This is accomplished through, for example, the development and dissemination of royaltyfree intellectual property. We present and analyze a model in which incumbents can influence the ease of entry in complementary markets. Cooperation between complementary monopolists decreases consumer welfare by reducing or even eliminating the entry inducement incentive but increases consumer welfare by eliminating double marginalization. We show that cooperation may decrease consumer welfare, contrary to Cournot's celebrated double monopoly result, and that the welfare comparison can be determined in terms of straightforward economic concepts. We also present and analyze a model in which each incumbent can induce entry in the complementary market through long-term price commitments which are common in patent licensing. © 2009 Elsevier B.V. All rights reserved.

1. Introduction In this paper we examine the effect of cooperation between complementary monopolists on consumer welfare. The importance of the complementary monopoly problem has increased due to both the fragmentation of patent ownership and the divided technical leadership in the computer industry. Recent analyses of cooperation between complementary patent owners have followed the double monopoly analysis of Cournot (1838) by focusing on the effect that double marginalization has on consumer welfare (see e.g. Shapiro (2001), Gilbert (2004) and Lerner and Tirole (2004)). In contrast, during United States v. Microsoft several analyses suggested that the divestiture of Microsoft's operating system and applications monopolies might benefit consumers because the two complementary monopolists would then have an incentive to facilitate entry against each other.1 The total effect of cooperation between complementors on consumer welfare depends on the impacts that cooperation has on consumer welfare through the elimination of double marginalization and through the reduction or elimination of the entry inducement incentive. However, the combined effect of cooperation through

E-mail address: [email protected]. See the declaration by Rebecca M. Henderson (http://www.usdoj.gov/atr/cases/ f219100/219129.htm), the declaration by Paul M. Romer (http://www.usdoj.gov/atr/cases/ f219100/219128.htm) and, the declaration by Carl Shapiro (http://www.usdoj.gov/atr/cases/ f219100/219127.htm). 1

0167-7187/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ijindorg.2009.08.005

these two channels has not been formally explored in the case that both monopolists face potential competition. To fill this gap, we formally examine the impact of cooperation between two complementary monopolists in two models that incorporate both the static double marginalization phenomenon and the dynamic entry inducement mechanism. The cooperative case in our analysis corresponds to the integrated case with the restriction that an integrated firm does not commit to bundling of its products. If an integrated firm can commit to bundling of its products through technical bundling, integration can create the twolevel entry problem (see Choi and Stefanadis, 2001; Dennis and Waldman, 2002). This potential effect of integration is separate from the effect that cooperation (or integration) has on the equilibrium outcome through the internalization of the entry inducement externality, which can be achieved without even contractual bundling.2 Among firms, the means to induce entry are numerous, and the incentive to induce entry into complementary markets appears to be well understood at least in the computer industry. For example, as Gawer and Henderson (2007) discussed, Intel has a long history of inducing entry into complementary markets by lowering the cost of entry in these markets. Intel has achieved this largely through the

2 Because an integrated firm would in some cases choose technical bundling over entry inducement, and technical bundling lowers entry even relative to the case without entry inducement, our cooperative case represents an upper bound for consumer welfare in the integrated case.

M. Packalen / Int. J. Ind. Organ. 28 (2010) 244–253

development and royalty-free dissemination of intellectual property. Another example of entry inducement is IBM's support of Linux. As Yoffie and Kwak (2006) describe, IBM has donated vast amounts of money, people and intellectual property to advance the development of Linux and thereby reduce IBM's dependence on Microsoft's products. A third example of entry inducement in the computer industry is Microsoft's continued support of AMD in an effort to maintain and strengthen AMD as a competitor of Intel. Microsoft has successfully demanded that Intel share technologies such as the MMX multimedia technology with AMD (see Yoffie and Kwak, 2006) and Microsoft and AMD have collaborated on the development of new products.3 In our formal analysis we examine two models, an ease of entry model and a price commitment model. In both models two complementary monopolists face potential entry, and entry is uncertain. The entry inducement mechanism is the only difference between the models. Together the analyses demonstrate that the impact that cooperation (or integration) has on consumer welfare is very modelspecific when also entry inducement is considered. The optimal policy must therefore be solved on a case-by-case basis. Our analysis offers constructive guidance on how such policy analyses can be conducted in practice as we show that the equilibrium comparison can be characterized in terms of straightforward and empirically malleable economic concepts. In the ease of entry model each incumbent monopolist can induce entry into the complementary market by lowering the marginal cost of entry in the complementary market. As the aforementioned examples suggest, this reduction in the marginal cost of entry is achieved by, for example, developing and disseminating royalty-free intellectual property or other technological know-how. We compare the expected consumer surplus when the two complementary incumbent monopolists set the entry cost parameters and prices non-cooperatively and when the incumbent monopolists set the entry cost parameters and prices cooperatively. We show that consumer surplus can be higher in the non-cooperative case than in the cooperative case, contrary to the celebrated double monopoly result of Cournot (1838). Importantly, while the comparisons of equilibrium outcomes in the cooperative and non-cooperative cases are ambiguous, throughout the paper we demonstrate that the comparison can be characterized in terms of straightforward economic concepts, namely the demand curve, the probability of entry without entry inducement, and the rewardelasticity of the probability of entry. The non-cooperative and cooperative cases yield different equilibrium outcomes because of the presence of two externalities: the entry inducement externality and the double marginalization (pricing) externality. These externalities are internalized only in the cooperative case. Internalization of these externalities has generally opposing effects on consumer welfare. If neither incumbent is displaced by an entrant, cooperation avoids double marginalization in pricing, and thereby decreases prices and increases consumer surplus relative to the non-cooperative case. In contrast, internalization of the entry inducement externality generally reduces and may even eliminate the entry inducement incentive, and thereby decreases the probability of entry and the expected consumer surplus. In the price commitment model each incumbent monopolist can induce entry into the complementary market through a long-term price commitment in their own market. Long-term price commitments are common in patent licensing. For example, the license to patents that cover the ATCS standard does not expire until the end of the year 2016. In addition to the royalty rate commitment until the end of the year 2016, the license includes a commitment not to increase royalty rates to current licensees by more than 10% during each 5-year renewal period 3 See e.g. the press release “AMD Collaborates With Microsoft on Windows Server 2008 to Deliver Industry Leading Solution to Customers” (available at http://www. microsoft.com/presspass/events/HHH launch/docs/amd.doc; last accessed 27 March 2009).

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after the year 2016.4 We emphasize that while our analysis shows that entry inducement is one rationale for long-term price commitments, we neither develop an empirical test for whether entry inducement is an important factor in patent licensing nor offer direct evidence on the motives of licensors in setting the licensing terms. In the analysis of the price commitment model, we compare the expected consumer surplus when the incumbents set prices noncooperatively and when the incumbents set prices cooperatively. These two pricing arrangements yield different outcomes because of the presence of the entry inducement externality and double marginalization (pricing) externality. We show that non-cooperative pricing can yield higher expected consumer surplus than cooperative pricing. However, this happens only for a limited set of parameterizations of the model. Hence, while the analysis shows that entry inducement can again overturn Cournot's celebrated double monopoly result, the results do not warrant prohibiting complementary patent owners from forming patent pools that set prices cooperatively.5 Our analysis departs from the earlier analyses of complementary monopolists in the presence of entry by Farrell and Katz (2000), Choi et al. (2003), Heeb (2003), and Cheng and Nahm (2007) in two ways. First, we assume that both incumbent monopolists face potential entry. When an incumbent monopolist itself also faces potential entry its incentive to induce entry into its complementary market is limited because inducing entry against the complementary incumbent monopolist indirectly also increases entry against the monopolist itself. We show that inducing entry against the complementary incumbent can nevertheless be profitable if entry is uncertain. Second, we assume that the complementary incumbent monopolists themselves do not enter their complementary markets but instead induce entry by other firms. Due to divided technical leadership entry into complementary markets by incumbent monopolists is often difficult (see Bresnahan, 2004), and therefore entry inducement is often a more realistic scenario. Casadedus-Masanell et al. (2007) provide a related analysis but focus on the effect of actual competition in one market on the complementary monopolist's profit in another market. Our analysis is obviously closely related to the Chicago School's single-monopoly-rent theorem and the more recent analyses on

4 The license is offered by the patent pool organization MPEG LA. The License Agreement is available at http://www.mpegla.com/atsc/atsc-agreement.cfm; last accessed 27 March 2009. 5 In the working paper version of our paper we examine two extensions of the price commitment model that demonstrate that forms of cooperation that fall short of full integration can have significant pro-competitive benefits compared to full integration. In the first extension we compare the cooperative outcome with the outcome when the incumbents cooperatively set the price of the bundle of both incumbent goods but noncooperatively set the price of each individual good. Such independent pricing provisions are common in patent licensing (see Lerner et al., 2007). In the second extension we examine the impact of independent pricing provisions on ex-ante consumer welfare which takes into account the effect that the pricing regime has on the incumbents' expected profit and, consequently, on the probability that the incumbent innovations are invented in the first place. The results indicate that if cooperation does not have pro-competitive effects other than the elimination of double marginalization, antitrust authorities should require that patent pooling be accomplished through a patent pool that allows for independent licensing rather than a cooperative arrangement that does not allow for independent licensing such as a merger, the acquisition of patents, or a patent pool that does not allow for independent licensing. This policy conclusion illustrates the importance of taking the entry inducement incentive into account as the current policy is to allow both types of cooperative arrangements between the owners of complementary patents and independent licensing provisions are seen only as protection against pooling of patents that are substitutes (see U.S. F.T.C./D.O.J. Antitrust Guidelines for Licensing of Intellectual Property, 1995, and U.S. D.O.J. Business Review Letters, 1997, 1998, 1999). The policy is largely based on the analysis of Cournot (1838) which recent articles on cooperative pricing of complements (Economides and Salop, 1992, Economides, 1999, Shapiro 2001, Gilbert, 2004, Lerner and Tirole, 2004) have reiterated and reinforced. Pooling of intellectual property has also been addressed in many law review articles (see e.g. Gollier, 1968, Tom and Newberg, 1997, Merges, 1996, 2001, and Carlson, 1999). These contributions echo the existing economics literature by distinguishing between competing and complementary patents. A novel conceptual contribution of our analysis is that the same two patents can be ex-ante substitutes but expost complements. According to Nalebuff (2003), the case when two goods are ex-ante substitutes but ex-post complements has not come up in the antitrust literature.

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M. Packalen / Int. J. Ind. Organ. 28 (2010) 244–253

monopoly leveraging.6 Whinston (1990) notes that a monopolist benefits from increased competition in a complementary market but does not examine the incentives for cooperation between firms with market power in complementary markets or the case with entry threats in both markets.7 Dennis and Waldman (2002) note that entry in a complementary market can affect entry in the essential good market but their analysis relies on inter-temporal cost efficiencies whereas our analysis centers on the effect that entry in one market has on the rewards for entry in a complementary market.8 Choi and Stefanadis (2001) and Gilbert and Katz (2006) examine tying of two complementary goods by a monopolist that faces potential entry. Neither analysis examines cooperation, integration, or double marginalization. Bresnahan and Greenstein (1999) argue that in the computer industry divided technical leadership across vertical components of platforms has been inevitable and made entry easier. We examine and provide formal analyses of specific channels that allow firms to influence entry in complementary markets. In the analyses of bundling by a monopolist by Nalebuff (2004) and Gilbert and Katz (2006), price commitments provide the means for entry deterrence, and in Gilbert and Katz (2006) price commitments also facilitate complementary investments by buyers. In our analysis price commitments facilitate the inducement of entry. Our analysis of the price commitment model differs also from the analysis of forward contracting and quantity competition by Allaz and Vila (1993) as we consider option contracting and complements.9 This paper is organized as follows. In the next section we present and analyze the ease of entry model with homogenous potential buyers. With homogenous potential buyers only the entry inducement externality is present. In the third section we then extend the ease of entry model to the case with heterogenous potential buyers so that both the double marginalization externality and the entry inducement externality are present. In the fourth section we present and analyze the price commitment model. The fifth section concludes.

2. The ease of entry model with homogenous buyers In this section we compare the non-cooperative and cooperative outcomes in a model with homogenous potential buyers. Only the entry inducement externality is present in the model.

2.1. The model with homogenous potential buyers We consider a setting with two incumbent monopolists, two potential entrants, and a unit mass of homogenous potential buyers. Incumbent 1 sells good 1, and incumbent 2 sells good 2. Absent entry, the incumbents' goods are perfect complements, and each potential buyer's valuation for the two incumbent goods is υ. The number of potential buyers is large enough to justify the assumption that the potential buyers are price-takers. 6 The single-monopoly-rent theorem states that a monopolist cannot increase its profits by monopolizing a competitive complementary market. The single-monopolyrent theorem was presented in Director and Levi (1956, p. 290) and Bowman (1957, p. 21), and later in Posner (1976, p. 173) and Bork (1978, p. 373). 7 See also Judge Richard Posner's opinion in Olympia Equipment Leasing Co. v. Western Union Telegraph Co., 797 F.2d 370, 374 (7th Cir. 1986) and Farrell and Weiser (2003). 8 Bresnahan (2004) notes that with network externalities the sudden development of a complementary market can increase the demand for the essential good so dramatically that the incumbent monopolist's essential good installed base advantage is threatened. This effect of increased provision of complementary goods was first understood by the Microsoft Corporation (see Bresnahan, 2004). 9 In contrast with the contestable markets literature (see e.g. Baumol et al., 1982, and Stefanadis, 2003), we assume that the potential entrants cannot contract with potential buyers before they enter. Asymmetric information about the potential entrants' capabilities and the quality of their final product makes such contracting between buyers and potential entrants unlikely in the type of innovative environments that motivate our analysis.

Potential entrants 1 and 2 attempt entry against the incumbents 1 and 2, respectively. Each buyer's marginal valuation for a successful entrant's good instead of the corresponding incumbent good is Δ.10 Therefore, each buyer's valuation for one incumbent's good and the complementary entrant's good is υ + Δ, and each buyer's valuation for both entrants' goods is υ + 2Δ. For notational convenience we assume that production costs are zero. R&D investments by the potential entrant i increase its probability of successful entry against the corresponding incumbent, which is denoted by μ i. The R&D investment cost C(μ i) of the potential entrant i is an increasing function of its probability of success: Cðμ i Þ = F + ai μ i +

b 2 μ ; 2 i

where ai > 0 and b > 0:

ð1Þ

The assumptions ai > 0 and b > 0 together imply that each incumbent's marginal cost of increasing the probability of entry is positive
 dCðμ i Þ > 0 . This assumption captures the feature that a firm must dμ i

expand the scale of its R&D investments to increase its probability of entry. The assumption (b > 0) ensures that the cost function is convex
 d2 Cðμ i Þ dμ 2i

> 0 . This assumption captures the feature that the expansion

of R&D investments is increasingly more expensive for a firm because the limited supply of suitable R&D capabilities makes adding the required additional resources increasingly more costly. As was indicated by the examples discussed in the Introduction, firms influence potential entrants' entry costs in complementary markets by, for example, developing and disseminating royalty-free intellectual property and other technological know-how. We model this particular entry inducement mechanism by assuming that the incumbent j can influence the entry cost in the complementary P market i ≠ j by setting ai ∈ (0, a].11,12 Timing in the model is as follows. In stage 1 the incumbents set the entry cost parameters a1 and a2. In stage 2 potential entrants noncooperatively choose their R&D investment levels as measured by the associated probabilities of success μ1 and μ2, and nature subsequently reveals the outcome of these R&D investments. In stage 3 the

10 An analytically equivalent alternative is to assume that each incumbent's marginal cost of production is c¯¯, and each successful entrant's marginal cost of production cost is c¯¯ − Δ. 11 Decreasing the entry cost parameter aj of the potential entrant j ≠i is a more profitable means of inducing entry for the incumbent i than decreasing the entry cost parameter ai of the potential entrant i. This can be seen by comparing the expressions Eqs. (5) and (6), which imply that an increase in αj increases μ j more than μ i whereas an increase in αi increases μ i more than μ j. Each incumbent of course prefers increasing entry against the complementary incumbent more than increasing entry against itself. 12 The assumption that the incumbents do not influence b is justified if increasing the probability of success requires that a potential entrant implements another research project, and entry inducement (say, in the form of provision of technical know-how) has the same impact on the cost of implementing each additional research project (as reflected by a decrease in αj) whereas the entry inducement has little or no impact on the parameter b, which reflects the feature that adding the resources required to complete each additional research project is increasingly more expensive due to the limited supply of suitable resources. When an incumbent j decreases aj, it shifts the best-response curve Eq. (2) of the potential entrant j ≠i upward. If each incumbent i could instead decrease the parameter b for the potential entrant j ≠i, doing so would simultaneously shift the best-response curve Eq. (2) of the potential entrant j ≠i upward and increase the slope of that best-response curve. The increase in the slope of the best-response curve for the potential entrant j ≠i makes inducing entry less attractive for the complementary incumbent j ≠i because any entry inducement by the incumbent j ≠i now has a higher indirect impact (see the end of Section 2.2) on the probability that the incumbent j ≠i itself is displaced by an entrant. Consequently, the incumbents would induce less entry against one another in equilibrium compared to the case when each incumbent i can influence the cost parameter aj. The assumption that the incumbents do not influence F is inconsequential as we have assumed that F is such that the equilibrium probability of entry without entry inducement is strictly positive. Without the latter assumption, at least one incumbent i would always prefer to decrease F of the potential entrant j ≠i so that the equilibrium probability of entry against the incumbent j ≠i is positive.

M. Packalen / Int. J. Ind. Organ. 28 (2010) 244–253

incumbents and successful entrants set prices. If entry against the incumbent i is successful, the incumbent i and the successful entrant i engage in Bertrand competition.

potential entrant i to increase its probability of success against the incumbent i. The parameter α i therefore measures the ease of entry. Combining the two potential entrants' best-response curves Eq. (3) yields each potential entrant's equilibrium probability of entry18

2.2. Equilibrium analysis: the non-cooperative case In this subsection we solve by backward induction the equilibrium when the incumbents non-cooperatively set prices and the parameters a1 and a2 that influence the ease of entry. We focus on perfectly coalition-proof subgame-perfect pure strategy Nash equilibria.13 2.2.1. Stage 3: incumbents and successful entrants set prices When neither potential entrant is successful in entry, the price of υ each good is .14 When both potential entrants are successful in entry, 2 the prices of each entrant good and the corresponding incumbent good are Δ and 0, respectively.15 When only the potential entrant i is successful in entry, the entrant i and the corresponding incumbent i Δ set prices and 0, respectively, and the price of the complementary 2 incumbent good j is υ + Δ2 .16 2.2.2. Stage 2: potential entrants choose R&D investments Each potential entrant chooses its probability of entry to maximize its expected profit ПRi = μ iRi − C(μ i), where C(μ i) is given by Eq. (1) and Ri is the expected reward for successful entry. The first-order condition for the optimum yields μ ⁎i =

1 a R− ia: b i b i

ð2Þ Δ

Substituting Ri = ð1−μ j Þ + μ j Δ for Ri in the Eq. (2) yields the 2 best-response curve17

μ i⁎ ðμ j Þ

Δ = + 2 μj b b |{z} |{z} Δ 2 −αi

≡αi

ð3Þ

≡β

for the potential entrant i. In the above expression (3) we introduce the P definitions of αi and β. When the incumbent j ≠i chooses ai ∈ (0, a], it Δ Δ − − a P α≡2 and − α ≡ 2 . The higher effectively chooses αi ∈ [α __ , α), where − b b the incumbent j sets the parameter α i, the less costly it is for the

μi⁎ =

2

not all of the surplus created by entry. Δ 17 When only the potential entrant i is successful in entry, it receives the reward for 2 successful entry. When both potential entrants are successful in entry, each entrant receives the reward Δ for entry.

αi + βαj 1−β2

:

ð4Þ

The result (4) implies that dμj⁎

=

dαj

1 1−β2

ð5Þ

and dμi⁎ β = : dαj 1−β2

dμ ⁎j dαj

ð6Þ

Because β ∈ (0.1), the results (5) and (6), respectively, imply that > 0 and

dμ ⁎i dαj

> 0. The result

dμ ⁎j

dαj

> 0 represents the direct effect of

increasing the ease of entry against the complementary incumbent j. Lower marginal entry cost of the potential entrant j increases the probability of entry against the complementary incumbent j. The result

dμ ⁎i dαj

> 0 represents the indirect effect of increasing the ease of

entry against the complementary incumbent j. The indirect effect Δ arises because an entrant's reward for entry increases from to Δ 2 when also the complementary entrant is successful in entry as neither entrant then has to share the surplus Δ generated by its entry with the complementary incumbent. This introduces a strategic complementary in the potential entrants' entry decisions. Consequently, when an incumbent i increases the ease of entry against the complementary incumbent j, the incumbent indirectly increases also the probability of entry against the incumbent i itself. 2.2.3. Stage 1: incumbents set the ease of entry Each incumbent i chooses αj to maximize its expected profit19 
 υ Δ I Πi = ð1−μ i⁎ Þ ð1−μ j⁎ Þ + μ j⁎ υ + : 2 2

ð7Þ

The first-order condition for the optimum yields20 −

13 In the non-cooperative case we further focus only on symmetric equilibria. This rules out equilibria in which one incumbent engages in full entry inducement against the complementary incumbent (the complementary incumbent is displaced by an entrant with certainty). Coalition-proofness eliminates the equilibrium in which the incumbents engage in full entry inducement against each other (it is an equilibrium as each incumbent's action then has no impact on its expected profit). 14 All price combinations that satisfy pI1 + pI2 = υ, where pI1 is the price set by the incumbent i, form an equilibrium. We select the symmetric equilibrium with υ pI1 = pI2 = . 2 15 Each incumbent and the corresponding entrant now compete on price. This drives the incumbents' prices to zero, and each entrant sets its price equal to the buyers' marginal valuation Δ. 16 Price competition between the successful entrant i and the corresponding incumbent i drives the price of the incumbent good i to zero. Let pIj and pEi denote the prices set by the incumbent j and the successful entrant i, respectively. All price combinations that satisfy the conditions pEi ≤ Δ and pIj + pEi − υ + Δ now form an equilibrium. We select the equilibrium in which the entrant i and the incumbent j Δ divide the surplus generated by the successful entry equally, so that pIj = υ + and 2 Δ pEi = . See Gawer and Henderson (2007) on how Intel seeks to appropriate some but

247



 dμ j⁎ υ dμ i⁎ υ υ Δ Δ + μ j⁎ + + ð1−μ i⁎ Þ + = 0: dαj 2 dαj 2 2 2 2

ð8Þ

An increase in the ease of entry αj against the complementary incumbent j increases the probability of entry against the incumbent j. This benefits the incumbent i because successful entry against the complementary incumbent j increases the revenue of the incumbent i υ Δ from to υ + when the incumbent i itself is not displaced by an 2 2 entrant. The second term on the left-hand side of the expression (8) represents this direct effect of a change in αj. Because the potential entrants' entry decisions are strategic complements, increased entry against the complementary incumbent j indirectly also increases the probability of entry against the incumbent i, which lowers the 18 To limit the scope of the analysis we assume that the fixed cost F, ai, bi and Δ are such that the equilibrium probability of entry without any entry inducement is strictly positive and less than one, which requires that α __ > 0 and α __ + β < 1. Together these two conditions imply that β < 1. 19 When neither potential entrant is successful in entry, the profit of the incumbent i υ is . When only entry against the incumbent j is successful, the profit of the incumbent 2 Δ
 i is υ + .    ⁎  2 d 2 ΠIi d μ i⁎ dμ j Δ 2β υ Δ 20 Because = −2 + υ+ =− < 0, also the second2 2 2

dαj

order condition holds.

dαj dαj

2

ð1−β Þ

2

2

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M. Packalen / Int. J. Ind. Organ. 28 (2010) 244–253

expected profit of the incumbent i. The first term on the left-hand side of the expression (8) represents this indirect effect of a change in αj. Solving the first-order condition (8) yields the (candidate) equi-

incumbents never induce entry against both incumbent goods.25 Hence, α1⁎ = α . The first-order condition for the optimal α2 is26

librium probability of entry μ ⁎ =

−

ðυ + ΔÞ−βv 21 . ð1 + βÞðυ + ΔÞ

In order to charac-

"

terize the equilibrium in terms of straightforward and empirically malleable economic concepts, we replace the parameters Δ and υ

γð1 + μ Þ− μ ε

μ − − − 23 ð1 + μ + μ ε μ Þγ. −

γ>

− −

The incumbents induce entry in equilibrium (μ⁎ > μ_) if 1 1 + εμ

μ < qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi. The intuition for the former

and

−

−

condition is that each incumbent induces entry if the relative size of the additional surplus that each incumbent captures from entry against the complementary incumbent is high (which is reflected in the model by a high value of γ) because then each incumbent's benefit from successful entry against the complementary incumbent is high.24 We now collect the results obtained in this subsection in a proposition. Proposition 1. When the incumbents choose the entry parameters and prices non-cooperatively, there exists a unique symmetric equilibrium. The equilibrium level of entry is

μ = max

8 < :

μ;

−

9 γð1 + μ− Þ− μ ε μ = − −

ð1 + μ + μ ε μ Þγ; −

:

ð9Þ

− −

The incumbents induce entry (μ⁎ > μ_) if and only if γ > 1 1 and μ < qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . −

ð10Þ

−

μ εμ −− 1− μ 2 ð1 + εμ Þ − −

⁎

" # #
 dμ ⁎2 dμ ⁎1 Δ Δ + = 0: ð1−μ ⁎1 Þ + ð1−μ ⁎2 Þ υ+ 2 2 dα2 dα2

μ

υ+Δ , υ

εμ , where μ and the parameter β with _ denotes 1 +μ −  the equilibrium probability of entry without entry inducement and εμ_ denotes the reward-elasticity of a potential entrant's probability of entry when the probability of entry equals μ_.22 This yields μ ⁎ =

with γ ≡

dμ ⁎1 ⁎ dμ ⁎2 ⁎ μ2 + μ dα2 dα2 1

1 + εμ

μ εμ −− μ 2 ð1 + ε μ Þ − −

−

2.3. Equilibrium analysis: the cooperative case We now consider the case when the incumbents set prices and the parameters α1 and α2 that influence the ease of entry cooperatively. Because there is no double marginalization, cooperation alters neither the equilibrium pricing in stage 3 nor the entry equilibrium in stage 2 as a function of the parameters α1 and α2, compared to the non-cooperative case. In stage 1 the incumbents set α1 and α2 to maximize their combined Δ expected profit ΠI = ð1−μ1 μ2 Þυ + ½ð1−μ1 Þμ2 + ð1−μ2 Þμ1  . The

An increase in the ease of entry against the incumbent good 2 increases the probability that both incumbents are displaced by entrants, and that consequently the incumbents do not receive the Δ revenue υ + . This effect of an increase in α2 is represented by the 2

first term on the left-hand side of the condition (10). An increase in α2 also increases the probability that only entry against one of the incumbents is successful, and that consequently the incumbents Δ receive as their share of the surplus generated by entry. This effect is 2 represented by the second term on the left-hand side of the condition (10). Δ ½1 + β 2 − μ 1−β :27 Solving the first-order condition (10) yields μ2⁎ = 2βðυ + ΔÞ − 2β


This can be rewritten as

μ2⁎ =

1 4



1 γ

1−

1+ μ μ εμ

−

− −

incumbents thus induce entry (μ2⁎ > μ_) if γ

!

+ 1 − 12 μ

−

1 1−2 μ

1+ μ μ εμ

!

−

−1

. The

− −

1 2

and μ < . The in−

−

tuition is that the incumbents induce entry if the surplus that they capture from entry is sufficiently high (as is reflected by a high value 1 of γ) except when μ ≥ because then any increase in the probability − 2 of entry μ 2⁎ increases the probability that both incumbents are displaced more than it increases the probability that only one incumbent is displaced. The result that the incumbents induce entry in the cooperative case may seem counterintuitive, or even unrealistic. However, the observation that the cooperative case can be interpreted as the integrated case (one firm is the incumbent in both markets) and the observation that Intel has actively induced entry into complementary markets even when it has been present in those markets (see Gawer and Henderson, 2007) together demonstrate that this prediction of the model is a plausible scenario. We now collect the results obtained in this subsection in a proposition. Proposition 2. When the incumbents choose the entry parameters and prices cooperatively, in equilibrium the incumbents induce entry against at most one of the two incumbent goods. The equilibrium entry probabilities are μ ⁎2

8 8 0 1 !99
 < < == μ 1 +μ 1 1 @1 + − 1 − 1− = min 1; max μ; + 1A− μ −1 : : − 4 ;; γ 2 − μ εμ μ εμ − −

−

−

ð11Þ

2

21

To derive this result, substitute the expressions (5) and (6) for

dμ ⁎j dαj

and

dμ ⁎i , dαj

respectively, into the Eq. (8), set μ ⁎i = μ ⁎j = μ ⁎, and solve the resulting expression for μ⁎. 22 Hence γ denotes the ratio of the buyers' valuations for an entrant good and for the corresponding incumbent good. The reward-elasticity of entry describes what happens to a potential entrant's probability of entry when its reward for entry increases, and is dμ ⁎i Ri j : Using the expression (2) for the probability of entry dRi μ i μ i = μ ;μ j = μ − − Δ expression Ri = ð1−μ j Þ + μ j Δ, and the definition of the parameter β given in 2

defined as ε μ ≡ −

μ ⁎i , the

and μ ⁎1 = −μ + if γ >

1 1−2 μ

1+ μ

23 − , the condition μ⁎ ≤ 1 is never Because β ∈ (0, 1) implies that ε μ ∈ 0; μ − − binding. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 24 The intuition for the condition μ < 1 = 1 + ε μ is that when μ_ is high, the − − υ

Δ marginal gain ð1− μ Þ 2 + 2 of the incumbent i from an increase in entry against the − complementary incumbent j is low (as the incumbent itself is often displaced by an

entrant and thereby receives no revenue) and the marginal loss υ2 + μ υ2 + Δ2 of the − incumbent i from an increase in entry against itself (through the indirect effect) is high (as the incumbent j is often displaced by an entrant and the incumbent i thus often receives the additional surplus 2v + Δ2 ).

1 2

and μ < . −

−

Fig. 1 shows the percentage difference between the expected consumer surplus μ1⁎μ2⁎v in the non-cooperative and cooperative

−

reward-elasticity of entry in innovative environments. !

⁎ μ Þ. The incumbents induce entry if and only 1 + μ ðμ 2 − − −

2.4. Comparison of non-cooperative and cooperative outcomes

the expression (3), the reward-elasticity of entry can be written as εμ = β (1 + μ_) / μ_ . See Acemoglu and Linn (2004) and Popp (2002) for recent empirical analyses of the

μ εμ − −


25

Because

d2 ∏I dα2j

2 −



d2 ∏I dαj dαi

2

= −ðv + ΔÞ < 0, there are no interior maxima for

(α1, α2). 26

Because

d2 ΠI dα22

dμ1⁎ dμ2⁎ Þðv dα2 dα2

= −2ð

+ ΔÞ = −2

β ð1−β2 Þ2

ðv + ΔÞ < 0, also the second-

order condition holds. 27 To derive this result, first substitute the expressions for correspond to the expressions (5) and (6) for

dμ ⁎2 dα2

and

dμ ⁎1 , dα2

dμ ⁎2 dα2

and

dμ 1⁎ dα2

that

and substitute μ⁎1 = α _+

⁎ βμ ⁎2 for μ⁎ 1 , into the Eq. (10), and solve the resulting expression for μ 2 . Next substitute α μ = _ for αi and αj in Eq. (4) to get − previously derived expression for μ ⁎2 .

ð1−βÞ . α −

Finally, substitute ð1−βÞ μ for α _ in the −

M. Packalen / Int. J. Ind. Organ. 28 (2010) 244–253

249

With these assumptions, the demand for one entrant good and the complementary incumbent good is D(p − Δ), where p is the total price of the two goods, provided that the quality-adjusted total price p − Δ is lower than the quality-adjusted total price of any other available combination of two complementary goods. The demand for two entrant goods is D(p − Δ − Δ), where p is the total price of the two goods, provided that the quality-adjusted price of each good is lower than the price of the corresponding incumbent good. 3.2. Equilibrium analysis: the non-cooperative case Fig. 1. Percentage difference in expected consumer surplus in the non-cooperative case vs. the cooperative case when μ̄ = 0.1 and γ = 2.

cases for different values of the reward-elasticity of entry when γ = 2 and μ = 0.1. In this example consumer welfare is higher in the noncooperative case than in the cooperative case (we have not found examples of the reverse result).28 Establishing analytical conditions is especially cumbersome due to the non-linearities in the equilibrium entry probabilities. Instead we emphasize that the results show that cooperation/integration between complementary incumbents can have a large (negative) impact on consumer welfare, which implies that it is important that the impact of cooperation/integration on entry inducement is considered in the relevant policy analyses, and that our analysis offers constructive guidance on how the policy analyses can be conducted in practice as it shows that the equilibrium comparison can be determined in terms of the straightforward economic concepts that are represented by the parameters γ, μ_ and εμ_. We now restate as a proposition the results obtained in this subsection. Proposition 3. In the ease of entry model with homogenous potential buyers, expected consumer surplus can be higher in the non-cooperative case than in the cooperative case. Equilibrium comparisons can be determined in terms of the probability of entry without entry inducement, the rewardelasticity of the probability of entry, and the ratio of the potential buyers' valuation for an entrant good and for the corresponding incumbent good.

In stage 3 the incumbents and successful entrants set prices. When neither potential entrant is successful in entry, each incumbent sets its price equal to the double monopoly price pDM.30 When only the potential entrant i is successful in entry, the entrant i sets its price equal to Δ and the complementary incumbent j sets its price equal to the monopoly price pM.31 When both potential entrants are successful in entry, each incumbent sets its price equal to zero and each entrant sets its price equal to Δ. In stage 2 each potential entrant again chooses μi to maximize its expected profit. Substituting Ri = (1 − μ j)ΔD(pM) + μ jΔD(0) for Ri in the Eq. (2) yields the best-response curve32 μ i⁎ ðμ j Þ =

ΔDðpM Þ−ai Δ½Dð0Þ−DðpM Þ μj: + b b

|{z}

|{z}

≡αi

≡β

ð12Þ

for the potential entrant i. With the definitions of the parameters αi and β given in the above expression (12), the rest of the analysis of the stage 2 is the same as the analysis of the model with homogenous buyers that follows the expression (3). In stage 1 each incumbent i sets αj to maximize its expected profit h i π I Πi = ð1−μ ⁎i Þ ð1−μ ⁎j Þ DM + μ ⁎j πM ; 2

ð13Þ

3. The ease of entry model with heterogenous buyers

where πDM ≡ (pDM + pDM)D(pDM) and πM ≡ pMD(pM).33 Defining v and π υ Δ Δ such that DM = and πM = υ + , we can see that the equilibrium

In this section we extend the ease of entry model to the case with heterogenous buyers, and compare the cooperative and non-cooperative outcomes in the model. With heterogenous buyers also the double marginalization externality is present.

analysis based on the above expression (13) will be identical to the equilibrium analysis of the model with homogenous buyers that follows the expression (7). Consequently, the equilibrium probability of entry against each incumbent is given by the expression (9) with 2π −π γ = M DM .

3.1. The model with heterogenous potential buyers We keep all other aspects of the model the same as in the model presented in Section 2.1, except that we now assume that absent entry the potential buyers' valuation for the two incumbent goods is heterogenous. The number of buyers with a valuation greater than p for the two incumbent goods is denoted by D(p). The buyers' marginal valuation for each potential entrant's good remains Δ for all buyers.29 28 For small values of the reward-elasticity consumer welfare is higher in the noncooperative case because entry inducement by the incumbent i then has only a negligible indirect effect on the probability that the incumbent i itself is displaced and it thus becomes optimal for each incumbent to engage in almost full entry inducement. The kink in Fig. 1 signifies the point to the left of which the incumbents engage in full entry inducement against one of the incumbent goods in the cooperative case (μ⁎ 2 = 1). For high values of the reward-elasticity entry inducement by the incumbent i has almost the same impact on the probability that the incumbent j is displaced and on the probability that the incumbent i itself is displaced, and hence also almost the same impact impact on each incumbent's expected profit. Cooperation can thus have only a small effect on the outcome when the reward-elasticity is high. 29 We assume that the improvement Δ is non-drastic, so that an entrant always sets 1 its price equal to Δ. With linear demand D(p) = 1 − p, the condition Δ < is a 2 sufficient condition for the potential entrant to always set its price equal to Δ.

2

2

2

πDM

3.3. Equilibrium analysis: the cooperative case In stage 3 the incumbents and successful entrants set prices. When neither potential entrant enters, the incumbents set the total price of the two incumbent goods equal to the monopoly price pM. A successful entrant always sets its price equal to Δ, and an incumbent that is not displaced by an entrant sets its price equal to the monopoly price pM. 30 The double monopoly price pDM satisfies pDM = p̂(pDM), where p̂(pj) ≡ arg maxp{pD (p + pj)} is the best-response curve of the incumbent i in stage 3. As was established formally by Cournot (1838), due to “double marginalization” the total price pDM + pDM exceeds the monopoly price pM ≡ arg maxp{pD(p)}. 31 The monopoly price is defined by pM ≡ arg maxp{pD(p)}. Price competition between the successful entrant and the corresponding incumbent drives the incumbent's price to zero. 32 When only one potential entrant is successful in entry, the successful entrant receives the reward ΔD(pM) for entry. When both entrants are successful in entry, each entrant receives the reward ΔD(0) for entry. Each entrant's expected reward for successful entry is therefore (1 − μj)ΔD(pM) + μjΔD(0). 33 When neither potential entrant is successful in entry, the revenue of the π incumbent i is DM , where πDM ≡ (pDM + pDM)D(pDM). When only entry against the 2 complementary incumbent j is successful, the revenue of the incumbent i is πM, where πM ≡ pMD(pM). Whenever entry against the incumbent i is successful, the incumbent i receives no revenue.

250

M. Packalen / Int. J. Ind. Organ. 28 (2010) 244–253

Proposition 4. In the ease of entry model with heterogenous potential buyers, expected consumer surplus can be higher in the non-cooperative case than in the cooperative case, and vice versa. For a given demand curve, equilibrium comparisons can be determined in terms of the probability of entry without entry inducement and the reward-elasticity of the probability of entry. 4. The price commitment model

Fig. 2. Percentage difference in expected consumer surplus in the non-cooperative case vs. the cooperative case when μ̄ = 0.2 and demand is linear.

The analysis of the stage 2 is the same as in the non-cooperative case because cooperation does not alter equilibrium pricing when one or both entrants are successful in entry. In stage 1 the incumbents set α1 and α2 to maximize their combined expected profit ПI = (1−μ1μ2)πM, where πM ≡ pMD(pM). The incumbents receive the same combined profit πM in stage 3 when one potential entrant is successful in entry and when neither potential entrant is successful in entry. Consequently, the incumbents never induce entry.

In this section we present and examine the price commitment model. Both the entry inducement externality and the double marginalization externality are present in the model. 4.1. The model with price Commitment We retain all other aspects of the ease of entry model with heterogenous buyers (see Section 3.1), except that now we assume that the incumbents cannot influence the potential entrants' entry costs, so that a1 = a2 = a . Instead, each incumbent can commit to a price for its own good in stage 1. Such long-term price commitments are common in patent licensing (see the Introduction). In stage 3 each incumbent can decrease but not increase its price. 4.2. Equilibrium analysis: the non-cooperative case

3.4. Comparison of non-cooperative and cooperative outcomes Fig. 2 shows the expected consumer welfare comparison for different values of the reward-elasticity of entry when the probability of entry without entry inducement is μ_ = 0.2 and the demand curve is linear.34 For low values of the reward-elasticity of entry, the expected consumer surplus is higher in the non-cooperative case than in the cooperative case because entry inducement by the incumbent i has only a negligible indirect effect on the probability that the incumbent i itself is displaced by an entrant and, consequently, each incumbent engages in almost full entry inducement in the non-cooperative case.35 When the reward-elasticity of entry is high, the expected consumer surplus is lower in the non-cooperative case than in the cooperative case because neither incumbent induces entry against the complementary incumbent in the non-cooperative case as any entry inducement would have a large indirect impact on the probability that the incumbent itself is displaced by an entrant.36 We now restate as a proposition these results, which show that entry inducement can overturn Cournot's celebrated double monopoly result even in the presence double marginalization. 34 Let csM, csDM and cs0 denote the consumer surplus in stage 3 when the qualityadjusted equilibrium price in stage 3 is the monopoly price pM, the double monopoly price pDM + pDM, and 0, respectively. The expected consumer surplus in stage 1 is

CSN = (μ⁎)2cs0 + 2 μ⁎(1 − μ⁎)csM + (1 − μ⁎)2csDM in the non-cooperative case, where μ⁎ is given by Eq. (9) with γ =

2πM −πDM , πDM

2 and CSC = μ_2cs0 + (1 – μ _ )csM in the

cooperative case, where _μ is the probability of entry without entry inducement. We use these expressions for CSN and CSC to calculate the percentage difference (CSN − CSC)/CSC × 100 in the expected consumer surplus between the non-cooperative and cooperative cases. 35 There is no entry inducement in the cooperative case. The expression (9) implies that in the non-cooperative case μ⁎ → 1 as εμ _ → 0. With full entry inducement against both incumbent goods, double marginalization is avoided also in the non-cooperative case. These observations imply that the expected consumer surplus is higher in the non-cooperative case than in the cooperative case when εμ _ is small enough. 36 There  is no entry inducement in the cooperative case. The expression (9) implies that μ ⁎ → max μ ; −

γ−1 2γ

as ε μ → −

μ

−

1+ μ

(the restriction β ∈ (0, 1) implies that ε μ ∈ð0;

−

With linear demand γ = 1.25 and, therefore, for all μ = 0:2 > −

1:25  1 2 × 1:25

−

μ

−

1+ μ

ÞÞ.



−

elasticity of entry. Double marginalization is avoided only in the cooperative case. These observations imply that the expected consumer surplus is higher in the cooperative case μ − and the demand curve is linear. than in the non-cooperative case when _μ >0.1, ε− μ → −

37 We again focus on perfectly coalition-proof subgame-perfect pure strategy Nash equilibria. Coalition-proofness refers to the assumption that in the non-cooperative case the incumbents coordinate on their most profitable equilibrium. 38 Price competition between the entrant and incumbent i drives the incumbent's price to zero and the entrant sets its price equal to Δ. Absent any price commitments by the incumbent j in stage 1, the incumbent j will set its price equal to the monopoly price pM, where pM ≡ arg maxp{pD (p)}. Any price commitment pj by the incumbent j in stage 1 limits the pricing of the incumbent j to p⁎j = min{pj,pM} in stage 3. 39 When both incumbents are displaced by an entrant the number of active consumers is D(0), and each entrant's reward for successful entry is ΔD(0). When only the incumbent i is displaced by a successful entrant, the number of active consumers is D(pj), where pj denotes the price that a buyer must then pay for the complementary incumbent good j in stage 3, and the entrant's reward for successful entry is ΔD(pj). 40 Combining the best-response curves for both potential entrants yields the equilibrium entry threat

= 0:1 there is no

entry inducement in the non-cooperative case either for large enough values of the reward-

1+ μ

In stage 3 the incumbents and successful entrants set prices.37 Consider first the case when neither incumbent is displaced by an entrant. If neither incumbent has committed to a price in stage 1, each incumbent sets its price equal to the double monopoly price pDM, which satisfies pDM =p̂ (pDM), where p̂ (pi) ≡ arg maxp{pD(p +pi)}. If only the incumbent i has committed in stage 1 to a price pi that satisfies pi
μ ⁎i =

41

Δ b

Dðpj Þ−

a

−

b

Δ b

+ ½Dð0Þ−Dðpj Þ

Δ b

Δ b

Dðpi Þ−

a



−

b

This requires that

Δ b

DðpM Þ−

a

−

b

> 0 and −

ð14Þ

:

Δ b

1− ½Dð0Þ−Dðpj Þ ½Dð0Þ−Dðpi Þ a

−

b

Δ b

+ Dð0Þ < 1.

M. Packalen / Int. J. Ind. Organ. 28 (2010) 244–253

251

Δ

slope ½Dð0Þ−Dðpj Þ of each potential entrant's best-response curve is b positive and less than one, which in turn implies that each equilibrium entry threat μ ⁎i is decreasing in the price commitment pj by the dμ⁎

complementary incumbent, i < 0, and that each equilibrium entry dpj threat μ ⁎i is also decreasing in the price commitment pi by the corresponding incumbent,

dμ i dpi

< 0.42

In stage 1 each incumbent can commit to a lower than ex-post optimal price. We assume that absent entry the goods are not strategic complements, so that the ex-post optimal price in stage 3 never exceeds the monopoly price pM. We can therefore restrict attention to price commitments that are smaller than the monopoly price, p1 ≤pM and (pj) denote the best-response correspondence of the p2 ≤pM. Let pNC i ⁎ incumbent i in stage 1.43 A symmetric equilibrium satisfies p⁎ =pNC 1 (p ) (p⁎). A price commitment increases an incumbent's and p⁎ =pNC 2 expected profit by inducing entry against the complementary incumbent but also decreases the incumbent's expected profit because the price commitment indirectly increases entry against the incumbent itself and lowers the incumbent's price. The equilibrium impact of price commitments on consumer welfare is examined in Subsection 4.4.

4.3. Equilibrium analysis: the cooperative case In stage 3 the incumbents set their prices cooperatively to maximize their combined expected profit. When neither incumbent is displaced by an entrant, the ex-post optimal price for the bundle of both goods is the monopoly price pM ≡arg maxp pD(p). If the incumbents have committed in stage 1 to prices p1 and p2 for the good 1 and the good 2, respectively, and to the price pB for the bundle of both goods, the incumbents set the price of the bundle of both goods at pB⁎ ≡min {pM,pB,p1 +p2} in stage 3. When at least one potential entrant is successful in entry, cooperation in stage 3 does not impact equilibrium pricing in stage 3.44 This also implies that the equilibrium analysis of the stage 2 is the same as in the non-cooperative case. In stage 1 the incumbents set p1,p2 and pB to maximize their combined expected profit ПI = (1 − μ1⁎)(1 − μ2⁎)pBD(pB) + (1 − μ1⁎)μ2⁎p1D(p1) + 42 These two properties of the model correspond to the properties (5) and (6), respectively, of the ease of entry model and also the intuitions are the same (see the end of Section 2.2.2). These properties of the model imply that by committing to a lower than ex-post optimal price pi for its good, each incumbent i can directly induce entry against the complementary incumbent j, and that such entry inducement will indirectly induce entry also against the incumbent i itself. The analytical proof of these

results is a straightforward calculation of

dμi⁎ dpi

and

However, the most accessible proof of the results

dμi⁎ dpj

dμi⁎ dpj

using the expression (14).

< 0 and

dμi⁎ dpi

< 0 is graphical. A

price commitment by the incumbent j decreases pj, which increases D(pj) and thereby increases the value of the best-response curve of potential entrant i for any level of μj. Hence, a decrease in pj shifts this best-response curve upward. Because the corresponding best-response curve μ⁎j (μi) of the potential entrant j is increasing in μi and remains unchanged when the price pj changes, this implies that when pj decreases, the equilibrium probabilities of entry μ⁎i and μ⁎j must both increase. 43 The best-response correspondence pNC i (pj) of the incumbent i in stage 1 is given by I I ⁎ ⁎ ⁎ pNC i (pj) ≡ argmaxpi ≤ pMПi(pi, pj), where Пi(pi, pj) = (1 −μi )[(1−μj )π(pi, pj) +μi piD(pi)], where 8 pDM DðpDM + pDM Þ if pi ≥pDM and pj ≥pDM > > < pi Dðpi + pðp ˆ i ÞÞ if pi < pDM and pj ≥ pðp ˆ iÞ πðpi ; pj Þ = p ˆ ðpj ÞDð pðp ˆ j Þ + pj Þ if pj < pDM and pi ≥ pðp ˆ jÞ > > : pi Dðpi + pj Þ otherwise: The separate expressions for π(pi,pj) in the four cases arise because in the event that neither incumbent is displaced by an entrant the equilibrium pricing in stage 3 depends on whether either incumbent has committed to a price lower than pDM in stage 1. 44 When only the incumbent i is displaced by an entrant, in equilibrium the incumbent sets its price equal to zero and the entrant sets its price equal to Δ. For the complementary incumbent j, the ex-post optimal price in stage 3 is the monopoly price pM. If the incumbents have committed to prices pj and pB in stage 1, the equilibrium price of the good j is pj* = min {pM,pB,pj} in stage 3. When both incumbents are displaced by entrants, each entrant sets its price equal to Δ.

Fig. 3. Percentage difference in expected consumer surplus in the non-cooperative case vs. the cooperative case when μ̄ = 0.05 and demand is linear.

μ1⁎(1−μ2⁎)p2D(p2) subject to the constraints p1 ≤pB,p2 ≤pB, and pB ≤ p1 +p2. Without price commitments the incumbents receive the same profit in stage 3 when one incumbent is displaced by an entrant and when both incumbents are displaced by entrants. Therefore, the incumbents have no incentive to induce entry and, consequently, the equilibrium price commitments in the cooperative case are trivial, so that p1 =p2 =pB =pM.

4.4. Comparison of non-cooperative and cooperative outcomes Fig. 3 shows the expected consumer welfare comparison for the case when the probability of entry against each incumbent is μ_ = 0.05 without entry inducement and the demand curve is linear.45 The equilibrium comparisons in Fig. 3 show that entry inducement by price commitment has the greatest effect on the equilibrium outcome for intermediate values of the reward-elasticity of entry. The incentive to induce entry is low for small values of the reward-elasticity because a price commitment then has only a small effect on entry. The incentive to induce entry is small also for large values of the rewardelasticity of entry because then the ratio of the effect that a price commitment has on the probability of entry against the incumbent itself and the effect that the price commitment has on the probability of entry against the complementary incumbent is almost one. The equilibrium comparisons in Fig. 3 also show that for some values of the reward-elasticity of entry Cournot's celebrated double monopoly result is overturned as consumer welfare is higher in the non-cooperative case than in the cooperative case. The region of parameterizations of the entry threat for which consumer welfare is higher in the non-cooperative case than in the cooperative case is indicated in Fig. 4. The results in Fig. 4 show that Cournot's double monopoly result is overturned only for a very limited (almost a knifeedge) set of parameterizations of the entry threat. Moreover, consumer 45 The equilibrium in the non-cooperative case is determined by first finding all prices p that satisfy p = pNC i (p) and then choosing the highest price among these prices for which the price is also a global optimum in stage 1 for each incumbent. The expression (14) shows that the effect of cooperation on the equilibrium outcome Δ a that govern the depends on the demand function D(p) and on parameters ¼ and b b Δ a entry threats. Because the parameters ¼ and themselves are not intuitive economic b b concepts, we instead express the results in terms of the probability of entry without

price commitments, μ ≡ μi⁎ ðpM ; pM Þ = −

probability of entry

j

a ΔDðp Þ−¼ M b b , 1−Δb ½Dð0Þ−DðpMÞ

dμi Ri ε μ ≡ dR i μi pi = pM ; pj = pM −

=

1 b

and the reward-elasticity of the

ð1− μ ÞΔDðpM Þ + μ ΔDð0Þ −

μ

−

−

, at the equilibrium

probability of entry without price commitment μ _. In a previous version of the paper we examined the comparison when the demand function is log-linear (so that absent entry the goods are neither strategic substitutes nor strategic complements, and hence pM = pDM). The welfare comparisons for the admissible range of the parameters μ_ and εμ indicated that the expected consumer ¯¯ surplus is always higher in the cooperative case than in the non-cooperative case.

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M. Packalen / Int. J. Ind. Organ. 28 (2010) 244–253

the probability of entry without entry inducement, and the rewardelasticity of the probability of entry, which are straightforward and empirically malleable economic concepts. Acknowledgments I thank Roger Noll, Jay Bhattacharya and Jon Levin for advice, and Susan Athey, Tim Bresnahan, Jeremy Bulow, Peter Coles, Liran Einav, Rob McMillan, Bruce Owen, Paul Riskind, Greg Rosston, Steven Tadelis and anonymous referees for comments and discussions. References Fig. 4. The set of entry threats for which the expected consumer surplus is higher in the non-cooperative case than in the cooperative case.

welfare is never more than 2% higher in the non-cooperative case than in the cooperative case. Therefore, from a policy perspective our analysis confirms that cooperative pricing in the form of patent pools is generally welfare-improving; price commitment is generally not a strong enough entry inducement mechanism to overturn this result. We now summarize the results obtained in this subsection. Proposition 5. With a linear demand curve, in the price commitment model the expected consumer surplus is generally though not always higher in the cooperative case than in the non-cooperative case. While this analysis only shows the results for linear demand, the analysis demonstrates how the effect of cooperation on consumer welfare can be determined in the price commitment model for a given demand function in terms of the probability of entry without entry inducement and the reward-elasticity of the probability of entry.

5. Conclusion Several commentators suggested during the Microsoft case that the divestiture of a firm that is a monopolist in two complementary markets might benefit consumers because two separate complementary monopolists have an incentive to induce entry against each other. An incumbent can induce entry against a complementary incumbent by developing and disseminating technological know-how that decreases the cost of entry in the complementary market. This has been a common strategy for incumbent (near) monopolists in the computer industry. Entry inducement can also be achieved through long-term price commitments, which are common in patent licensing. Cooperative patent licensing through patent pools may therefore decrease consumer welfare by eliminating the entry inducement incentive. Our analysis provides the first formal analysis of the impact that entry inducement has on the equilibrium comparison between the noncooperative/non-integrated outcome and the cooperative/integrated outcome. We show that because cooperation/integration between complementary incumbent monopolists reduces or even eliminates the incumbents' entry inducement incentive, cooperation/integration may decrease entry and, consequently, consumer welfare, contrary to Cournot's celebrated double monopoly result. We find that the equilibrium impact of entry inducement is different when the incumbents influence the ease of entry and when they use price commitments to induce entry. This demonstrates that when the impacts of cooperation/integration on both entry inducement and double marginalization are considered, the optimal policy must be solved on a case-by-case basis and requires careful modelling of the demand structure and the entry technology. While detailed analysis of a particular case — such as the Microsoft case or a specific patent pool — is beyond the scope of this paper, our analysis offers constructive guidance for how such analysis can be conducted because we show that the equilibrium comparison can be characterized in terms of the demand,

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