THREE ESSAYS ON COMPETITION AND REGULATION By Dong-Ryeol Lee A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY ECONOMICS 2010 ABSTRACT THREE ESSAYS ON COMPETITION AND REGULATION By Dong-Ryeol Lee Chapter 1: Cost-based Termination Charge Regulation when Fixed and Mobile Networks Compete for Subscribers This paper studies termination charges in the telecommunications industry (i.e., the fees for receiver's network to impose on caller's network for call termination services). I address two unsettled questions on termination charges: (i) why mobile networks have incentives to set above-cost termination charges and (ii) what are the welfare consequences of symmetric costbased termination charge regulation. I propose an oligopolistic Hotelling model which explicitly considers the competition for subscribers between fixed and mobile networks and show that such competition can potentially explain high mobile termination charges. When both mobile-tomobile and fixed-to-mobile substitutions are present, there exists a tradeoff from above-cost mobile termination charges: (i) profit gain from mobile market expansion and (ii) profit loss from intense price competition. I show that above-cost mobile termination charges are profitable when the market share effect outweighs the price competition effect - which is likely to occur for a large inter-network customer base or a small inter-network product differentiation. Moreover, the cost-based regulation on fixed and mobile termination charges, which was recommended by European Commission (2009), may have potential welfare-enhancing effects. Chapter 2: Exclusive Dealing and Investment Incentives in the Presence of Risk of Renegotiation Breakdown Exclusive dealing (i.e., a contract that prohibits a buyer from trading with other sellers) may affect competition through the investment incentives and entry. My model considers the case where the contracts are renegotiable and the incumbent seller facing a potential entry threat is able to invest in the relationship with a buyer. My paper departs from the existing literature by considering the risk of breakdown in the renegotiation process. In this setup, exclusivity may have contrasting effects on competition through (i) investment promotion and (ii) foreclosure of efficient entry. The profitability and welfare consequences of exclusive dealing are decided by the relative importance of these two effects which in turn mainly relies on the risk of renegotiation breakdown. More specifically, if the risk of breakdown is very low, exclusive contracts will be profitable and welfare-enhancing. However, the profitable and welfare-reducing exclusive dealing is feasible for a sufficiently high risk of breakdown. This paper restores the inefficient foreclosure by exclusive dealing even considering investments and renegotiation, highlighting the role of risk of renegotiation breakdown. Chapter 3: Dynamic Incentives of Tying in Two-sided Markets This paper investigates tying arrangements in two-sided markets. Optimal pricing structure of two-sided markets differs from that of standard one-sided markets. In two-sided markets, platforms charge subscription fees in order to utilize inter-group externalities. The main purpose of this paper is to explore how inter-group externalities affect tying incentives through platforms' price and R&D competition. I adopt a two-sided Hotelling model where two platforms compete in prices and investments and show that tying leads to the distortion of R&D incentives as well as the exclusion of rival platforms. Moreover, there exist certain parameter configurations such that tying is profitable and welfare-reducing through foreclosing rival's R&D investments. Dynamic incentives of tying, which have not been considered in the existing literature, provide a new rationale for the regulation on tying in two-sided markets. Dedicated to my parents and family iv ACKNOWLEDGMENTS First of all, I am deeply indebted to my advisor, Jay Pil Choi, for his invaluable guidance and support throughout the writing of this dissertation. This work would not have been completed without his comments, suggestions and encouragements in every step. I am also indebted to all my committee members, Thomas Jeitschko, Arijit Mukherjee and Steven Wildman, for their thoughtful comments and suggestions. They have shared their deep insights and knowledge without reservation which have improved my dissertation in many respects. I would like to thank my wife, Youngmi Chu, and my two daughters, Seoyoon and Seojin for their love and support during my study. They have been my best friends who have been always with me at the good times or bad times. I owe my deepest gratitude to my parents for their endless love. I am also grateful to my colleagues in the Department of Economics at Michigan State University who shared their knowledge and friendship with me, although I cannot list all of them here. I also thank the Bank of Korea for providing financial support and allowing me to focus on my study. v TABLE OF CONTENTS LIST OF FIGURES ........................................................................................................ vii CHAPTER 1: COST-BASED TERMINATION CHARGE REGULATION WHEN FIXED AND MOBILE NETWORKS COMPETE FOR SUBSCRIBERS .................... 1.1 Introduction.................................................................................................... 1.2 The Model...................................................................................................... 1.3 Fixed-Mobile Substitution with Singlehoming Subscribers .......................... 1.4 Fixed-Mobile Substitution with Multihoming Subscribers ........................... 1.5 Concluding Remarks...................................................................................... Appendix.............................................................................................................. Bibliography ........................................................................................................ 1 1 7 14 20 27 30 37 CHAPTER 2: EXCLUSIVE DEALING AND INVESTMENT INCENTIVES IN THE PRESENCE OF RISK OF RENEGOTIATION BREAKDOWN................................... 39 2.1 Introduction ................................................................................................... 39 2.2 The model ...................................................................................................... 45 2.3 Exclusive Dealing and Imperfect Renegotiation ........................................... 46 2.4 Extensions ...................................................................................................... 59 2.5 Concluding Remarks...................................................................................... 61 Appendix.............................................................................................................. 65 Bibliography ........................................................................................................ 72 CHAPTER 3: DYNAMIC INCENTIVES OF TYING IN TWO-SIDED MARKETS .. 74 3.1 Introduction.................................................................................................... 74 3.2 The Model ..................................................................................................... 79 3.3 Two-sided Singlehoming ............................................................................... 81 3.4 Competitive Bottlenecks................................................................................ 93 3.5 Concluding Remarks......................................................................................100 Appendix..............................................................................................................102 Bibliography ........................................................................................................107 vi LIST OF FIGURES 1.1 Competition structure among fixed and mobile networks......................................... 9 1.2 Network competition with singlehoming subscribers................................................15 1.3 Network competition with multihoming subscribers.................................................21 A.1 Network competition in the full mobile penetration model......................................33 2.1 Payoffs under non-exclusivity and exclusivity ..........................................................49 2.2 Investment incentives under non-exclusivity and exclusivity ( α = 0.5, θ = 0.1).......53 2.3 Profitability and social welfare under non-exclusivity and exclusivity.....................57 2.4 Profitability and welfare effects of exclusive dealing ( α = 0.5)................................59 3.1 Platform competition in the two-sided singlehoming model.....................................80 3.2 Effects of tying on R&D investments........................................................................86 3.3 Tying incentives in the two-sided singlehoming model ( α = 0.5) ............................91 3.4 Platform competition in the competitive bottlenecks model .....................................93 3.5 Tying incentives in the competitive bottlenecks model.............................................99 vii Chapter 1 Cost-based Termination Charge Regulation when Fixed and Mobile Networks Compete for Subscribers 1.1 Introduction In the telecommunications industry, when a caller places a phone call, the receiver’ network s imposes a fee to the caller’ network for call termination services, known as ‘ s termination charges.’In many countries, the regulatory authorities have deemed the termination charges for mobile networks to be much higher than the relevant costs.1 However, the existing models on termination charges predict that above-cost termination charges are suboptimal when network operators compete in two-part tari¤s and may charge di¤erent prices for on-net and o¤-net calls. The equilibrium termination charges critically depend on the assumption regarding a 1 For instance, European Commission (2009) states that “the absolute level of mobile ter- mination rates remains high in a number of Member States compared to those applied in a number of countries outside of the European Union, and also compared to …xed termination rates generally, thus continuing to translate into high, albeit decreasing, prices for end consumers (p. 67).” 1 speci…c pricing strategy which network operators choose. Assuming a linear pricing, high termination charges serve as an instrument of collusion due to the “raise-each-other’ s-cost” e¤ect (Armstrong, 1998; La¤ont, Rey and Tirole, 1998a). In contrast, under two-part tari¤s with termination-based price discrimination, above-cost termination charges are suboptimal in the standard duopoly model (La¤ont, Rey and Tirole, 1998b; Gans and King, 2001).2 As two-part tari¤s and termination-based price discrimination are commonly adopted in the telecommunications industry, above-cost termination charges remain a puzzle to be explained.3 This study proposes an answer to this puzzle cost termination fees why mobile networks may charge above- by incorporating the inter-network (i.e., between …xed and mobile networks) competition for subscribers. My model departs from the existing literature by endogenizing the market shares between …xed and mobile networks. The existing literature mostly has treated …xed and mobile network subscribers as disjoint groups. In practice, however, the recent dramatic increase in mobile network subscribers has been accompanied by a signi…cant decline in the number of …xed network subscribers in many developed countries.4 I explore whether above-cost mobile termination charges can be supported as an equilibrium in the presence of inter-network competition for subscribers. Furthermore, I assess the desirability of symmetric and cost-based termination charge regulation (i.e., both …xed and mobile termination charges are regulated at marginal costs). 2 Correcting the analysis of La¤ont, Rey and Tirole (1998b), Gans and King (2001) show that network operators have incentives to negotiate termination charges below marginal costs to reduce price competition. 3 OECD (2009) shows that 44% of mobile subscribers choose prepaid cards in OECD countries. This fact implies that most of the other 56% may choose a plan of two-part tari¤s. Also, Table 4 in Armstrong and Wright (2009) shows that there exists a signi…cant price discrimination between on-net and o¤-net calls in the UK. 4 According to the statistics from International Telecommunication Union, the mobile penetration rate has increased but the …xed penetration rate has decreased in most developed countries between 2000 and 2009. For instance, in the US, the mobile penetration rate has increased by 56.80%p (38.03 ! 94.83%) but the …xed penetration rate has decreased by 17.62%p (66.88 ! 49.26%) during this period. In the UK, the mobile penetration rate has increased by 56.79%p (73.76 ! 130.55%) but the …xed penetration rate has decreased by 5.20%p (59.80 ! 54.60%). Further information can be available at http://www.itu.int/ITUD/icteye/Indicators/Indicators.aspx 2 Regulatory authorities often adopt a cost-based termination charge regulation in order to prevent network operators from transferring high termination charges to …nal consumers. In many countries, however, this cost-based termination charge regulation has been implemented asymmetrically between …xed and mobile networks; usually …xed networks’termination charges has been more tightly regulated than mobile networks’termination charges. European Commission (2009) stresses the potential competitive distortions from asymmetric treatment on …xed and mobile termination charges and recommends the symmetric and cost-based termination charge regulation to the national regulatory authorities. “Signi…cant divergences in the regulatory treatment of …xed and mobile termination rates create fundamental competitive distortions [...]: Where termination rates are set above e¢ cient costs, this creates substantial transfers between …xed and mobile markets and consumers [...]. NRAs (National Regulatory Authorities) should set termination rates based on the costs incurred by an e¢ cient operator. This implies that they would also be symmetric.” (European Commission (2009), pages 67 and 70, italics added) This recommendation aims to build a consistent regulation which applies to both …xed and mobile networks and to all the European Union (EU) member countries. However, it causes a controversy among related groups due to the di¤erent position each group is placed in.5 This paper proposes a formal model to evaluate the symmetric and cost-based termination charge regulation. I extend a standard duopoly model to an oligopoly model within a Hotelling framework. My model considers the oligopoly competition structure where two symmetric mobile networks and a …xed network compete for subscribers each other. In many developed countries 5 In 2007, European Regulators Group (ERG) performed a public consultation on a draft “Common position on symmetry of mobile/…xed call termination rates” and received responses from 33 operators in member countries. According to the ERG report on the consultation, “mobile operators are in principle against converging MTRs (mobile termination rates) and FTRs (…xed termination rates), mainly arguing that …xed and mobile networks are technologically di¤erent.” 3 (e.g., EU and US), the competition among network operators can be well characterized by the oligopoly structure.6 My model allows the asymmetry between …xed and mobile networks in the customer base (represented by and 1 ) and product di¤erentiation (represented ~ by t and t). I consider two di¤erent models regarding consumers’subscription decision: (i) singlehoming subscription model (i.e., all consumers subscribe to a single network) and (ii) multihoming subscription model (i.e., some consumers subscribe to both …xed and mobile networks). In this setup, I explore the pro…tability and welfare e¤ects of above-cost mobile termination charges when …xed termination charges are regulated at marginal costs. This study brings out two main …ndings. First, mobile networks may have incentives to set their termination charges above marginal costs when …xed and mobile networks compete for subscribers. The intuition behind this result is as follows. When both mobile-to-mobile and …xed-to-mobile substitutions are present, there exists a tradeo¤ from above-cost mobile termination charges: (i) pro…t gain from mobile market expansion and (ii) pro…t loss from intense price competition. The equilibrium termination charges are decided by the relative importance of these contrasting e¤ects. In both singlehoming and multihoming subscription models, there exist certain parameter values such that the market share e¤ect outweighs the price competition e¤ect (which ensures the existence of jointly optimal above-cost mobile termination charges). This …nding suggests a potential explanation for the prevalence of high mobile termination charges in the telecommunications industry where a nonlinear pricing and termination-based price discrimination are common. More speci…cally, my model shows that above-cost termination charges may be pro…table for a large inter-network customer base (1 ) or a small inter-network product di¤erentiation ~ (t). The intuition behind this result is as follows. The market share e¤ect (which raises mobile networks’pro…t) is strengthened for a large inter-network customer base or a small inter-network product di¤erentiation. In contrast, the price competition e¤ect (which reduces 6 In the EU countries (e.g., UK, Spain, France and Sweden), a single …xed network operator has a monopolistic market share but there exist multiple (more than two) mobile network operators having signi…cant market shares. See Armstrong and Wright (2009), and Harbord and Pagnozzi (2010) for further details. 4 mobile networks’pro…t) is weakened for a large inter-network customer base.7 As a result, the market share e¤ect outweighs the price competition e¤ect for a large inter-network customer base or a small inter-network product di¤erentiation. The parameter values regarding the customer base and product di¤erentiation can be interpreted in terms of the development stages of telecommunications industry. It would be typical that the inter-network customer base decreases and the inter-network product di¤erentiation increases in a more developed telecommunications industry.8 This implies that above-cost termination charges are more likely to be pro…table in a less developed telecommunications industry. This also explains why high mobile termination charges have been prevalent over the past few decades. In addition, the mobile market expansion from above-cost termination charges suggests a new channel for …xed-to-mobile substitution which has not been considered in the existing literature.9 This paper shows that regulatory handicaps on …xed networks can facilitate …xed-to-mobile substitution. Second, the asymmetric regulation on …xed and mobile termination charges may have welfare-reducing e¤ects. In my model, the asymmetric regulation induces the social ine¢ ciency from the excessive expansion of mobile market. The symmetric and cost-based termination charge regulation, which was recommended by European Commission (2009), can reduce competitive distortions caused by the asymmetric regulation. Related literature. As discussed above, this paper extends the existing literature on termination charges to bridge the gap between theory and practice.10 Several articles have analyzed the termination charge pricing in the symmetric duopoly framework (Armstrong, 1998; La¤ont, Rey, and Tirole, 1998a, 1998b; Gans and King, 2001). In this framework, 7 This feature follows from Assumption 1 which states that the product di¤erentiation is ~ larger within inter-network than within intra-network (i.e., t > t). 8 Recently, mobile networks provide more di¤erentiated services from …xed networks (e.g., internet, camera, game and movie). 9 Vogelsang (2010) presents several potential channels for …xed-to-mobile substitution including the relative reduction in mobile call prices and costs, the network e¤ects in demand, and the quality improvements of mobile services. 10 See Armstrong (2002) for the general review of the literature on termination charges. 5 above-cost termination charges are optimal under a linear pricing but are suboptimal when two-part tari¤s and termination-based price discrimination are feasible. More recently, several authors have extended the symmetric duopoly model to capture the practice in the telecommunications industry: (i) to allow an elastic subscription and a heterogeneous demand (Dessein, 2003; Hurkens and Jeon, 2009; Jullien, Rey and SandZantman, 2009), (ii) to introduce an oligopolistic network competition (Calzada and Valletti, 2008; Jeon and Hurkens, 2008) and (iii) to consider biased calling patterns (Gabrielsen and Vagstad, 2008). Some of these extensions were able to restore the optimality of above-cost termination charges under a nonlinear pricing (e.g., Calzada and Valletti, 2008; Gabrielsen and Vagstad, 2008; Jullien, Rey and Sand-Zantman, 2009). However, none of these works consider the subscription level competition between …xed and mobile networks which is central in my model. Another avenue of extension introduces the asymmetric competition between …xed and mobile networks (which is the main focus of my paper). Armstrong and Wright (2009), and Hansen (2006) have considered both (symmetric) intra-network competition and (asymmetric) inter-network competition in the oligopoly model. Armstrong and Wright (2009) adopt an oligopoly model to introduce the inter-network di¤erence in cost and demand structures. However, the inter-network competition for subscribers is not considered in their model. While they introduce the mobile market expansion through the creation of new demands, the increase in mobile market share does not result in the decline of …xed network’ market share due to the absence of inter-network competition s for subscribers. They show that above-cost mobile termination charges can be optimal when there exists a su¢ ciently large inter-network di¤erence in call demands.11 In my model, the mobile market expansion occurs as a result of the decline in …xed network subscribers and …xed-to-mobile substitution is the key factor to induce the optimality of above-cost mobile 11 They consider several cases depending on the determination of termination charges: (i) non-uniform …xed-to-mobile and mobile-to-mobile termination charges, (ii) jointly-chosen uniform termination charges and (iii) unilateral choice of uniform termination charges. Note that (ii) is the case that my model considers. 6 termination charges. The model in Armstrong and Wright (2009) and mine are complementary in several respects. Most of all, they incorporate the inter-network cost and demand di¤erence without inter-network subscription level competition, but I introduce the internetwork subscription level competition by assuming the symmetric inter-network cost and demand structures. Hansen (2006) develops a model where both intra-network and inter-network competition for subscribers are present. He adopts a two-dimensional (both horizontal and vertical) di¤erentiation model but does not allow termination-based price discrimination. I present a simple horizontal di¤erentiation model which allows both two-part tari¤s and terminationbased price discrimination. Unlike Hansen (2006), my model shows that the market shares play a crucial role in determining the market outcomes in the presence of termination-based price discrimination. The rest of the paper proceeds as follows. Section 2 describes the basic model of this paper and reproduces a standard below-cost termination charge result in the oligopoly model without inter-network competition for subscribers. In Section 3, I allow the inter-network competition for subscribers and explore the pro…tability and welfare consequences of abovecost termination charges in the singlehoming subscription model. Section 4 extends the model to allow some customers to subscribe to both …xed and mobile networks (multihome). Section 5 concludes and discusses the future research. All proofs are given in Appendix A. 1.2 The Model My model explicitly considers the subscription level competition between …xed and mobile networks to explore the competition e¤ects of asymmetric regulation on …xed and mobile termination charges. 7 1.2.1 Basic Model Two mobile networks (denoted by M1 and M2 ) and a …xed network (denoted by F ) compete for subscribers. Fixed and mobile networks are symmetric in cost and demand structures but they are asymmetric in the customer base and product di¤erentiation.12 Cost structure. All networks are assumed to have the symmetric cost structure. Serving a consumer involves a …xed cost f . Per call, each network incurs a marginal cost c = co + ct where co and ct respectively denote the marginal costs for originating and terminating a call. Termination charges. I consider the uniform termination charges in which network operators are not allowed to set di¤erent termination charges according to originating (i.e., caller’ network.13 This assumption is adopted to capture the practice of uniform terminas) tion charges and also to represent the regulatory principle of non-discriminatory termination charges adopted in the EU and US.14 Accordingly, each network has a single termination fee which applies to all calls terminating on its own network. Let a1 ; a2 and af denote the termination charges of M1 ; M2 and F . To terminate o¤-net calls, the originating (caller’ s) network must pay termination fee ai to the terminating (receiver’ network. My model s) focuses on the case where mobile networks jointly choose their uniform termination charges (denoted by a). Thus, mobile networks’termination mark-up is equal to m a ct . On the other hand, I assume that …xed termination charges are regulated at marginal termination costs (i.e., af = ct ) to represent the practice of strict regulation on …xed termination charges in many countries. 12 I assume the symmetric cost and demand structures in order to focus on the e¤ects of asymmetric termination charges on the market outcomes. 13 Uniform termination charges are commonly assumed in the literature. See, for instance, Armstrong (1998), La¤ont, Rey and Tirole (1998a, 1998b), Gans and King (2001), and Armstrong and Wright (2009). 14 In the EU, Directive 2002/19/EC establishes the principle that termination charges should be non-discriminatory. US establishes the same principle in Telecommunications Act of 1996. 8 p1 p2 α ˆ < p1, a2 > M1 ˆ < p2 , a1 > M2 < ~2 , a f > p < ~1, a f > p 1− α 2 1−α 2 < ~1 , a1 > pf < ~ 2 , a2 > pf F pf Figure 1.1: Competition structure among …xed and mobile networks Retail pricing. On the retail pricing of network operators, I allow both two-part tari¤s and termination-based price discrimination. Nonlinear tari¤s and termination-based price discrimination are commonly used in practice, and also several authors adopt the same retail pricing structure as mine to analyze the network competition in the telecommunications industry.15 Each mobile network o¤ers two-part tari¤s fri ; pi ; pi ; pi g where ri represents the ^ ~ subscription fee for Mi and pi refers to the per-minute price for on-net calls while pi ; pi ^ ~ denote the variable prices for o¤-net calls to Mj (i 6= j) and F . Similarly, the …xed network o¤ers two-part tari¤s frf ; pf ; p1 ; p2 g where rf denotes the subscription fee for F and pf ; pi ~f ~f ~f refer to the variable prices for on-net calls and o¤-net calls. Figure 1.1 summarizes the price competition structure among …xed and mobile networks. Demand structure. I assume the balanced calling patterns in which the call volume terminated on each network is proportional to the market share of terminating (i.e., receiver’ s) 15 See, for example, La¤ont, Rey and Tirole (1998b), Gans and King (2001), Calzada and Valleti (2008), Armstrong and Wright (2009), Hurkens and Jeon (2009), and Lopez and Rey (2009). 9 network.16 I extend a standard duopoly model to an oligopoly model within a Hotelling framework. M1 ; M2 and F are located at each end of a triangle and each side of the triangle corresponds to a Hotelling line between each pair of competing networks. Consumers are uniformly distributed on the Hotelling lines where the length of each line is equal to 1. There exist three di¤erent customer types.17 (i) Mobile type: proportion of consumers characterized by subscribing to M1 or M2 . (ii) M1 -F type: (1 )=2 proportion of consumers characterized by subscribing to M1 or F . (iii) M2 -F type: (1 )=2 proportion of consumers characterized by subscribing to M2 or F. This con…guration implies that the density of mobile (intra-network) customer base is equal to and the density of …xed-mobile (inter-network) customer base is equal to 1 . Mobile type customer located at s1 from M1 incurs a transportation cost ts1 for subscribing to M1 and t(1 s1 ) for subscribing to M2 . Similarly, Mi -F type customer located ~~ ~ at si from Mi incurs a transportation cost tsi for subscribing to Mi and t(1 ~ si ) for sub~ ~ scribing to F . Transportation costs t and t represent the intra-network and inter-network product di¤erentiation respectively. The parameter values on the customer base and product di¤erentiation are assumed as follows. Assumption 1 (Customer base and product di¤erentiation) Parameter values satisfy the following conditions. (i) Density of mobile type customer: 0 < <1 ~ (ii) Degree of product di¤erentiation: 0 < t < t: The assumption of 2 (0; 1) ensures the positive fraction of each type customer. I ad- ~ ditionally assume t > t to capture the degree of product di¤erentiation is larger within 16 The balanced calling patterns are commonly adopted in the literature. See, for instance, Armstrong (1998), La¤ont, Rey and Tirole (1998a, 1998b), Gans and King (2001), and Armstrong and Wright (2009). 17 I assume that the total mass of subscribers is normalized to 1 and the fraction of customers on the mobile type and …xed-mobile type are given by and 1 . I also assume …xed-mobile type consumers are equally distributed between M1 -F and M2 -F customer types due to the symmetry of two mobile networks. 10 inter-network than within intra-network. Let v(p) denote the consumer surplus associated with the demand function q(p) such that v 0 (p) = q(p) (I also assume all networks have the same demand function). Utilities from subscribing to mobile network i (denoted by ui ) and …xed network (denoted by uf ) are written as ui = v0 ri + ni v(pi ) + nj v(^i ) + nf v(~i ) p p uf = v 0 rf + ni v(~i ) + nj v(~f ) + nf v(pf ) pf p j where v0 denotes a …xed surplus from subscribing to each network and is assumed to be suf…ciently large to ensure the full coverage of markets. Net utilities (excluding transportation costs) of a customer located at si from Mi and subscribing to Mi and Mj are ui uj t(1 tsi and si ). Consequently, the market share of Mi on the intra-network customer base is given by si = 1 u i uj + 2 2t (1.1) Similarly, net utilities of a customer located at si from Mi and subscribing Mi and F are ~ ui ~~ tsi and uf ~ t(1 si ). The market share of Mi on the inter-network customer base is ~ given by si = ~ 1 ui u f + ~ 2 2t Timing. The timing of the game is as follows. Stage 1: Mobile networks jointly determine their uniform termination charges. Stage 2: All networks simultaneously determine their two-part tari¤s. Stage 3: Consumers make subscription and consumption decisions. 11 (1.2) 1.2.2 Benchmark Case: Absence of Fixed-Mobile Substitution Before examining the model of …xed-mobile substitution, as a benchmark, I explore whether the standard below-cost termination charge result holds in the oligopoly model without …xedmobile substitution.18 I use the backward induction to …nd a subgame perfect equilibrium. First, I examine how retail call prices are determined given termination charges. Next, I check whether the equilibrium termination charges are above or below marginal costs. Retail tari¤s. Suppose the market shares of …xed and mobile networks are constant at 1 and . Each network has two sources of pro…t: (i) pro…t from providing retail services to its own subscribers and (ii) pro…t from providing call termination services to other networks. The pro…t functions of mobile network i (denoted by i ) and …xed network (denoted by f ) are written as i = n i ri | f + ni (pi c)q(pi ) + nj (^i p {z c m)q(^i ) + nf (~i p p c)q(~i ) p } retail pro…t +ni nj mq(^j ) + ni nf mq(~i ) p pf f | termination pro…t = nf [rf | where nj = {z f + nf (pf ni and nf = 1 } c)q(pf ) + ni (~i pf {z c j m)q(~i ) + nj (~f pf p c retail pro…t (1.3) j m)q(~f )] p } (1.4) . Note that …xed network’ pro…t consists of retail pro…t s only as …xed network’ termination charges are regulated at marginal costs. s In this model, network operators set their call prices at ‘ perceived’marginal costs and extract the whole consumer surplus using subscription fees. The marginal-cost pricing is well-known result when …rms compete in two-part tari¤s.19 18 See, for instance, Gans and King (2001) and Armstrong and Wright (2009) for below-cost termination charges under two-part tari¤s with termination-based price discrimination. 19 See, for instance, La¤ont, Rey and Tirole (1998b), Gans and King (2001), Calzada and Valletti (2008), Hurkens and Jeon (2009), and Lopez and Rey (2009) for the margial-cost 12 Lemma 1 (Marginal-cost pricing) In two-part tari¤s with termination-based price discrimination, the equilibrium call prices are determined at ‘ perceived’ marginal costs. That is, (i) mobile networks’pro…t-maximizing call prices are pi = c; pi = c + m and pi = c ^ ~ (ii) …xed network’ pro…t-maximizing call prices are pf = c and pi = c + m: s ~f From Lemma 1, mobile network i’ pro…t function is reduced to s i = ni (ri f ) + ni (1 ni )mq(c + m) From (1.1), the market share of mobile network i is decided by ni = 2 (rj ri ) 2 [t + v(c + m) + (1.5) v(c)] In a symmetric equilibrium (ri = rj = r), the mobile subscription fees are given by r =f +t (1 ) mq (c + m) + [v(c + m) v(c)] (1.6) Mobile termination charges. From (1.6) and ni = nj = =2 in a symmetric equilibrium, mobile networks’ joint pro…t (denoted by 12 s 12 (m) = n t+ 2 1 + 2 ) is given by mq(c + m) + [v(c + m) o v(c)] (1.7) As the …rst-order derivative of (1.7) is negative at m = 0, above-cost mobile termination charges are suboptimal in the oligopoly model without …xed-mobile substitution. Above-cost termination charges induce more intense price competition between mobile networks which reduces mobile networks’pro…ts. The result implies that the inclusion of an exogenous …xed network in the mobile network competition model does not have a signi…cant impact on the pricing under two-part tari¤s. 13 equilibrium mobile termination charges.20 In the following sections, I introduce …xed-mobile substitution in the oligopoly model to explain why mobile networks may have incentives to set above-cost termination charges. I consider two di¤erent models regarding customers’ subscription decision: (i) singlehoming subscription model (Section 3) and (ii) multihoming subscription model (Section 4). 1.3 Fixed-Mobile Substitution with Singlehoming Subscribers This section investigates the determination of call prices and termination charges in the presence of …xed-mobile substitution. With …xed-mobile substitution, termination charges can a¤ect both price competition and market shares. I consider the case where all customers subscribe to a single network (i.e., singlehoming subscription model). Figure 1.2 summarizes customers’subscription decision in the singlehoming subscription model. 1.3.1 Retail tari¤s The market shares of each network are no longer constant in the mobile and …xed networks’ pro…t functions (which are given by (1.3) and (1.4)). Moreover, the market share of the …xed network can be determined by the residual of mobile networks’ market shares (i.e., nf = 1 n1 n2 ).21 In this subsection, I investigate how subscription fees and market shares are a¤ected by above-cost termination charges. Recall that Mi ’ market share is decided by ni = s (1 si + )~i =2 where si and si denote Mi ’ proportions on the intra-network and inter-network s ~ s 20 Note that below-cost termination charges hold in a more general setting. Armstrong and Wright (2009) show that above-cost mobile termination charges are suboptimal in the absence of …xed-mobile substitution even allowing inter-network cost and demand di¤erences. 21 This feature is the main di¤erence from existing literature which allows elastic subscription demands (e.g., Dessein, 2003; Armstrong and Wright, 2009; Hurkens and Jeon, 2009; Rey and Sand-Zantman, 2009). The only exception is Hansen (2006) which explicitly considers …xed-mobile substitution. 14 Singlehoming M1 Singlehoming M2 M1 Singlehoming M2 M1 Singlehoming Singlehoming F Singlehoming M2 F F Figure 1.2: Network competition with singlehoming subscribers customer bases. From (1.1) and (1.2), the total mobile market share (de…ned as N n1 +n2 ) is written as N= ~ 2t(1 + ) + (1 )(2rf ri rj ) ~ 4t (1 ) [v(c) v(c + m)] (1.8) In a symmetric equilibrium (rj = ri = r) and marginal-cost termination charges (m = 0), the total mobile market share is given by N= + |{z} intra-network subscribers 1 | 2 1+ {z rf r ~ t } inter-network subscribers This expression implies that customers’subscription decision depends on the relative size of …xed and mobile subscription fees. More customers subscribe to the network which charges lower subscription fees. The equilibrium call prices are set equal to ‘ perceived’ marginal costs when networks 15 compete in two-part tari¤s (Lemma 1). Thus, the pro…t functions are reduced to i = ni (ri f f ) + ni (1 = nf (rf ni )mq(c + m) f) In a symmetric equilibrium, the equilibrium subscription fees are decided by r = f rf = f + where @ni =@ri and (1 N ) mq (c + m) + 1 N 2 N 2 (1.9) (1.10) @ni =@rf : Note that the equilibrium subscription fees depend on the impacts of subscription fees on market shares ( and ). From (1.8) (1.10), the total mobile market share is decided by N= ~ 2t(1 + ) + (1 ) [2mq(c + m) + 1= ] ~ 4t + (1 ) [v(c + m) v(c) + 2mq(c + m) + 1= + 1= ] (1.11) From these equations, one can notice that the market outcomes are decided by the interaction between subscription fees and market shares. I focus on the e¤ects of above-cost termination charges on the market outcomes. Lemma 2 characterizes the e¤ects of above-cost mobile termination charges on the equilibrium subscription fees and market shares. Lemma 2 In the singlehoming subscription model with …xed-mobile substitution, above-cost mobile termination charges (i) reduce subscription fees of both …xed and mobile networks and (ii) raise mobile networks’market share but reduce …xed network’ market share. s The e¤ects on subscription fees are unambiguous. Above-cost mobile termination charges induce network operators to compete more aggressively for both intra-network and internetwork subscribers. This result con…rms the existence of “waterbed”e¤ect (i.e., the negative relationship between termination charges and subscriptions fees) in the presence of …xed16 mobile substitution.22 On the market shares, above-cost mobile termination charges have the asymmetric impacts on …xed and mobile networks’market shares through the asymmetric e¤ects on …xed and mobile networks’call prices and subscription fees. The intuition behind this result is as follows. With termination-based price discrimination, above-cost mobile termination charges lead to higher mobile call prices compared to …xed call prices, which in turn induce mobile networks to set subscription fees more aggressively.23 Lower mobile subscription fees make mobile networks more attractive to customers and result in the increase of subscription to mobile networks. 1.3.2 Mobile termination charges This subsection explores the conditions under which above-cost mobile termination charges are pro…table. In equilibrium, mobile networks’ joint pro…t (de…ned as 12 1+ 2 ) is given by 12 (m) = N (m)[r(m) f ] + N (m) 1 N (m) mq(c + m) 2 (1.12) The e¤ect on mobile networks’ retail pro…t is ambiguous because above-cost termination charges raise the pro…t source (N (m)) but reduce the pro…t margin (r(m) f ). On the other hand, the termination pro…t unambiguously increases with above-cost termination charges. Consequently, the pro…tability of above-cost termination charges is decided by the relative importance of these countervailing e¤ects which in turn depends on the parameter values characterizing the inter-network di¤erences in the customer base ( and 1 ) and ~ product di¤erentiation (t and t). The sign of …rst-order derivative of (1.12) with respect to m at m = 0 is determined by 22 See Cunningham, Alexander and Candeub (2010) and Genakos and Valletti (2008) for the empirical evidence for the exisitence of “waterbed”e¤ect in the mobile telephone industry. 23 Among the o¤-net call prices, above-cost mobile termination charges (m > 0) lead to higher …xed-to-mobile call prices compared to mobile-to-…xed call prices (i.e., pi = c + m > ~f c = pi ). ~ 17 the sign of (1.13) (see Proof of Proposition 1 in Appendix A for details). ( ; b) t where b t (1 )3 (19+4 )b3 +4 (1 t )2 (17+4 )b2 +4 2 (1 t )(13+5 )b 16 3 (3+ ) (1.13) t ~ t=t 2 (0; 1) measures the relative intra-network product di¤erentiation compared to inter-network di¤erentiation. As ( ; b) is decreasing in t but is increasing in b, above-cost t termination charges are more likely to be optimal for a small a large 1 ~ or a small t). or a large b (equivalently, for t Proposition 1 In the singlehoming subscription model with …xed-mobile substitution, there exists cuto¤ functions (b): (0; 1) ! (0; 1) or t( ): (0; 1) ! (0; 1) such that t (i) above-cost mobile termination charges raise the joint pro…t if (ii) above-cost mobile termination charges reduce the joint pro…t if < (b) or b > t( ) t t > (b) or b < t( ). t t Proposition 1 shows that above-cost mobile termination charges may be pro…table for a large inter-network customer base (1 ) or a small inter-network product di¤erentiation ~ (t). The intuition behind this result is as follows. The market share e¤ect (which raises mobile networks’pro…t) is strengthened for a large inter-network customer base and a small inter-network product di¤erentiation. In contrast, the price competition e¤ect (which reduces mobile networks’pro…t) is weakened for a large inter-network customer base.24 As a result, the market share e¤ect outweighs the price competition e¤ect for a large inter-network customer base or a small inter-network product di¤erentiation. In addition, the parameter values regarding the customer base and product di¤erentiation can be interpreted in terms of the development stages of telecommunications industry. It would be typical that the inter-network customer base decreases and the inter-network product di¤erentiation increases in a more developed telecommunications industry.25 This 24 This feature follows from Assumption 1 which states that the product di¤erentiation is ~ larger within inter-network than within intra-network (i.e., t > t). 25 Recently, mobile networks provide more di¤erentiated services from …xed networks (e.g., internet, camera, game and movie). 18 implies that above-cost termination charges are more likely to be pro…table in a less developed telecommunications industry. This also explains why high mobile termination charges have been prevalent over the past few decades. 1.3.3 Welfare analysis I also study the welfare implications of above-cost mobile termination charges. The social welfare can be de…ned as the sum of consumer surplus (denoted by CS) and total network pro…ts ( 12 + f ). In equilibrium, this can be written as W (m) = v0 1h f+ 2N (m) 2 1h + 2 2 i N (m)2 [v(c + m) + mq(c + m)] i 2N (m) + N (m)2 v(c) T C(m) (1.14) where T C denotes the transportation costs. Proposition 2 shows that the social welfare is unambiguously reduced by above-cost mobile termination charges. Proposition 2 In the singlehoming subscription model with …xed-mobile substitution, abovecost mobile termination charges reduce the social welfare. With symmetric cost and demand structures among network operators, the symmetric market shares on both intra-network and inter-network segments are socially optimal. However, higher mobile termination charges cause an excessive mobile market expansion in my model. More rigorously, with a covered market assumption on the consumer side, the total e¤ects on the social welfare excluding transportation costs are cancelled out. Consequently, the welfare e¤ects are decided by the impact on the transportation costs. By setting abovecost mobile termination charges, mobile networks’ market share on inter-network segment (~i ) is determined as larger than 1=2 (at which the transportation costs are minimized). This s implies that the symmetric and cost-based termination charge regulation, which was recommended by European Commission (2009), can be socially bene…cial by reducing competitive distortions from the asymmetric regulation. 19 1.3.4 Discussion In my model, the cost and demand structures between …xed and mobile networks are assumed to be symmetric. However, the main results of this paper are robust in the asymmetric cost and demand structures between …xed and mobile networks. As higher (lower) call demands for the …xed network can raise (reduce) both market share e¤ect and price competition e¤ect, the pro…table above-cost mobile termination charges are feasible for a large inter-network customer base or a small inter-network product di¤erentiation (with di¤erent cuto¤ values from the case of symmetric costs and demands.26 Moreover, the di¤erence in the …xed call demands and mobile call demands may not be large as the demands and costs for …xed and mobile networks usually move in the opposite direction. Let us denote (i) the …xed call demand function as Q( ) and the mobile call demand function as q( ) and (ii) the marginal cost of the …xed network as C = Co + Ct and that of mobile networks as c = co + ct . It would be realistic to assume that Q(p) < q(p) and C < c to capture the various services provided by mobile networks (which raises both mobile call demands and costs). In this case, the equilibrium (o¤-net) …xed and mobile call demands are respectively Q(C + m) and q(c + m) and the relative size of these call demands are ambiguous. 1.4 Fixed-Mobile Substitution with Multihoming Subscribers This section considers the case where some customers are allowed to subscribe to both …xed and mobile networks (i.e., multihoming subscription model). As, historically, mobile networks have penetrated into …xed network markets to expand their market shares, the assumption of Section 3 is relaxed to allow customers closely located to mobile networks 26 Note that, in Armstrong and Wright (2009), above-cost mobile termination charges can be optimal without …xed-mobile substitution when …xed call demands are su¢ ciently large. 20 Singlehoming M1 Singlehoming M2 M1 Multihoming M2 M1 & F Singlehoming Multihoming F Singlehoming M2&F F F Figure 1.3: Network competition with multihoming subscribers to multihome. Figure 1.3 summarizes customers’subscription decision in the multihoming subscription model. Only a few formal models have explicitly considered the case of multihoming subscribers. Armstrong and Wright (2009) introduce the case where all subscribers multihome and analyze how the call level substitution a¤ects mobile termination charges by abstracting the subscription level competition. On the other hand, Hansen (2006) examines …xed-mobile substitution in the mature phase of mobile market expansion without considering call level substitution. I extend these models to consider both subscription level and call level …xedmobile substitution in the presence of multihoming subscribers. For the simplicity of analysis, I restrict attention to the case where only inter-network subscribers exist (i.e., = 0).27 This assumption allows us to focus on how inter-network competition (in both subscription level and call level) plays a role in the determination of termination charges. In this setup, …xed-mobile substitution is feasible by connecting to or disconnecting from the multihoming subscribers’ mobile phone. Fixed and mobile 27 In Section 4.4, I will discuss the robustness and implications of the analyses for the case where both the intra-network and inter-network subscribers exist. 21 networks compete in call usage as well as customers’ subscription because multihoming subscribers can choose either …xed or mobile phones whenever they are available. I assume multihoming subscribers use the cheaper phone to call when both phones are available. Similarly, singlehoming subscribers call to the cheaper phone when the receivers have both …xed and mobile phones. Assumption 2 describes the call usage of subscribers when both …xed and mobile phones are available to callers or receivers. Assumption 2 (Call usage of subscribers) Subscribers choose a cheaper phone to call when both …xed and mobile phones are available to callers or receivers. If multiple networks are available at the same price, call usages are equally distributed (i.e., if there exist h di¤erent ways at the same price, each way can be used with a probability 1=h). I also assume the availability of …xed phone to multihoming subscribers because the …xed phone is unavailable and the mobile phone is used to call or receive phone calls when multihoming subscribers are moving. The value of represents the mobility of multihoming subscribers. Assumption 3 (Mobility of multihoming subscribers) Fixed phone is unavailable to multihoming subscribers with a probability 1.4.1 2 [0; 1]. Retail tari¤s In the presence of call substitution, the consumer surplus is decided by the lowest price among available call prices (Assumption 2). Utilities of singlehoming and multihoming subscribers are written as h i j p rf + nf v(pf ) + nif v(~i ) + njf v(~f ) pf h i j +(1 ) nif v(minfpf ; pi g) + njf v(minfpf ; pf g) ~f ~ uf = v0 22 p rf + nf v(~i ) + (1 p )nf v(minf~i ; pf g) + 2 nif v(pi ) + njf v(^i ) p h i j ~ ~f p ~ ~ +(1 )2 nif v(minfpi ; pf ; pi ; pi g) + njf v(minf^i ; pf ; pi ; pf g) h + (1 ) nif v(minfpi ; pi g) + njf v(minf^i ; pi g) + nif v(minfpi ; pi g) ~ p ~ ~f i j +njf v(minf^i ; pf g) p ~ uif = v0 ~ ri where v0 and v0 denote the …xed bene…ts from singlehoming and multihoming subscription ~ respectively. I also restrict the additional …xed bene…ts from multihoming subscription to be less than the additional …xed cost to represent the potential duplication of …xed bene…ts. Assumption 4 (Fixed bene…ts of multihoming subscription) 0 < v0 v0 ~ v0 < f where v0 . I focus on m > 0 case. In equilibrium, the utility functions are reduced to uf = v0 rf + nf v(c) + nif [ v(c + m) + (1 uif = v0 ~ ri )v(c)] + njf [ v(c + m) + (1 rf + nf v(c) + nif v(c) + njf [ v(c + m) + (1 )v(c)] )v(c)] As the proportion of multihoming subscribers on each Hotelling line is decided by sif = 1=2 + (uif ~ uf )=2t, the market share of multihoming subscribers (nif = sif =2) is given by nif = ~ 4t ~ t + v 0 ri [v(c) v(c + m)] Note that the market share of singlehoming subscribers can be derived from nf = 1 njf . From Lemma 1, the pro…t function of mobile networks is given by if = nif (ri f ) + nif (nf + njf )mq(c + m) 23 (1.15) nif In a symmetric equilibrium (ri = rj = r), the mobile subscription fees are written as28 ~ r = f + 4t [v(c) v(c + m)] nif + (2nif 1)mq(c + m) Thus, the equilibrium mobile subscription fees and market shares are given by r = nif = ~ 4t [v(c) ~ 2 4t ~ 4t [v(c) ~ 2 4t ~ v(c + m)] f + t + v0 mq(c + m) (1.16) [v(c) v(c + m)] + mq(c + m) ~ ~ v(c + m)] t + v0 f + mq(c + m) + 2(t + v0 ) mq(c + m) ~ [v(c) v(c + m)] 4t [v(c) v(c + m)] + mq(c + m) (1.17) Lemma 3 Suppose that there exist only inter-network subscribers (i.e., = 0). In the multihoming subscription model with …xed-mobile substitution, above-cost mobile termination charges (i) reduce mobile networks’ subscription fees and (ii) raise multihoming subscribers but reduce singlehoming subscribers. The intuition for the e¤ect on the mobile subscription fees is similar to the singlehoming subscription model. Above-cost mobile termination charges lead more intense competition for subscribers which results in the reduction of mobile subscription fees. In turn, lower mobile subscription fees make mobile networks more attractive to customers and result in the increase of subscription to mobile networks (which is feasible only through the multihoming subscription in the current model). 1.4.2 Mobile termination charges Mobile networks’joint pro…t is given by 12 (m) = 2nif (m)[r(m) f ] + 2 nif (m)[1 nif (m)]mq(c + m) (1.18) 28 I implicitly assume that the …xed subscription fee is regulated by regulatory authorities (say at rf ). In the current model, the …xed network has an incentive to set subscription fee as high as possible without regulation. 24 Proposition 3 Suppose that there exist only inter-network subscribers (i.e., = 0). In the multihoming subscription model with …xed-mobile substitution, above-cost mobile termination charges raise mobile networks’joint pro…t. By setting above-cost mobile termination charges, (i) the subscription pro…t gain from market share e¤ect outweighs the loss from price competition e¤ect and (ii) the termination pro…t is unambiguously raised. Note that the unambiguous result on the joint pro…t crucially relies on the assumption of 1.4.3 = 0 (see Section 4.4 for the discussion on > 0 case). Welfare analysis The social welfare can be de…ned as W CS + 12 + f . In equilibrium, this can be written as W (m) = v0 f + v(c) + 2nif (m)( v0 +2 nif (m)[1 f) nif (m)] [v(c + m) v(c) + mq(c + m)] Proposition 4 Suppose that there exist only inter-network subscribers (i.e., T C(m) (1.19) = 0). In the multihoming subscription model with …xed-mobile substitution, above-cost mobile termination charges reduce the social welfare. In the presence of multihoming subscribers, above-cost mobile termination charges may reduce the social welfare through two di¤erent channels: (i) the duplication of …xed costs (the excessive multihoming subscription) and (ii) the increase of transportation costs (the excessive mobile market expansion). Proposition 4 shows that the symmetric and costbased termination charge regulation can be socially bene…cial even considering customers’ multihoming subscription. 25 1.4.4 Discussion The analyses on this section have focused on the case where only inter-network subscribers exist ( = 0), but the main results can be extended to more general case where intra-network subscribers exist ( > 0). In the presence of intra-network competition, the pro…tability of above-cost termination charges may not be unambiguous as the market share e¤ect is weakened but the price competition e¤ect is strengthened. However, the pro…table abovecost mobile termination charges are still feasible for a su¢ ciently small . More speci…cally, for nif = 2(1 > 0, the market share of multihoming subscribers is decided by ~ ) t + v0 r(m) + (1 ) [v(c) v(c + m)] ~ 2 4t (1 ) [v(c) v(c + m)] (1.20) From (1.20), the market share e¤ect always exists if above-cost mobile termination charges reduce the equilibrium mobile subscription fees.29 This implies that there exist some parameter values such that above-cost mobile termination charges are optimal through the mobile market expansion. Another extension of the model is to consider the alternative multihoming subscription model. The model in this section (i.e., all inter-network subscribers already have a …xed phone and subscribers closely located to mobile networks choose multihoming) is plausible when the mobile penetration rate is very low. On the other hand, when the mobile penetration rate is very high, it is more realistic to assume that all inter-network subscribers have a mobile phone and subscribers closely located to the …xed network choose multihoming. The main results of this section is robust to this alternative model. Although …xed-mobile substitution does not occur when mobile networks have fully penetrated into …xed network markets, above-cost mobile termination charges can be optimal for a large inter-network customer base or a small inter-network product di¤erentiation (see Appendix B for detailed 29 Consider r 0 (0) < 0. n0 (0) > 0 because the …rst-order derivative of numerator is positve if ( 2(1 )r0 (0) + (1 )q(c) > 0) but the …rst-order derivative of denominator is negative ( 2(1 ) q(c) < 0): 26 analyses in this alternative model). 1.5 Concluding Remarks This paper addresses two unsettled questions on termination charges: (i) why mobile networks may have incentives to set termination charges above marginal costs and (ii) what are the policy implications of the symmetric and cost-based regulation on …xed and mobile termination charges. I present a model with …xed-mobile substitution in which above-cost termination charges may be optimal under two-part tari¤s with termination-based price discrimination. In the presence of …xed-mobile substitution, above-cost mobile termination charges have two contrasting e¤ects on mobile networks’pro…ts. While high mobile termination rate cause more intense price competition among network operators, it also helps mobile networks to expand their market shares. I show that above-cost termination charges are likely to be pro…table for a large inter-network customer base or a small inter-network product di¤erentiation. Moreover, the regulatory movement in the EU (which requires the symmetric and cost-based termination charges on …xed and mobile termination charges) may raise the social welfare by reducing competitive distortions. In addition, the main results of this paper are robust in the asymmetric cost and demand structures between …xed and mobile networks. As higher (lower) call demands for the …xed network raise (reduce) both market share e¤ect and price competition e¤ect, the pro…table above-cost mobile termination charges are more likely for a large inter-network customer base or a small inter-network product di¤erentiation. I conclude by discussing the potential future research. First, my model can be extended to consider the vertical integration between …xed and mobile networks which are often observed in many countries. The vertically integrated network may have di¤erent incentives from independent networks in determining termination charges. The integrated network 27 can internalize network externalities for the calls between its sub-networks and also has less incentives to penetrate into …xed network markets. Second, the network competition for singlehoming and multihoming subscribers can be analyzed in the competitive bottlenecks model of two-sided markets. The growing literature on the optimal pricing structure in two-sided markets might be helpful to understand the relatively high mobile termination charges (see, for instance, Armstrong (2006) and Rochet and Tirole (2006) for details). 28 APPENDIX 29 Appendix A. Proofs omitted in the text Proof of Lemma 2. (1) E¤ect on mobile subscription fee. From (1.9), the …rst-order derivative of r with respect to m is at m = 0, (1 r0 (0) = )(2 2 3t(1 ~ )t + 2 (1 + )t q(c) ~ ) + 4t t2 (1 where a = 2 t (1 ~ )t + (3 + )t a q(c) ~ 2 3t(1 ) + 4t 2(1 ~ )2 + 4tt (1 2 + 4tt (1 ~ ) (A.1) ~ ) + 8t2 2 ~ ) + 4t2 2 Using a > 1, (A.1) can be rewritten as r0 (0) < 2 )(3 (1 )t2 + 4 (1 4 3t(1 )(8 ~ 3 )tt + 8 2 (1 ~ )t2 ~ 2 ) + 4t q(c) This implies r0 (0) < 0 because the right-hand side of the equation is negative under Assumption 1. (2) E¤ect on market shares. From (1.11), the …rst-order derivative of N with respect to m is at m = 0, (1 N 0 (0) = ~ ) t(1 ) + 2t (1 q(c) + ~ ~ 4t 3t(1 ) + 4t (A.2) is positive since 0 < )(1 + 3 ) t(1 ~ 8t 3t(1 ~ 2 ) + 2t ~ 2 ) + 4t a q(c) < 1 and a > 1: Also, n0 (0) < 0 follows from nf = 1 f (3) E¤ect on …xed subscription fee. (A.2) N. From (1.10), the …rst-order derivative of rf with respect to m is at m = 0, 0 rf (0) = ~ 4t 1 N 0 (0) + [1 2 1 (A.3) is negative since N 0 (0) > 0 and < 1: 30 N (0)] q(c) (A.3) Proof of Proposition 1. From (1.12), (A.1) and (A.2), the …rst-order derivative of 12 with respect to m is at m = 0, 0 (0) = 12 3+ 8 3b(1 t )+4 ( ; b)q(c) t 3 (A.4) where ( ; b) is given by (1.13) and the sign of (A.4) is determined by the sign of ( ; b). t t For b; t ^ 2 (0; 1), the following properties (i) (iv) hold. (i) ( ; t) is continuous in (ii) (0; b) > 0 and (1; b) < 0, (iii) ( ; 0) < 0, ( ; 1) > 0 for t t , (iv) @ ( ; b)=@ b > 0 and @ ( ; b)=@ t t t for any b; t < and b, t and ( ; 1) < 0 for < 0 as (A.5) is negative and (A.6) is positive 2 (0; 1). @ ( ; b) t = @ @ ( ; b) t = (1 @b t Case 1 ( h ) 3(1 (1 )2 (16 + 53)b3 t 8 (10 2 + 12 13)b t )(12 2 + 57 4(1 16 2 (2 + 9) )2 (4 + 19)b2 + 8 (1 t < ): There exists a unique threshold of 21)b2 t i )(4 + 17)b + 4 2 (5 + 13) t (A.5) (A.6) and b such that ( ; b) = 0 because t t of @ ( ; b)=@ b > 0 and @ ( ; b)=@ < 0 (by intermediate value theorem). t t t Case 2 ( ): There exists a unique threshold of such that ( ; b) = 0 because of t @ ( ; b)=@ b > 0. On the other hand, ( ; b) < 0 for any b 2 (0; 1) which means the threshold t t t t level t( ) = 1. Proof of Proposition 2. From (1.14), the …rst-order derivative of W with respect to m is at m = 0, W 0 (0) = T C 0 (0) As T C is minimized at s1 = 1=2 and s0 (0) > 0, the sign of W 0 (0) is decided by the sign of ~ ~1 ~ [~1 (0) 1=2] where s1 (0) = 1=2 + rf (0) ri (0) =2t. In equilibrium, this is given by s ~ s1 (0) ~ ~ 1 (t t) = ~ 2 3(1 )t + 4 t 31 (A.7) (A.7) is positive under Assumption 1 which implies W 0 (0) < 0. Proof of Lemma 3. (1) E¤ect on mobile subscription fee. From (1.16), the …rst-order derivative of r with respect to m is at m = 0, ~ (5t + f + ~ 8t r0 (0) = v0 ) (A.8) q(c) (A.8) is negative under Assumption 1. (2) E¤ect on market shares. From (1.17), the …rst-order derivative of nif with respect to m is at m = 0, n0 (0) = if ~ (3t + v0 ) q(c) ~ 16t2 (A.9) is positive under Assumption 1. Also, n0 (0) < 0 follows from nf = 1 f Proof of Proposition 3. (A.9) 2nif . From (1.18), (A.8) and (A.9), the …rst-order derivative of 12 with respect to m is at m = 0, ~ (t + v0 ~ 4t (A.10) is positive under Assumption 1 and t + v0 0 (0) = 12 f) q(c) (A.10) f > 0 which follows from nif (0) > 0. Proof of Proposition 4. From (1.19), the …rst-order derivative of W with respect to m is at m = 0, W 0 (0) = (A.11) is negative since 3( v0 f) 2 ~ t 0 nif (0) (A.11) v0 < f from Assumption 4 and n0 (0) > 0. if B. Supplementary analysis in the full mobile penetration model This appendix explores the case where mobile networks have fully penetrated into …xed network markets. Alternative to the model in Section 4, customers closely located to mobile networks choose singlehoming on mobile networks and customers closely located to the …xed 32 network choose multihoming. Figure A.1 summarizes customers’ subscription decision in this model. Singlehoming M1 Singlehoming M2 M1 Singlehoming M2 M1 Multihoming Singlehoming M1& F Multihoming M2 M2&F F Figure A.1: Network competition in the full mobile penetration model Retail tari¤s. Utilities of singlehoming and multihoming subscribers are written as ui = v 0 ri + ni v(pi ) + nj v(^i ) + p ) nif v(minfpi ; pi g) + njf v(minf^i ; pi g) ~ p ~ +(1 uif = v0 ~ nif v(pi ) + njf v(^i ) p ri rf + ni v(pi ) + nj v(^i ) + (1 p + 2 nif v(pi ) + njf v(^i ) + (1 p j )[ni v(minfpi ; pi g) + nj v(minf^i ; pf g)] ~f p ~ j )2 [nif v(minfpi ; pf ; pi ; pi g) + njf v(minf^i ; pf ; pi ; pf g)] ~ ~f p ~ ~ j p ~ )[nif v(minfpi ; pi g) + njf v(minf^i ; pi g) + nif v(minfpi ; pi g) + njf v(minf^i ; pf g)] ~ p ~ ~f + (1 In equilibrium, utility functions are reduced to ui = v0 uif = v0 ~ ri + ni v(c) + nj v(c + m) + nif v(c) + njf [ v(c + m) + (1 ri )v(c)] rf + ni v(c) + nj v(c + m) + nif v(c) + njf [ v(c + m) + (1 33 )v(c)] The market shares of singlehoming subscribers and multihoming subscribers (ni = (1 )~i =2 and nif = (1 s 1+ 4 1 nif = 4 ni = )(1 + si + si )=2) are written as ~ (1 )(rf ~ 4t v0 rf v0 ) + 2 ft rj ri [v(c) v(c + m)]g ~ 4t From Lemma 1, the pro…t functions are given as i = (ni + nif )(ri f = (nif + njf )(rf f ) + (ni + nif )(nj + njf )mq(c + m) f) In a symmetric equilibrium, the subscription fees and market shares are given by r = f +t ni = 1+ 4 1 ~ v(c + m)] ; rf = (f + t + v0 ) 2 1 1 1 ~ ~ + (f + t v0 ); nif = (f + t ~ ~ 4 8t 8t [v(c) v0 ) Lemma 4 In the full mobile penetration model with …xed-mobile substitution, above-cost mobile termination charges (i) reduce mobile subscription fees but have no impact on …xed subscription fee and (ii) have no impact on market shares between singlehoming and multihoming subscribers. Above-cost termination charges have no impact on the market shares and …xed termination charges since they do not depend on termination charges. However, above-cost mobile termination charges reduce mobile subscription fees because of r0 (0) = q(c) < 0. Mobile termination charges. From ni + nif = nj + njf = 1=2, mobile networks’joint pro…t is given by 12 (m) = r(m) f + [ni (m) + nif (m)]mq(c + m) 34 Proposition 5 In the full mobile penetration model with …xed-mobile substitution, there exist certain parameter values such that above-cost mobile termination charges raise mobile networks’joint pro…t. Proof. The …rst-order derivative of 12 with respect to m is at m = 0, 0 (0) = [(1 12 )(1 + ) + 2(1 ~ 3 )] t + (1 ~ 8t (A.12) is positive for a su¢ ciently small (e.g., )(1 ) (f v0 ) q(c) (A.12) < 1=3). (A.12) implies that above-cost termination charges are more likely to be optimal for a small ~ or a small t in which the price competition e¤ect is weakened. Welfare analysis. The welfare function can be written as W (m) = v0 f + 2nif (m)( v0 f ) + ni (m)v(c) + nj (m)v(c + m) + njf (m) [v(c + m) +[ni (m) + nif (m)]mq(c + m) T C(m) Proposition 6 In the full mobile penetration model with …xed-mobile substitution, abovecost mobile termination charges do not a¤ect the social welfare. Proof. From Lemma 4, the market shares and transportation costs are not a¤ected by mobile termination charges. Thus, the …rst-order derivative of W with respect to m is at m = 0, W 0 (0) = (nj + njf )q(c) + (ni + nif )q(c) W 0 (0) = 0 follows from ni + nif = nj + njf in a symmetric equilibrium. 35 v(c)] BIBLIOGRAPHY 36 Bibliography [1] Armstrong, M. (1998), “Network Interconnection.” Economic Journal, Vol. 108, pp. 545– 564. [2] Armstrong, M. (2002), “The Theory of Access Pricing and Interconnection.”In M. Cave, S. Majumdar, and I. Vogelsang, eds., Handbook of Telecommunications Economics. Amsterdam: North Holland. [3] Armstrong, M. (2006), “Competition in Two-Sided Markets.” RAND Journal of Economics, Vol. 37, pp. 668 691. [4] Armstrong, M. and Wright, J. (2009), “Mobile Call Termination.” Economic Journal, Vol. 119, pp. 270– 307. [5] Calzada, J. and Valletti, T. (2008), “Network Competition and Entry Deterrence.” Economic Journal, Vol. 118, pp. 1223– 1244. [6] Cambini, C. (2001), “Competition Between Vertically Integrated Networks.” Information Economics and Policy, Vol. 13, pp. 137– 165. [7] Cunningham, B.M., Alexander, P.J. and Candeub, A. (2010), “Network Growth: Theory and Evidence form the Mobile Telephone Industry.” Information Economics and Policy, Vol. 22, pp. 91– 102. [8] Dessein, W. (2003), “Network Competition in Nonlinear Pricing.” Rand Journal of Economics, Vol. 34, pp. 593– 611. [9] European Commission (2009), “Commission Recommendation of 7 May 2009 on the Regulatory Treatment of Fixed and Mobile Termination Rates in the EU.” Brussels, available at http://ec.europa.eu/information_society/policy/ecomm/library/recomm_guidelines. [10] Gabrielsen, T.S. and Vagstad, S. (2008), “Why Is On-net Tra¢ c Cheaper than O¤-net Tra¢ c? Access Markup as a Collusive Device.” European Economic Review, Vol. 52, pp. 99– 115. [11] Gans, J.S. and King, S.P. (2001), “Using ‘ Bill and Keep’Interconnect Arrangements to Soften Network Competition.”Economics Letters, Vol. 71, pp. 413– 420. 37 [12] Genakos, C. and Valletti, T. (2008), “Testing the “Waterbed” E¤ect in Mobile Telephony.”CEIS Working Paper 110. [13] Hansen, B. (2006), “Termination Rates and Fixed Mobile Substitution.” Mimeo, Norwegian School of Management. [14] Harbord, D. and Pagnozzi, M. (2010), “Network-Based Price Discrimination and ‘ Billand-Keep’vs. ‘ Cost-Based’Regulation of Mobile Termination Rates.” Review of Network Economics, Vol. 9, pp. 1– 44. [15] Hurkens, S. and Jeon, D.S. (2009), “Mobile Termination and Mobile Penetration.”IEDI Working Papers 575. [16] Jeon, D.S. and Hurkens, S. (2008), “A Retail Benchmarking Approach to E¢ cient Two-Way Access Pricing: No Termination-based Price Discrimination.” Rand Journal of Economics, Vol. 39, pp. 822– 849. [17] Jullien, B., Rey, P. and Sand-Zantman, W. (2009), “Mobile Call Termination Revisited.” IEDI Working Papers 551. [18] La¤ont, J.J., Rey, P. and Tirlole, J. (1998a), “Network Competition I: Overview and Nondiscriminatory Pricing.”RAND Journal of Economics, Vol. 29, pp. 1– 37. [19] La¤ont, J.J., Rey, P. and Tirlole, J. (1998b), “Network Competition II: Price Discrimination.”RAND Journal of Economics, Vol. 29, pp. 38– 56. [20] Lepez, A.L and Rey, P. (2009), “Foreclosing Competition Through Access Charges and Price Discrimination.”IEDI Working Papers 570. [21] OECD (2009), “OECD Communications Outlook 2009.”Paris. [22] Rochet, J.-C. and Tirole, J. (2006), “Two-Sided Markets: A Progress Report.” RAND Journal of Economics, Vol. 37, pp. 645 667. [23] Vogelsang, I. (2010), “The Relationship between Mobile and Fixed-line Communications: A Survey.”Information Economics and Policy, Vol. 22, pp. 4– 17. 38 Chapter 2 Exclusive Dealing and Investment Incentives in the Presence of Risk of Renegotiation Breakdown 2.1 Introduction Exclusive dealing is a contract between a buyer and a seller that prohibits the buyer from trading with other sellers.1 The competition e¤ects of exclusive dealing have been at the center of attention from economists and regulatory authorities for a long time but are still controversial.2 The Chicago School argument for exclusive contracts remains highly in‡ uential in the debate on the e¤ects of exclusive dealing. According to Posner (1976) and Bork (1978), buyers will not accept exclusive dealing that prevents competition and lowers the total 1 This paper focuses on the case where exclusive contracts specify only the exclusivity provision except for a lump-sum payment. See Segal (1999) for a formal justi…cation of incomplete contracts. Also, note that this type of exclusive contracts was adopted in many articles examining the e¤ects of exclusive dealing on investment incentives (e.g., Segal and Whinston, 2000b; de Meza and Selvaggi, 2007; Fumagalli, Motta and Persson, 2009). 2 Regarding the recent cases involving exclusive dealing, see U.S. v. Microsoft (1995 Consent Decree), U.S. v. Dentsply (399 F.3d 181 [2001]), Conwood v. United States Tobacco (290 F.3d 768 [2002]) and U.S. v. Visa USA (344 F.3d 229 [2003]). 39 surplus available to buyers because the incumbent seller is not able to compensate buyers’ loss fully. In the simple model where buyers are …nal consumers, buyers’loss amounts to the di¤erence between consumer surplus under entry and under monopoly and the monopoly pro…t is insu¢ cient to compensate buyers’loss from exclusivity due to the deadweight loss.3 My paper introduces both investments and renegotiation (which are key elements to induce the pro-competitive e¤ect of exclusive dealing) in their frameworks to assess their arguments in a more realistic setup.4 Beginning in the mid-1980s, two divergent strands of literature have investigated the competition e¤ects of exclusive dealing. One strand stresses the pro-competitive e¤ect through investment promotion and the other focuses on the anti-competitive e¤ect from foreclosure of e¢ cient entry.5 The assumption on the renegotiation plays a central role in inducing these contrasting competition e¤ects. The articles stressing the investment promotion e¤ect mostly allows the renegotiation of initial contracts. The foreclosure e¤ect can be ignored in their model as the ex post trade e¢ ciency is always ensured by the renegotiation. In contrast, the articles emphasizing the foreclosure e¤ect do not consider the renegotiation of original contracts and investment incentives. The anti-competitive e¤ect from foreclosure may be pronounced without considering the renegotiation and investments. In my model, exclusive dealing induces both investment promotion and ine¢ cient foreclosure and the interaction between these two e¤ects is a key factor to determine the e¤ects on competition. My paper departs from the existing literature by considering the risk of renegotiation breakdown by which the ine¢ cient foreclosure is driven. While most articles assume a perfect renegotiation or an absent renegotiation, the probabilistic breakdown of renegotiation is more 3 See Motta (2004) and Whinston (2006) for a formal illustration of the Chicago School argument. 4 Farrell (2005), and Fumagalli, Motta and Persson (2009) also assess the Chicago School argument in di¤erent setups. Farrell (2005) introduces a quantity competition instead of a price competition and restores the anti-competitiveness of exclusive dealing. Fumagalli, Motta and Persson (2009) allows a merger between the incumbent and entrant which facilitates an ine¢ cient foreclosure. 5 Excellent surveys on the articles about exclusive dealing are found in Motta (2004), and Rey and Tirole (2007). 40 realistic. The insight was pointed out by Binmore, Rubinstein and Wolinsky (1986), “they [bargaining parties] face a risk that if agreement is delayed, then the opportunity they hope 6 to exploit jointly may be lost (italics added, p. 178).” I adopt their insight to the renegotiation of exclusive dealing in which the renegotiation is exposed to the risk of irrevocable breakdown.7 In the renegotiation of exclusive contracts, the renegotiation may break down for several reasons even when both contracting parties’payo¤s can be improved. First, the negotiation breaks down in random if the impatient parties get fed up with the delay of agreement and walk away from the negotiating table (Muthoo, 1999). Alternatively, the probabilistic breakdown of renegotiation can be explained by the irrational behavior of buyer or seller. In terms of bounded rationality, the risk of breakdown can be interpreted as the probability that contracting parties behave irrationally or miscalculate the surplus from renegotiation.8 The ine¢ cient foreclosure from renegotiation breakdown causes the ex post trade ine¢ ciency. In this setup, the interaction between investment promotion and ine¢ cient foreclosure plays a crucial role in determining the market outcomes. This implies that the separate consideration of these two e¤ects by abstracting the other e¤ect (which has been adopted in most existing literature) may misrepresent the competition e¤ects of exclusive dealing. The main purpose of this article is to propose a formal model to assess the competition e¤ects when exclusive dealing induces both investment promotion and ine¢ cient foreclosure. For this purpose, I propose a model in which (i) the incumbent can engage in relationshipspeci…c investments after the contract is signed but before potential rival’ entry decision s 6 They introduced the risk of negotiation breakdown to formalize the Nash bargaining solution in the alternating bargaining model. See, for instance, Binmore, Rubinstein and Wolinsky (1986), and Muthoo (1999) for details. de Meza and Selvaggi (2007) also adopt the risk of negotiation breakdown in the analysis of investment e¤ects of exclusive dealing to formalize the use of Nash bargaining solution. 7 Although the cases of renegotiation breakdown have not been found extensively in the real world (partly because the breakdown of renegotiation may not be publicly known), the unplentiful evidence of renegotiation agreement indirectly suggests the existence of breakdown. 8 See Ellison (2006), and Armstrong and Huck (2010) for the excellent surveys on the growing industrial organization literature that incorporates the bounded rationality. 41 is made and (ii) the initial contract may be renegotiated after the entry decision is taken. I also assume that (iii) the incumbent di¤ers in the e¢ ciency of cost-reducing investments (represented by k), (iv) the renegotiation process is exposed to an exogenous risk of breakdown (represented by ) and (v) the renegotiation surplus is distributed by the bargaining power between contracting parties (represented by ). This paper explores how the com- petition e¤ects of exclusive dealing depend on the abovementioned parameter values which characterize the contracting environments. This paper presents two key …ndings. First, exclusive dealing raises relatively ine¢ cient incumbent’ investment incentives (but reduces su¢ ciently e¢ cient incumbent’ ins s vestments). The intuition behind this result is as follows. In my model with a potential entry, exclusive dealing may have a tradeo¤ on incumbent’ investment incentives: (i) ins vestment promotion from resolving a hold-up problem and (ii) investment reduction from reducing entry deterrence incentives. On the one hand, exclusive dealing helps the incumbent to be less concerned about the ex post pro…t loss from relationship-speci…c investments. This e¤ect encourages the incumbent to invest in the relationship with a buyer. On the other hand, the incumbent may have less incentives to deter rival’ entry under exclusivity. By s signing exclusive contracts with a buyer, the incumbent is able to earn larger pro…ts when more e¢ cient rivals enter the market. As the entry deterrence is feasible through investments (i.e., higher investments reduce the probability of entry in my model), exclusive dealing plays a role to reduce investment incentives.9 Thus, the relative size of these countervailing e¤ects determines whether exclusive contracts promote or reduce incumbent’ relationship-speci…c s investments. My model shows that the investment promotion e¤ect outweighs the investment reduction e¤ect for a relatively ine¢ cient incumbent as the ine¢ cient seller has strong incentives to mitigate the hold-up problem. The indecisive investment e¤ects of this paper does not contradict to the “irrelevance result”of Segal and Whinston (2000b). Their result relies on the assumption that relationshipspeci…c investments do not a¤ect the value of trade between non-contracting parties. In my 9 Note that this investment reduction e¤ect has not been considered in most literature. 42 model, relationship-speci…c investments may have impacts on the value of trade between non-contracting parties through the e¤ects on potential rival’ entry. Externalities on nons contracting parties are key elements to induce the di¤erent investment e¤ects from Segal and Whinston (2000b). Second, the pro…tability and welfare e¤ects of exclusivity are decided by the relative importance between investment promotion and foreclosure. My model shows that exclusive dealing has di¤erent implications on the pro…tability and social welfare depending on the level of risk of breakdown ( ). More speci…cally, exclusive dealing is pro…table and welfareenhancing when the risk of breakdown is very low. However, it can be pro…table but welfarereducing when there exists a su¢ ciently high risk of breakdown. Moreover, contrary to the Chicago School critique, the pro…table and welfare-reducing exclusive dealing is always feasible for certain parameter con…gurations. The intuition behind this result is as follows. Although both pro…tability and welfare e¤ects are decided by the interaction between investment promotion and foreclosure, these two e¤ects are not symmetric on the joint payo¤ and social welfare. Investment promotion has stronger impact on the joint payo¤ but foreclosure has stronger impact on the social welfare. As increases, both the joint payo¤ and social welfare decreases but the joint payo¤ decreases more slowly than the social welfare (which ensures the existence of pro…table and welfare-reducing exclusive contracts). In addition, a numerical example shows that the welfare reduction may occur for reasonable risk levels. This paper may have important implications for the recent antitrust cases on exclusive dealing where the investments and entry are treated signi…cantly. My model shows that (i) exclusive contracts can have both anti-competitive and pro-competitive e¤ects and (ii) the relative importance of these two e¤ects is decided by the underlying model speci…cations which characterize the contracting environments. The results imply that regulatory authority needs to take into account the speci…c contracting environments of each case to assess the overall competition e¤ects of exclusive dealing. 43 Related literature. As discussed above, this article contributes to the literature on exclusive contracts by …lling the gap between two divergent strands of literature. Several authors have analyzed the anti-competitive e¤ect of exclusive dealing from the foreclosure of e¢ cient entry. Starting from the seminal work by Aghion and Bolton (1987), many economists have stressed that the negative externalities imposed on non-contracting parties are the main sources of ine¢ cient foreclosure (e.g., Rasmusen, Ramseyer and Wiley, 1991; Bernheim and Whinston, 1998; Segal and Whinston, 2000a). More recently, some others extend the models to consider the downstream competition among buyers and show that ine¢ cient foreclosure may occur without negative externalities in the presence of downstream competition (e.g., Fumagalli and Motta, 2006; Simpson and Wickelgren, 2007; Abito and Wright, 2008). Another strand of literature focuses on the investment e¤ect of exclusive contracts. Segal and Whinston (2000b) show that relationship-speci…c investments are irrelevant to exclusivity if the renegotiation of original contracts is feasible. Recently, the investment promotion e¤ect has been restored in a di¤erent bargaining setup (de Meza and Selvaggi, 2007) and in a di¤erent information structure (Vasconcelos, 2009). Speci…cally, de Meza and Selvaggi (2007) show that exclusive contracts can promote investment incentives in the three-party bargaining model where the resale of product is feasible. Vasconcelos (2009) …nds that exclusivity may restore the investment e¢ ciency by resolving the con‡ between information ict signalling and distortion of investment incentives when there exists asymmetric information among contracting parties. None of abovementioned articles consider both investments and entry in their model. It is notable that Spier and Whinston (1995), and Fumagalli, Motta and R nde (2009) introduce these two important elements in the unifying model. Spier and Whinston (1995) present the ex ante over-investment incentives to deter entry as a main driving force of ine¢ ciency under a perfect renegotiation.10 In Fumagalli, Motta and R nde (2009), the interaction 10 Under a perfect renegotiation, ine¢ cient foreclosure does not occur given the equilibrium investment level. In this case, only the ex ante over-investments caused by exclusivity is the source of social ine¢ ciency. 44 between investment promotion and foreclosure plays an important role in determining the competition e¤ects in the absence of renegotiation. However, none of these papers consider the risk of renegotiation breakdown (i.e., the imperfectness of renegotiation). The novel part of my analyses is to show how ine¢ cient foreclosure resulting from the risk of renegotiation breakdown interacts with investment promotion and to present its implications on the pro…tability and social welfare. The rest of this paper proceeds as follows. Section 2 presents the basic model of this paper. Section 3 analyzes the e¤ects of exclusive dealing on the investment incentives, pro…tability and social welfare when the renegotiation process faces an exogenous risk of breakdown. Section 4 extends the basic model and checks the robustness. Section 5 summarizes and concludes. All proofs are relegated to Appendix. 2.2 The Model This paper presents a model in which exclusive contracts a¤ect both incumbent’ investment s incentives and potential rival’ entry decision. s Players. An incumbent seller (I) o¤ers a buyer (B) an exclusive contract which prohibits B from trading with a potential entrant (E) in exchange for a lump-sum payment. After B decides whether to sign the contract but before E decides whether to enter the market, I is able to invest in the relationship with B. If the entry occurs, I and E compete à la Bertrand. In this setup, exclusivity can a¤ect both I’ investment decision and E’ entry s s decision. In addition, the renegotiation of original contracts is allowed after E’ entry decision is s taken. The renegotiation surplus is divided by the bargaining power between I and B. In other words, I receives where proportion and B receives 1 proportion of renegotiation surplus 2 [0; 1] represents the bargaining power of I.11 More importantly, the renegotiation 11 Some articles assume a speci…c bargaining solution to characterize the division of rene- gotiation surplus. For instance, Segal and Whinston (2000b), and de Meza and Selvaggi 45 irrevocably breaks down with probability 2 [0; 1] and reaches an agreement with probability . If the renegotiation breaks down, the initial contract must be complied (i.e., B must 1 trade with I if they signed the contracts). Technology. The buyer’ demand is given by q = q(p). For simplicity, I assume the buyer’ s s demand as a simple linear function q = 1 p.12 1 On the cost side, I suppose that the marginal cost of I is decided by c(r) = 2 r where r denotes the investment level chosen by I. Spending r incurs the investment cost C(r) where C 0 (r) > 0 and C 00 (r) > 0: For simplicity, I assume C(r) = k r2 where k denotes the 2 investment cost (in)e¢ ciency parameter (i.e., the incumbent with larger k is less e¢ cient in cost-reducing investments). At the contract and investment stages, the marginal cost of E (denoted by cE ) is unknown by I and B and only the distribution of cE is a common knowledge. cE is assumed to be uniformly distributed on [0; 1]. Timing. The timing of the game is as follows. Stage 1: I o¤ers B an exclusive contract and B decides whether to sign the contract. Stage 2: I chooses his relationship-speci…c investment level. Stage 3: cE realizes and E decides whether to enter the market. Stage 4: I and B may renegotiate their initial contract if they signed the contract. Stage 5: Active sellers simultaneously determine prices and trade occurs. 2.3 Exclusive Dealing and Imperfect Renegotiation This section explores how the risk of renegotiation breakdown plays a role in determining the e¤ects of exclusive dealing on the investment incentives and entry. The pro…tability (2007) assume the Nash bargaining solution (i.e., = 0:5). 12 The same form of demand function is assumed in Fumagalli and Motta (2006), and Fumagalli, Motta and Persson (2009). In my model, this simple functional form facilitates the analyses without much loss of generality. 46 and welfare implications of exclusive dealing are also investigated. Throughout the paper, I consider the status quo (which is compared to the outcomes under exclusive dealing) as the market outcomes under non-exclusivity. I look for a subgame perfect equilibrium and solve the game by backward induction. Price decision. I start from the last stage of the game where prices are determined. I restrict attention to a linear pricing. If no entry occurs, the incumbent I charges a monopoly price. On the other hand, if the potential entrant E enters the market, the price decision depends on the contract decision and renegotiation. I and E compete à la Bertrand upon entry. The optimal pricing strategy can be summarized as follows.13 No entry: I charges pI = pm (c(r)). Entry: I and E set their prices in the following way.14 8 > c(r) if c < c(r) < E 0 = pI > : c if cE c(r), E 8 > c(r) < if renegotiation was agreed 1 = pI > m : p (c(r)) if renegotiation broke down, 8 > c(r) if c < c(r) < E pE = > : c if cE c(r). E Renegotiation. After observing the realization of cE and E’ entry decision, I and B are s allowed to renegotiate the initial contract. If the renegotiation reaches an agreement, B may purchase products from E and the renegotiation surplus (denoted by ) is distributed to I 13 Throughout the paper, I use the superscript 0 and 1 to denote non-exclusivity and exclusivity and the subscript B; I and E to denote each player. For instance, p0 and p1 I I respectively denote incumbent’ prices under non-exclusivity and exclusivity. s 14 With E’ entry and the agreement of renegotiation, p1 = c(r) is optimal irrespective of s I the realization of cE . For cE < c(r), it is optimal for I to charge p1 = c(r) from Bertrand I 1 competition. We can also show that 1 (c(r)) = 4 (1 c(r))2 + 8 (1 c(r))2 is always larger I than 1 (cE ) = (cE c(r))(1 cE ) + 2 (cE c(r))2 for cE c(r). I 47 and B according to each party’ bargaining power. The …nal payo¤s after renegotiation are s determined as dI + for I and dB + (1 ) for B where di denotes the disagreement payo¤ of i (i = I; B). However, if the renegotiation breaks down, B must trade with I even when there exists the renegotiation surplus. More speci…cally, if the renegotiation is agreed, the joint payo¤ of I and B equals to the consumer surplus at a price c(r). If the renegotiation breaks down, the joint payo¤ is equal to the sum of consumer surplus and I’ pro…t at a price pm (c(r)). Thus, the renegotiation s surplus is measured by the di¤erence between the joint payo¤s with or without renegotiation breakdown and it is written as CS(c(r)) [CS(pm (c(r))) + (pm (c(r)))] = 1 [1 8 c(r)]2 (2.1) where (pm (c(r))) denotes the monopoly pro…t at a cost c(r) and CS(c(r)), CS(pm (c(r))) denote the consumer surpluses at prices c(r) and pm (c(r)) respectively. The disagreement payo¤ is de…ned as the payo¤ that each player would get if the renegotiation broke down and the original contract was complied. Thus, the disagreement payo¤s of I and B are respectively equal to the consumer surplus and pro…t at a monopoly price pm (c(r)). 8 > d < B > : d I CS(pm (c(r))) = (pm (c(r))) = 1 [1 8 1 [1 4 c(r)]2 (2.2) c(r)]2 Entry decision. I assume that E enters the market only when the expected pro…t from entry is positive. As E could not earn positive pro…ts if cE c(r), E will not enter the market in this case. On the other hand, E will enter the market if cE < c(r) as the expected pro…ts of E under non-exclusivity and exclusivity are given by 8 > < > : 0 = [c(r) E 1 = (1 E cE ] [1 ) [c(r) 48 c(r)] cE ] [1 c(r)] p p p 1 B B p m (c(r )) B c(r ) cE I E c E < c(r ) I B+I E 1 q p q q p p 1 p m (c(r )) B B B c E ≥ c(r ) I I I c(r ) 1 q q q Breakdown (θ ) No breakdown (1 − θ ) Non-exclusivity Exclusivity Figure 2.1: Payo¤s under non-exclusivity and exclusivity “For interpretation of the references to color in this and all other …gures, the reader is referred to the electronic version of this dissertation.” In both exclusive and non-exclusive regimes, E enters the market if its marginal cost cE is lower than I’ marginal cost c(r). Figure 2.1 summarizes each player’ payo¤s depending on s s whether (i) the contract has been signed, (ii) the entry has occurred and (iii) the renegotiation has broken down or not. 2.3.1 Investment incentives Now we can examine the e¤ects of exclusive dealing on I’ relationship-speci…c investments. s At the investment stage, I determines the investment level to maximize his expected pro…t. Without exclusive contracts, I earns a positive pro…t only when more e¢ cient rival E does not enter the market (i.e., cE c(r)). The expected pro…t of I under non-exclusivity 49 is written as 0 (r) = [1 I c(r)] (pm (c(r)) C(r) = 1 [1 4 c(r)]3 (2.3) C(r) I assume that the equilibrium investment levels cannot exceed 1=2 to exclude negative marginal costs which is not plausible in the real world. The equilibrium investment level under non-exclusivity is given by 8 h > 1 > 4k < 6 0= r > 1 > : 2 p 2 2k(2k 3 In what follows, the analyses are restricted to k i 3) if k 3 2 (2.4) 3 if 0 < k < 2 3=2 as the consideration of 0 < k < 3=2 case does not have much di¤erence except exclusive dealing has no impact on investment incentives for su¢ ciently small k. With exclusive contracts, I earns a positive pro…t in both entry and no entry case. With entry, I earns the renegotiation payo¤ (dI + (the probability of this event is 1 ) if the renegotiation reaches an agreement ) but earns the disagreement payo¤ (dI ) if the renego- tiation breaks down (the probability of this event is ). Without entry, I earns a monopoly pro…t. Ignoring a lump-sum payment (which has no e¤ect on investment incentives), the expected pro…t of I under exclusivity is written as 1 (r) = c(r) [(1 I = where 1 [1 4 )(dI + c(r)]2 + ) + dI ] + [1 (1 ) 8 c(r) [1 c(r)] (pm (c(r)) c(r)]2 C(r) C(r) (2.5) and dI are given by (2.1) and (2.2) respectively. The following proposition charac- terizes the e¤ect of exclusivity on I’ investment incentives. s Proposition 7 (Investment incentives) Suppose that the renegotiation breaks down with a probability 2 [0; 1]. For k 3=2 and 2 [0; 1], there exists a cuto¤ value of investment 50 cost e¢ ciency k such that exclusive dealing raises I’ investments if k > k but reduces I’ s s investments otherwise. k = 2 is uniquely determined. Proposition 7 shows that exclusive dealing raises relatively ine¢ cient incumbent’ invests ment incentives. The intuition behind this proposition is as follows. In my model with a potential entry, exclusive dealing may have a tradeo¤ on incumbent’ investment incentives: s (i) investment promotion from resolving a hold-up problem and (ii) investment reduction from reducing entry deterrence incentives. On the one hand, exclusive dealing helps the incumbent to be less concerned about the ex post pro…t loss from relationship-speci…c investments. This e¤ect encourages the incumbent to invest in the relationship with a buyer. On the other hand, however, the incumbent may have less incentives to deter rival’ ens try under exclusivity. By signing exclusive contracts with a buyer, the incumbent can earn larger pro…ts when more e¢ cient rivals enter the market. As the entry deterrence is feasible through investments (i.e., higher investments reduce the probability of entry in my model), exclusive dealing plays a role to reduce investment incentives. Thus, the relative size of these countervailing e¤ects determines whether exclusive contracts promote or reduce incumbent’ s relationship-speci…c investments. My model shows that the investment promotion e¤ect outweighs the investment reduction e¤ect for a relatively ine¢ cient incumbent seller as the ine¢ cient seller has strong incentives to mitigate the hold-up problem. More formally, given investments at r = r0 , the di¤erence between I’ exclusive and s non-exclusive pro…ts is given by 1 (r 0 ) I 0 (r 0 ) = 2 + I (1 8 ) c(r0 ) h | {z } | ( ) 1 i 0) 2 c(r {z (+) (2.6) } As is clear in (2.6), exclusivity has a tradeo¤ on I’ investment incentives: (i) investment s reduction through the impact on entry probability and (ii) investment promotion through the impact on the ex post pro…ts. The relative size of these e¤ects depends on the investment level under non-exclusivity which in turn depends on the investment cost e¢ ciency k. Speci…cally, 51 the investment promotion e¤ect outweighs the investment reduction e¤ect for a su¢ ciently low r0 (high k). Also, the sign of investment e¤ect solely depends on k and other exogenous parameter values (e.g., and ) are irrelevant to the sign of investment e¤ect because the investment level under non-exclusivity (which is the status quo compared to the investment level under exclusivity) is determined by k only. I would also like to mention that the “irrelevance result”of Segal and Whinston (2000b) does not contradict to this proposition. The “irrelevance result” relies on the assumption that relationship-speci…c investments do not a¤ect the value of trade between non-contracting parties. In my model, relationship-speci…c investments may have impacts on the value of trade between non-contracting parties through the e¤ect on potential rival’ entry. s Example (Investment incentives: = 0:5; = 0:1 case) 15 A numerical example illustrates Proposition 7. At investment level under exclusivity is given for k r1 = 1 71 54 = 0:5 and = 0:1, the equilibrium 3=2, p 160k + 2 6400k 2 5680k + 2401 (2.7) Figure 2.2 plots (2.4) and (2.7) which represent the investment levels under non-exclusivity and exclusivity associated with the investment cost e¢ ciency k. We can observe that the investment promotion occurs for k > 2 but the investment reduction occurs for k < 2. The same qualitative result can be obtained for any ; 2 [0; 1]. 2.3.2 Pro…tability and welfare analysis Given I’ investment decision, I study whether (i) exclusive dealing can be signed in equis librium and (ii) the pro…table contracts raise or reduce the social welfare. To check the pro…tability (which I de…ne as the existence of contracts improving contracting parties’joint 15 The assumpiton of = 0:5 can be justi…ed by the Nash bargaining solution and has been adopted in many articles. See, for instance, Segal and Whinston (2000b), and de Meza and Selvaggi (2007) to adopt this assumption in the analysis of exclusive dealing. 52 0.5 0.4 r0 0.3 r1 0.2 0.1 0 1.5 2 2.5 3 3.5 4 k Figure 2.2: Investment incentives under non-exclusivity and exclusivity ( = 0:5; = 0:1) payo¤), I compare I and B’ joint payo¤s under non-exclusivity and exclusivity. Moreover, I s identify the conditions under which exclusive contracts are more likely to be anti-competitive or pro-competitive. The joint payo¤ under non-exclusivity is written as h 0 (r 0 ) = c(r 0 )CS(c(r 0 )) + 1 IB i h 1h 0 2 = 8 1 c(r ) ih c(r0 ) i 3 + c(r0 ) i CS(pm (c(r0 ))) + (pm (c(r0 ))) C(r0 ) C(r0 ) (2.8) where r0 denotes the equilibrium investment level under non-exclusivity and it is given by (2.4). On the other hand, the joint payo¤ under exclusivity is written as n h io )CS(c(r1 )) + CS(pm (c(r1 ))) + (pm (c(r1 ))) h ih i 1 ) CS(pm (c(r 1 ))) + (pm (c(r 1 ))) + 1 c(r C(r1 ) h i2 3 h i3 1 = c(r1 ) 1 c(r1 ) + 1 c(r1 ) C(r1 ) 2 8 8 1 (r 1 ) = c(r 1 ) (1 IB (2.9) where r1 denotes the equilibrium investment level under exclusivity. I also compare the social welfare under non-exclusivity and exclusivity to explore welfare 53 consequences of exclusive dealing. The social welfare under non-exclusivity is written as Z c(r0 ) h i CS(c(r0 )) + E (c(r0 )) dcE 0h ih i + 1 c(r0 ) CS(pm (c(r0 ))) + (pm (c(r0 ))) i 3h i3 1 0 h c(r ) 1 c(r0 ) + 1 c(r0 ) = C(r0 ) 2 8 W 0 (r0 ) = where E (c(r)) = [c(r) cE ] [1 C(r0 ) (2.10) c(r)]. On the other hand, the social welfare under exclu- sivity is written as W 1 (r1 ) = Z c(r1 ) 0h + 1 = 1 (1 2 )[CS(c(r1 )) + E (c(r1 ))] + [CS(pm (c(r1 ))) + (pm (c(r1 )))]gdcE ih i c(r1 ) CS(pm (c(r1 ))) + (pm (c(r1 ))) C(r1 ) h i 3 h i2 3 h i3 )c(r1 ) 1 c(r1 ) + c(r1 ) 1 c(r1 ) + 1 c(r1 ) C(r1 )(2.11) 8 8 f(1 As a benchmark, I …rst consider two extreme cases on the risk of renegotiation breakdown: i.e., (i) perfect renegotiation ( = 0) and (ii) absent renegotiation ( = 1).16 The results on these two cases highlight the role of risk of breakdown in determining the e¤ects of exclusivity on the pro…tability and social welfare. Finally, I will generalize the analyses to the imperfect renegotiation case (0 < < 1) using the results on the extreme cases. Case 1: Perfect renegotiation. In the perfect renegotiation case, the condition of pro…tability is the same as the condition of investment promotion. As the ine¢ cient foreclosure does not occur (since the buyer always purchases products from the lower-cost seller in equilibrium), the pro…tability is solely decided by the investment e¤ect. In other words, the total surplus available to I and B increases with investment promotion but decreases with 16 Note that most existing literature supposes these two cases in either explicitly or implic- itly. See, for instance, Spier and Whinston (1995), Segal and Whinston (2000b), de Meza and Selvaggi (2007), and Vasconcelos (2009) for a perfect renegotiation. In contrast, an absent renegotiation is implicitly assumed in most articles which analyze the foreclosure e¤ect of exclusive dealing (e.g., Fumagalli and Motta, 2006; Simpson and Wickelgren, 2007; Abito and Wright, 2008). 54 investment reduction. On the social welfare, exclusive dealing raises the social welfare irrespective of investment e¤ect because the ine¢ cient foreclosure does not occur under a perfect renegotiation. For the ine¢ cient incumbent, exclusivity resolves a hold-up problem and mitigates ex ante underinvestment incentives. On the other hand, exclusive dealing reduces e¢ cient seller’ overs investment incentives. Lemma 1 demonstrates these results. Lemma 5 (Perfect renegotiation) Suppose that the renegotiation always reaches an agreement (i.e., = 0). For k 3=2 and 2 [0; 1], (i) there exists a cuto¤ value of investment cost e¢ ciency (k = 2) such that exclusive dealing raises the joint payo¤ for k > k but reduces the joint payo¤ otherwise (ii) exclusive dealing raises the social welfare for any k 3=2. Lemma 5 shows that the pro…table exclusive dealing is always welfare-enhancing through investment promotion under a perfect renegotiation. This implies that the pro-competitiveness of exclusive dealing through investment promotion critically relies on the perfect renegotiation assumption. Case 2: Absent renegotiation. On the other extreme case where the renegotiation is not feasible, the pro…tability of exclusive dealing changes dramatically. Without renegotiation, the pro…table exclusive contracts are not feasible for any parameter values. The buyer has no incentive to lock his trade to the incumbent because he knows the incumbent has no way to compensate his loss fully due to the monopoly deadweight loss. On the welfare e¤ect, exclusive dealing is always welfare-reducing. As the probability of foreclosure (which is equal to c(r)) is pronounced at = 1, the welfare loss from foreclosure outweighs the welfare gain from investment promotion. The results are characterized by Lemma 6. Lemma 6 (Absent renegotiation) Suppose that the renegotiation is not feasible (i.e., 1). For k 3=2 and = 2 [0; 1], exclusive dealing reduces both the joint payo¤ and social 55 welfare. Lemma 6 shows that the pro…table exclusive dealing is not feasible without renegotiation. Lemma 5 and 6 highlight that the risk of breakdown plays a central role in determining the pro…tability and welfare e¤ects of exclusive dealing. Case 3: Imperfect renegotiation. As discussed in the introduction, the risk of renegotiation breakdown is feasible in the real world. Thus, I extend the analyses on the profitability and welfare e¤ects to the imperfect renegotiation case (0 < < 1). For this purpose, I establish several useful properties regarding the joint payo¤ and social welfare functions. As r0 is a function of k and r1 is a function of ; k, the associated joint payo¤ functions under non-exclusivity and exclusivity can be denoted as 0 (k) and 1 ( ; k). Similarly, IB IB the welfare functions can be written as W 0 (k) and W 1 ( ; k). Lemma 7 states some useful properties on these functions. Lemma 7 For k 3=2 and ; 2 [0; 1], the joint payo¤ and welfare functions satisfy the following properties. 1 ( ; k) 0 (k) for 3=2 k 2: IB IB P2. 1 ( ; k) and W 1 ( ; k) are continuous in : IB @ 1 ( ;k) IB < 0 for k > 2. P3. @ P1. P1 implies that the pro…table exclusive dealing is not feasible without investment promotion (i.e., investment promotion is a necessary condition for pro…tability). The intuition behind this property is straightforward from Figure 2.1. Given investments r, exclusive contracts reduce the joint payo¤ by (which is equal to the monopoly deadweight loss) with a probability c(r) (which is equal to the joint probability of renegotiation breakdown and entry). Consequently, the pro…table exclusive contracts are feasible only with a large investment promotion e¤ect. Afterwards, I restrict the analyses to k > 2 which is a potential candidate for pro…tability. 56 W0(k) W1(θ, k) 0 π IB (k ) π1 (θ , k) IB 0 θ θ 1 θ Figure 2.3: Pro…tability and social welfare under non-exclusivity and exclusivity P2 and P3 imply that, given k > 2, there exists a unique cuto¤ value of such that the joint payo¤ is una¤ected by exclusivity. In addition, P2 (combined with Lemma 5 and 6) ensures the existence of cuto¤ value of where the social welfare is una¤ected by exclusivity. Lemma 5 and 6 imply that (i) 1 (0; k) > IB 0 (k), 1 (1; k) < 0 (k) and IB IB IB (ii) W 1 (0; k) > W 0 (k), W 1 (1; k) < W 0 (k). From Lemma 7, 1 ( ; k) and W 1 ( ; k) can IB be represented as a continuous and strictly decreasing function of .17 Moreover, one can show that the cuto¤ value of joint payo¤ (denoted by ) is higher than that of social welfare (denoted by ). Figure 2.3 summarizes the joint payo¤ and welfare functions satisfying Lemma 5 Lemma 7. From this …gure, the pro…tability and welfare e¤ects in the presence of risk of renegotiation breakdown can be characterized by Proposition 8. Proposition 8 (Imperfect renegotiation) Suppose that the renegotiation breaks down with a probability 2 [0; 1]. For k > 2 and renegotiation breakdown, 2 [0; 1], there exist cuto¤ values of risk of and , such that (i) exclusive dealing raises both the joint payo¤ and social welfare for 0 < (ii) exclusive dealing raises the joint payo¤ but reduces the social welfare for 17 Although the proof of @W e ( ; k)=@ < < < 0 is not easy for all possible parameter con…gurations, one can show that this property holds for reasonable parameter values. 57 (iii) exclusive dealing reduces both the joint payo¤ and social welfare for For given k, and < 1. are uniquely determined. Proposition 8 implies that exclusive contracts can be signed in equilibrium for a su¢ ciently low (0 < ). The intuition is as follows. Exclusive dealing may have a tradeo¤ on contracting parties’joint payo¤: (i) payo¤ increase from investment promotion and (ii) payo¤ decrease from foreclosure. As increases, the e¤ect of investment promotion becomes weaker but the e¤ect of foreclosure becomes stronger.18 The positive e¤ect of investment promotion outweighs the negative e¤ect of foreclosure for a low (the opposite result applies to a high ). In addition, exclusive contracts can be welfare-improving for a su¢ ciently low . The intuition for this result is similar to the former one. Moreover, the cuto¤ value of pro…tability is always higher than that of welfare e¤ect. Accordingly, the pro…table exclusive dealing raises the social welfare for a low but reduces the social welfare for an intermediate ( < (0 < ) < ). The intuition behind this result is as follows. Although both the pro…tability and welfare e¤ects are decided by the interaction between investment promotion and foreclosure, these two e¤ects are not symmetric on the joint payo¤ and social welfare. Investment promotion has larger impact on the joint payo¤ but foreclosure has larger impact on the social welfare. Therefore, as increases, both joint payo¤ and social welfare decreases but the joint payo¤ decreases more slowly than the social welfare (which ensures the existence of pro…table and welfare-reducing exclusive contracts). Example (Pro…tability and welfare e¤ect: = 0:5 case) A numerical example highlights how the risk of breakdown a¤ects the pro…tability and welfare implications. At = 0:5, the equilibrium investment level under exclusivity is given 18 The decreasing investment e¤ect can be shown by @r 1 =@ < 0 (see Proof of Lemma 7 in Appendix). 58 θ 0 (III) π 1 < π IB , W 1 < W 0 IB 0.2 0.15 0 (II) π 1 > π IB , W 1 < W 0 IB 0.1 0 (I) π 1 > π IB , W 1 > W 0 IB 0.05 0 2 2.5 3.5 3 4 k Figure 2.4: Pro…tability and welfare e¤ects of exclusive dealing ( = 0:5) for k 3=2, r1 = 1 6(1 ) 7 The area, associated with q 16k + + 2 64k 2 56k + 25 + 2 2(4k + 5) (2.12) and k, can be divided into three regions depending on the e¤ects on the pro…tability and social welfare. In Figure 2.4, each region represents the parameter con…gurations such that exclusive dealing is (I) pro…table and welfare-enhancing, (II) pro…table and welfare-reducing and (III) unpro…table. This example shows that the necessary probability of breakdown for welfare reduction ( ) is not unreasonably high (e.g., < 0:01 for any k 2.4 3=2). Extensions In this section, I extend the basic model in two dimensions and illustrate that the main results of the paper are robust to the extensions. 59 2.4.1 Degree of exclusivity Suppose the ex post probability that the incumbent has exclusivity is e 2 [0; 1].19 While the analysis of the previous section was restricted to a fully exclusive regime (e = 1), we can easily extend the analysis to e 2 (0; 1). The expected pro…t of I under non-exclusivity is written as e (r) = (1 I e) 0 (r) + e 1 (r) , I I e (r) I 0 (r) = e[ 1 (r) I I 0 (r)] I Above equation implies that the investment e¤ect at e = 1 carries over to any e 2 (0; 1). That is, exclusive contracts raise the relatively ine¢ cient incumbent’ investment incentives: One s can also easily infer the implications on the pro…tability and social welfare. For a su¢ ciently high e, the pro…table and welfare-reducing exclusive dealing is feasible for an intermediate . However, the necessary probability of breakdown for welfare reduction ( ) is negatively related with e (i.e., higher e requires lower ). 2.4.2 Buyer investments Now suppose that the buyer is able to invest in the relationship with the incumbent. With buyer’ investments r, the marginal cost of I is given by c(r) = 1=2 s r. The expected pro…t of B under non-exclusivity is written as 0 (r) = c(r)CS(c(r)) + [1 B = 1 [1 8 c(r)] CS(pm (c(r))) c(r)]2 [1 + 3c(r)] C(r) C(r) (2.13) 19 Segal and Whinston (2000b) consider a continuous degree of exclusivity. They interpret e 2 [0; 1] as the duration of exclusivity. 60 On the other hand, the expected pro…t of B under exclusivity is written as 1 (r) = c(r) f(1 B = where 1 [1 8 ) [dB + (1 c(r)]2 [1 + (1 ) ] + dB g + [1 )(1 )c(r)] c(r)] CS(pm (c(r))) C(r) C(r) (2.14) and dB are given by (2.1) and (2.2) respectively. The following proposition char- acterizes the e¤ect of exclusivity on buyer’ investment incentives. Note that, contrary to s incumbent’ investment case, exclusive dealing raises relatively e¢ cient buyer’ investment s s incentives. Proposition 9 (Buyer’ investment incentives) Suppose that the renegotiation breaks s down with a probability 2 [0; 1]. For k > 0 and 2 [0; 1], there exists a cuto¤ value of investment cost e¢ ciency k such that exclusive dealing raises B’ investments if k < k but s reduces B’ investments otherwise. k = 2 is uniquely determined. s We can also obtain the same results on the pro…tability and social welfare as in incumbent’ investment case because the joint payo¤ and welfare functions are the same irrespective s of the identity of investing party. That is, the pro…table exclusive dealing will reduce the social welfare when there exists a su¢ ciently high risk of breakdown: 2.5 Concluding Remarks Exclusive dealing is widely used in the real world but its e¤ects on competition are still controversial. The coexistence of pro-competitive e¤ect from investment promotion and anti-competitive e¤ect from foreclosure makes it di¢ cult to decide the overall competition e¤ects of exclusive dealing in one direction. Moreover, my paper shows that the investment e¤ect of exclusive dealing also depends on the investing party’ cost e¢ ciency when there s exists a threat of potential entry. Exclusivity raises relatively ine¢ cient incumbent’ invests ment incentives by resolving a hold-up problem but reduces relatively e¢ cient incumbent’ s 61 investment incentives by reducing entry deterrence incentives. I would also like to mention that the investment e¤ect of this paper is complementary to the “irrelevance result” of Segal and Whinston (2000b). In my model, relationship-speci…c investments cannot be purely internal because potential rival’ entry is a¤ected by investments. The “irrelevance s result” seems to be a special case where relationship-speci…c investments do not cause any externalities on non-contracting parties. In the presence of the risk of renegotiation breakdown, exclusive dealing may have both investment promotion e¤ect and foreclosure e¤ect. The main purpose of this paper is to propose a formal model to compare the relative importance between these contrasting e¤ects. In my model, the risk of renegotiation breakdown plays a crucial role in determining the relative size of these e¤ects. As the risk of breakdown increases, the investment promotion e¤ect becomes weaker but the foreclosing e¤ect becomes stronger. Thus, exclusive dealing may have di¤erent implications on the pro…tability and social welfare depending on the level of risk of breakdown. My model shows that exclusive dealing is (i) pro…table and welfare-enhancing when the risk of breakdown is very low but (ii) pro…table and welfarereducing for a su¢ ciently high risk of renegotiation. Moreover, contrary to the Chicago School critique, the pro…table and welfare-reducing exclusive dealing is always feasible for certain parameter con…gurations. This paper restores the ine¢ cient foreclosure by exclusive contracts in the presence of risk of renegotiation breakdown even considering renegotiation and investments. Ironically, the investment promotion e¤ect (which has been considered as a pro-competitive e¤ect of exclusive dealing in most literature) may serve anti-competitive purposes by interacting with ine¢ cient foreclosure. In my paper, the risk of renegotiation breakdown ( ) has been given exogenously. However, it would be interesting to analyze the implications of exclusive dealing when the risk of breakdown is determined endogenously. For instance, the risk of breakdown would be related with the size of renegotiation surplus (which can be thought as the opportunity cost of renegotiation breakdown). The contracting parties would have strong incentives to reduce the probability of breakdown when the renegotiation surplus is large, which in turn a¤ects 62 investment incentives and entry decision. In future work, it would be interesting to analyze how the risk of negotiation breakdown interacts with investment promotion and foreclosure in more detail. 63 APPENDIX 64 Appendix Proofs omitted in the text Proof of Proposition 7. From (2.6), the …rst-order derivative of 1 (r) at r = r0 is given I by 10 (r 0 ) = I 00 (r 0 ) + 2 + (1 I 8 h c0 (r0 ) 1 ) ih c(r0 ) 1 i 3c(r0 ) (A.1) where r0 denotes the equilibrium investment level under non-exclusivity and it is given by (2.4). Using 00 (r0 ) = 0; c0 (r) < 0 and 0 I 8 > < 9 > = 10 (r 0 ) I > : > > ; 1=2, the sign of (A.1) is decided by c(r) if 1=6 0; if 0 r0 1=2 r0 < 1=6 Since r0 is strictly decreasing in k and solely determined by k, the condition of 1=6 (0 r0 < 1=6) is equivalent to 3=2 k r0 1=2 2 (k > 2). Proof of Lemma 5. (1) Joint payo¤: Plugging = 0 into (2.9), the joint payo¤ under non-exclusivity and exclusivity is written as 0 (r) = IB 1 (r) = 1 [1 IB 8 c(r)]2 [3 + c(r)] C(r) which can be rewritten as 0 (r) = IB 1 (r) = IB 0 (r) + 1 [1 I 8 c(r)]2 [5 c(r)] Using 00 (r0 ) = 0; the …rst-order derivative at r = r0 is given by I 00 (r 0 ) = IB 10 (r 0 ) = IB 1 0 0 h c (r ) 1 8 65 ih c(r0 ) 11 i 3c(r0 ) (A.2) As (A.2) is positive from c0 (r0 ) < 0; 1 c(r0 ) > 0 and 11 8 > < > 1 (r 1 ) IB > : The condition of r1 > r0 (r1 9 > = 3c(r0 ) > 0, we can conclude that if r1 > r0 0 (r 0 ); > IB ; if r1 r0 r0 ) is equivalent to k > 2 (3=2 (2) Social welfare: Plugging k 2) from Proposition 7. = 0 into (2.11), the social welfare under non-exclusivity and exclusivity is written as 1 W 0 (r) = W 1 (r) = c(r) [1 2 c(r)] + 3 [1 8 c(r)]3 C(r) 1 [1 8 c(r)]3 which can be rewritten as 1 W 0 (r) = W 1 (r) = 0 (r) + c(r) [1 I 2 c(r)] + Using 00 (r0 ) = 0; the …rst-order derivative at r = r0 is given by I W 00 (r0 ) = W 10 (r0 ) = ih 1 0 0 h 0 ) 3c(r 0 ) c (r ) 1 + c(r 8 The sign of (A.3) is decided by the sign of 3c(r0 ) That is, W 00 (r0 ) = W 10 (r0 ) > 0 for 0 1=6 r0 1=2. As r1 > r0 for 0 conclude that W 1 (r1 ) i 1 (A.3) 1 from c0 (r0 ) < 0 and 1 + c(r0 ) > 0. r0 < 1=6 and W 00 (r0 ) = W 10 (r0 ) r0 < 1=6 and r1 W 0 (r0 ) for any 0 r0 r0 for 1=6 r0 1=2 (equivalently, for any k 0 for 1=2, we can 3=2 from Proposition 7). Proof of Lemma 6. (1) Joint payo¤: From the …rst order condition of (2.5) at = 1, the equilibrium investment level under exclusivity is given by r1 = 1 2(2k 1) 66 (A.4) Plugging = 1 into (2.9), the joint payo¤s under non-exclusivity and exclusivity are written as 1h 1 8 h 1 (r 1 ) = 3 1 IB 8 i2 h i c(r0 ) 3 + c(r0 ) i2 c(r1 ) C(r1 ) 0 (r 0 ) = IB C(r0 ) where r0 and r1 are given by (2.4) and (A.4) respectively. The comparison of joint payo¤s shows 1 (r1 ) < 0 (r0 ) for any k IB IB (2) Social welfare: Plugging 3=2. = 1 into (2.11), the social welfares under non-exclusivity and exclusivity are written as i 3h 1 0 h c(r ) 1 c(r0 ) + 1 2 8 h i 1 (r 1 ) = 3 1 c(r 1 ) 2 W C(r1 ) 8 W 0 (r0 ) = i3 c(r0 ) C(r0 ) The comparison of social welfares shows W 1 (r1 ) < W 0 (r0 ) for any k 3=2. Proof of Lemma 7. P1: Let us denote 1 (r1 ; = 0) and 1 (r1 ; = 1) as 1 (r1 ) in (2.9) evaluated at IB IB IB = 0 and = 1 respectively. Using these notations, equation (2.9) can be rewritten as 1 (r 1 ) = IB For 3=2 2, r1 k (i) 1 (r1 ) < 1 (r1 ; IB IB 0 (r 0 ; IB 1 (r 1 ; IB ) 1 (r1 ; = 0) IB r0 from Proposition 7. We can also get the following conditions: = 0) from 1 (r1 ; IB = 1) from Lemma 5 and r1 = 0) > 1 (r1 ; IB = 1), (ii) 1 (r1 ; IB = 0) r0 and (iii) 0 (r0 ) = 0 (r0 ; = 1) by de…nition. IB IB From these conditions, we obtain 1 (r1 ) IB P2: For = 1) + (1 0 (r 0 ). IB 2 [0; 1], the continuity of 1 ( ; k) in IB and 1 in r1 . Similarly, the continuity of W 1 ( ; k) in IB and W 1 in r1 . 67 follows from the continuity of r1 in follows from the continuity of r1 in P3: Consider k > 2. The e¤ect of risk of breakdown on the joint payo¤ can be divided into two channels: (i) the direct e¤ect and (ii) the indirect e¤ect through the impact on investments. @ 1 IB = @ d 1 IB d } | {z direct e¤ect @r1 + 10 (r1 ) IB | {z @ } indirect e¤ect First, the direct e¤ect is negative as the sign of (A.5) is negative. d 1 IB = d 1 c(r) [1 8 c(r)]2 (A.5) Second, the indirect e¤ect is decided by the sign of 10 (r1 ) and @r1 =@ . From (2.9), the IB joint payo¤ under exclusivity can be rewritten as 1 (r) = IB 1 (r) + 1 [1 I 8 c(r)]2 [5 + (1 )(1 )c(r)] The …rst-order derivative 1 (r) at r = r1 is given by IB 10 (r 1 ) = IB 10 (r 1 ) I 1 0 1 h c (r ) 1 8 ih c(r1 ) 10 (1 )(1 (A.6) is positive from 10 (r1 ) = 0; c0 (r1 ) < 0 and 1 I I ) + 3(1 )(1 i )c(r1 ) (A.6) cI (r1 ) > 0. In order to determine the sign of @r1 =@ , I will use the …rst order condition of pro…t maximization problem under exclusivity which is given by 10 (r 1 ) I 1 0 1 h c (r ) 1 8 i c(r1 ) [ (1 ) 4 3 (1 )c(r1 )] C 0 (r1 ) = 0 By totally di¤erentiating both sides of the above condition, @r1 = @ c0 (r1 ) 1 c(r1 ) 1 8 100 (r1 ) I 3c(r1 ) (A.7) where 100 (r1 ) < 0 from the second order condition of pro…t maximization problem. The I 68 sign of (A.7) is negative for k > 2, since c0 (r1 ) < 0, 1 cI (r1 ) > 0, 1 3c(r1 ) < 0 and 100 (r 1 ) < 0. I Therefore, we obtain @ 1 =@ < 0 from the negative direct and indirect e¤ects. IB Proof of Proposition 8. One can show that 1 ( ; k) IB (denoted by ) and at least one solution for W 1 ( ; k) 0 (k) = 0 has a unique solution IB W 0 (k) = 0 (denoted by ) by using Lemma 5 Lemma 7, intermediate value theorem and …xed point theorem. From these conditions, and = = can be written as 4fc(r1 )[1 c(r1 )]2 4fc(r1 )[1 c(r1 )] c(r0 )[1 c(r0 )[1 c(r0 )]2 g + 3f[1 c(r1 )]3 [1 c(r0 )]3 g + C(r0 ) C(r1 ) c(r1 )[1 c(r1 )]2 c(r0 )]g + 3f[1 c(r1 )]3 [1 c(r0 )]3 g + C(r0 ) C(r1 ) c(r1 )[1 c(r1 )][3 + c(r1 )] where r0 is given by (2.4) and r1 denotes the equilibrium investment level under exclusivity. The uniqueness of is ensured by the monotonicity of r0 , r1 in r1 > r0 for k > 2, the numerator of smaller than that of . This implies is larger than that of and that of in r0 , r1 . As and the denominator of is > . Therefore, 9 8 9 8 > > > > > > > > > > > > > > > > > > = < = < 0 (r 0 ) and W 1 ( ; k) 1 (r 1 ) W 0 (k), > IB IB > > > > > > > > > > > > > > > > ; : ; : if 0 < if < if 1 which characterizes the pro…tability and welfare e¤ects of exclusivity depending on the level of risk of breakdown. Proof of Proposition 9. From (2.13) and (2.14), the …rst-order derivative of 1 (r) at I r = r0 is given by 10 (r 0 ) = B 00 (r 0 ) + (1 B )(1 8 ) 3 0 0 h c (r ) 1 ih c(r0 ) 1 i 3c(r0 ) (A.8) where r0 denotes the equilibrium investment level under non-exclusivity. Using 00 (r0 ) = 0; B 69 c0 (r) < 0 and 0 c(r) 1=2, the sign of (A.8) is decided by 8 > < > 10 (r 0 ) B > : 9 > = > ; if 1=6 < r0 0; if 0 r0 1=2 1=6 Since r0 is strictly decreasing in k and solely determined by k, the condition of 1=6 < r0 (0 r0 1=6) is equivalent to 3=2 k < 2 (k 70 2). 1=2 BIBLIOGRAPHY 71 Bibliography [1] Abito, J.M. and Wright, J. (2008), “Exclusive Dealing with Imperfect Downstream Competition.”International Journal of Industrial Organization, Vol. 26, pp. 227– 246. [2] Aghion, P. and Bolton, P. (1987), “Contracts as a Barrier to Entry.”American Economic Review, Vol. 77, pp. 388 401. [3] Armstrong, M. and Huck, S. (2010) “Behavioral Economics as Applied to Firms: A Primer.”Competition Policy International, Vol. 6, pp. 3 45. 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(2009), “Contractual Signalling, Relationship-Speci…c Investment and Exclusive Agreements.”mimeo, Universidade Nova de Lisboa. [24] Whinston, M.D. (2006), Lectures on Antitrust Economics. Cambridge: MIT Press. 73 Chapter 3 Dynamic Incentives of Tying in Two-sided Markets 3.1 Introduction Two-sided markets involve two distinct groups of agents interacting via platforms and each group obtains bene…ts from interacting with the other group agents. Optimal pricing structure of two-sided markets di¤ers from that of one-sided markets. In two-sided markets, platforms charge subscription fees in order to utilize inter-group externalities. Inter-group externalities intensify the price competition between platforms as a platform should perform well on the other side in order to compete e¤ectively on one side of the market.1 This paper explores tying arrangements in two-sided markets. Tying practice is prevalent in two-sided markets. For instance, the media platforms, payment card platforms and software platforms, which have two-sided markets features, often engage in tying arrangements.2 The main purpose of this paper is to examine how inter-group externalities a¤ect tying incentives through platforms’price and R&D competition. 1 See Armstrong (2006) for the discussion on the optimal pricing structure in two-sided markets. 2 See Evans (2003) for the examples of tying practice in two-sided markets. 74 Evans (2003) provides a general discussion on the antitrust policy in two-sided markets and emphasizes the need for caution in applying a one-sided logic to two-sided markets. He suggests several potential di¤erences in the implications of tying in two-sided markets from one-sided markets: (i) foreclosing a rival …rm on one side of the market may prevent the …rm from succeeding on the other side and thereby deter entry, (ii) the potential pro…ts on the other side provide additional incentives for tying as the market power on one side may help platforms to gain a market power on the other side and (iii) tying on one side may cause bene…ts to agents on the other side in the presence of inter-group externalities.3 The insights imply that, in two-sided markets, we should consider both the potential e¢ ciencyenhancing e¤ect from network bene…ts and the e¢ ciency-reducing e¤ect from competitive distortions. In this paper, I present a formal model to analyze the relative importance of these contrasting competition e¤ects of tying in two-sided markets. The motivating example of this paper is Microsoft’ tying practice of requiring Windows s Operating System users to accept its Windows Media Player software. The European Union alleges that tying practice of Microsoft is anti-competitive since it hurts Microsoft’ digital s media rivals such as RealNetworks.4 Microsoft’ tying practice has a two-sided markets s feature in the sense that platforms intermediate both sides of the market where content providers are located on one side and consumers are located on the other side. Microsoft’ tying case has been studied in both one-sided and two-sided markets frames works. In the one-sided markets setup, Choi (2004) examines this case from the perspective of leverage theory of tying.5 He stresses the role of R&D investments which is considered to play a crucial role in the antitrust policy concerning the network industry, in explain3 See also Tirole (2005) for a general discussion on the implications of tying in two-sided markets. 4 Microsoft v Commission, T-201/04 [2007]. See Choi (2010) for a brief summary on this case. “On March 24, 2004, the European Union ruled that Microsoft was guilty of abusing the ‘ near-monopoly’of its Windows PC operating system and …ned it a record 497 million euros ($613 million). The ruling was appealed, but upheld by the Court of First Instance on September 17, 2007 (Footnote 1, p. 607).” 5 The leverage theory argues that a …rm possessing a monopoly power in one market can monopolize another market by tying the products of these two markets. 75 ing Microsoft’ tying incentives to leverage its monopoly power in the Windows Operating s System markets to the digital media software markets.6 My paper reconsiders the leverage theory of tying in the framework of two-sided markets and investigates how tying a¤ects the price and R&D decision of platforms. On the other hand, Choi (2010) analyzes Microsoft’ s tying case in the two-sided markets framework. His analyses focus on the e¤ects of tying on agents’subscription decision when agents are allowed to multihome (i.e., to subscribe to multiple platforms). However, the paper does not consider the e¤ect of tying on platforms’ R&D incentives. My paper attempts to …ll the gap between these two papers by considering both R&D incentives and two-sidedness which are important aspects in the investigation on competition e¤ects of Microsoft’ tying practice. s I adopt a two-sided Hotelling competition model of Armstrong (2006), and Armstrong and Wright (2007) to analyze the platform competition in two-sided markets. In order to explore the implications of tying, I allow one platform to tie its product with a monopolistic product in another market and also consider R&D competition between platforms. The novel part of my model is to consider the impact of tying on R&D incentives in the twosided markets model. My model considers two di¤erent platform competition structures regarding agents’subscription decision: i.e., (i) two-sided singlehoming (both group-1 and group-2 agents subscribe to a single platform) and (ii) competitive bottlenecks (group-1 agents singlehome and group-2 agents multihome).7 Optimal pricing structure depends on the assumption regarding agents’ subscription decision which in turn may change the e¤ect of tying on R&D incentives. Therefore, the interaction between R&D competition and price competition (which is a¤ected by agents’subscription decision) plays a central role in determining the competition 6 The importance of R&D investments in the network industry has been emphasized in several papers. See, for instance, Farrell and Katz (2000), Choi and Stefanadis (2001), Choi (2004), and Gilbert and Riordan (2007). 7 This paper restricts the analyses to these two platform competition structures, because the other possible case, where all agents on both sides choose to multihome, is not very common. Moreover, there exists no incentive for agents to multihome for nonnegative prices if all agents on the other side multihome. See Armstrong (2006), and Armstrong and Wright (2007) for more details. 76 e¤ects of tying in two-sided markets. This paper presents two main …ndings. First, this study con…rms that the main results of leverage theory of tying in one-sided markets also apply to two-sided markets. I show that tying can be a pro…table strategy even without foreclosure of rival platform in twosided markets. The intuition behind this result is as follows. Tying has a tradeo¤ on tying platform’ pro…t: (i) pro…t loss from intense price competition and (ii) pro…t gain s from foreclosure of rival’ R&D incentives. In the pricing stage, tying acts to commit more s aggressive pricing on both sides of the market. In the R&D stage, tying plays a role to commit more aggressive R&D investments on both sides of the market. Numerical analyses con…rm that tying is optimal for certain parameter values even without exclusion of rival platform when the pro…t gain from R&D e¤ect outweighs the pro…t loss from price competition e¤ect. I also show that the social welfare can be reduced by this tying arrangements through (i) the distortion of R&D incentives, (ii) the increase of transportation costs and (iii) the reduction in the consumption of tying products. I derive the results in both two-sided singlehoming and competition bottlenecks models. Second, this paper suggests that there exists a potential di¤erence in tying incentives between one-sided and two-sided markets. I show that tying intensi…es the price and R&D competition on the non-tying side as well as on the tying side in the two-sided singlehoming model. Inter-group externalities play a role to transfer the impacts on the one side to the other side which may reinforce the potential anti-competitive e¤ects of tying. Related literature. This paper relates to two strands of literature: (i) the leverage theory of tying and (ii) the platform competition in two-sided markets. This study explores the implications of leverage theory of tying in two-sided markets. More speci…cally, this paper examines whether the leverage theory of tying in Whinston (1990) and Choi (2004) applies to the two-sided markets model. The literature on the leverage theory of tying concerns that a …rm with a monopoly power in one market can 77 monopolize another market using a monopoly power in the …rst market.8 Whinston (1990) shows that when the tied good market structure is oligopoly and the scale economies are present, tying can be optimal by inducing the rival …rm to exit from the product market. Choi (2004) extends the model to consider R&D incentives and shows that tying in the primary market can be used as a leverage to gain pro…ts in the tied good market by foreclosing rival’ s R&D investments. Moreover, he …nds that tying can be privately optimal even without exclusion of rival …rm from the product market. I extend the analysis of Choi (2004) to two-sided markets and examine the e¤ects of tying on the price and R&D competition in the presence of inter-group externalities.9 In the same vein, Choi and Stefanadis (2001) extend the leverage theory to analyze the implications of tying on R&D incentives. They show that when the monopolistic incumbent faces a threat of entry in system markets, tying makes the prospects of successful entry less certain and discourages rivals from investing in innovation. Carlton and Waldman (2002) also analyze how tying between complementary products can be used to preserve a monopoly power by focusing on the entry costs and network externalities. This paper is also related to the literature on the two-sided platform competition (e.g., Armstrong, 2006; Armstrong and Wright, 2007; Rochet and Tirole, 2003, 2006). The main focus of the literature is the optimal pricing structure in the presence of inter-group externalities. In the two-sided singlehoming model, platforms charge lower price for the group which causes larger bene…ts to the other group and/or which is more competitive side of the market. In the competitive bottlenecks model, platforms may charge lower price for singlehoming agents (more competitive side) and higher price for multihoming agents (less competitive side). My paper adopts the two-sided platform competition model to analyze the competition e¤ects of tying when the tying platform is able to invest in cost-reducing 8 In addition to the leverage theory of tying, the e¢ ciency rationale and price discrimi- nation device are the other veins to explain the incentives of tying. See Motta (2004) for details. 9 As in Choi (2004), I analyze the e¤ects of tying between independent products instead of complementary products in order to avoid a multiple equilibria problem. The intuition behind the main results applies to the complementary products (Choi, 2004; Choi, Lee and Stefanadis, 2003). 78 R&D. I analyze how the optimal pricing structure in two-sided markets interacts with R&D e¤ects. Recently, several authors have analyzed tying arrangements in the two-sided markets model (e.g., Rochet and Tirole, 2008; Amelio and Jullien, 2007; Choi, 2010). They …nd that tying in two-sided markets may be welfare-enhancing through (i) rebalancing interchange fees (Rochet and Tirole, 2008), (ii) relaxing nonnegative price constraints (Amelio and Jullien, 2007) and (iii) increasing multihoming subscription (Choi, 2010).10 None of these articles consider the e¤ects of tying on competing platforms’R&D incentives which is the main focus of my paper. Contrary to these articles, I …nd that tying can be socially ine¢ cient through distorting platforms’R&D incentives. The rest of this paper proceeds as follows. Section 2 describes the basic model of this paper. Section 3 and 4 examine the implications of tying on the price competition and innovation incentives in di¤erent platform competition models: (i) two-sided singlehoming model (Section 3) and competitive bottlenecks model (Section 4). Section 5 summarizes and concludes. 3.2 The Model In this section, I explain the basic setup of the model which will be used throughout the paper. I consider both two-sided singlehoming and competitive bottlenecks models which extend the two-sided Hotelling competition model of Armstrong (2006), and Armstrong and Wright (2007). The additional assumptions or setups needed in each model will be introduced as needed in each subsequent section. Demand structure. Two symmetric platforms (A and B) compete in a standard Hotelling speci…cation they are located at either end of a unit interval on both sides of the market. 10 Rochet and Tirole (2008) analyze the implications of “honor-all-cards”rule of Visa and MasterCard which forces merchants who accept their credit cards also to accept their debit cards. In 2003, Visa and MasterCard agreed to abandon this rule in the US. 79 0 1 A n2 B n2 M B A n1A B n1 1 0 Figure 3.1: Platform competition in the two-sided singlehoming model Platform A is able to tie its product with a monopolistic product M .11 Two agent groups (1 and 2), representing consumers and content providers, are uniformly distributed along the unit interval and each agent has a unit demand. The measure of group-i agents who join platform H is denoted by nH (i = 1; 2 and H = A; B) and the total measure of each group i agents is normalized to 1. Only group-1 agents value product M as vM and platform A’ s marginal cost of product M is cM . Thus, platform A’ monopoly surplus from product M s is de…ned as sM vM cM . Figure 3.1 summarizes the platform competition structure in the two-sided singlehoming model which will be analyzed in Section 3. I consider two cases of agents’subscription decision: i.e., (i) two-sided singlehoming (both group-1 and group-2 agents subscribe to a single platform) and (ii) competitive bottlenecks (group-1 agents singlehome and group-2 agents subscribe to both platforms). In each case, the parameter values are assumed to satisfy the conditions of two-sided singlehoming or competitive bottlenecks.12 11 In Microsoft’ tying case, platform A, platform B and product M can be regarded as s Windows Media Player, Real Player, and Windows Operating System, respectively. 12 See Assumption 5 (Section 3) and Assumption 6 (Section 4) for the speci…c conditions on the parameter values in each case. 80 Cost structure. I assume a symmetric cost structure for platform A and B in which each platform incurs a per-agent cost ci for each group. Platforms are able to invest in R&D H on both sides of the market. Let Ii denote the cost reduction on the group-i agent side (i = 1; 2) by platform H (H = A; B). After R&D investment decision is made, the cost of platform H is given by ci H Ii on the group-i agent side. Additionally, I suppose several simplifying assumptions. First, the possibility of R&D investments in product M is ignored in order to focus on the e¤ect of tying on R&D incentives in the tied good market. Second, each platform can reduce the unit production cost by I with incurring the investment cost C(I) where C 0 (I) > 0 and C 00 (I) > 0. I assume C(I) = k I 2 2 where k measures the R&D cost e¢ ciency (i.e., larger k implies more ine¢ cient in costreducing R&D investments). Finally, I assume that each product cannot be sold separately under tying.13 Timing. The timing of the game is as follows. Stage 1: Platform A decides whether or not to tie its product with product M . Stage 2: Platform A and B simultaneously determine their own R&D investment levels. Stage 3: Platform A and B simultaneously determine their own prices. Stage 4: Group-1 and group-2 agents make a subscription decision. 3.3 Two-sided Singlehoming This section considers the case where agents on both sides of the market subscribe to a single platform. The analyses focus on the e¤ects of tying on the price and R&D decision of competing platforms. In the two-sided singlehoming model, the utility of group-i agent located at xi 2 [0; 1] 13 This can be justi…ed by assuming a technological tying from the costly investments in the product design and production process. 81 from platform H is written as 0 uH = v i i pH i ti xi + i nH j (3.1) 0 where i; j = 1; 2 (i 6= j) and H = A; B.14 vi denotes the …xed bene…t from subscribing to each platform which is assumed to be su¢ ciently large such that all agents are willing to join at least one platform in equilibrium. pH denotes the subscription fee from joining each i platform and ti , s i represent group-i agent’ transportation costs and inter-group bene…ts from interacting with each group-j agent. I also assume the following restrictions on the parameter values throughout this section. Assumption 5 (Two-sided singlehoming conditions) Parameter values satisfy the following conditions. (5.1) t1 > 1 ; t2 > 2 (5.2) 4t1 t2 > ( 1 + 2 )2 (5.3) c1 + t1 2 ; c2 + t2 1 Assumption 5 ensures that both group-1 and group-2 agents choose singlehoming and the nonnegative price constraints are not binding in equilibrium. Speci…cally, Assumption (5.1) ensures that agents on both sides never choose to multihome at nonnegative prices. The unique and nonnegative equilibrium prices are ensured by Assumption (5.2) and (5.3).15 I use a backward induction to …nd a subgame perfect equilibrium. 3.3.1 Price decision The price decision of each platform depends on the tying decision of platform A. 14 Throughout the paper, I use the superscript H, K to denote each platform and the subscript i, j to denote each group agent. I will also use a tilde (~) to denote the variables corresponding to the tying case. 15 See Proposition 1 of Armstrong and Wright (2007) for details. 82 No tying. Suppose that platform A does not engage in tying. In this case, each market can be analyzed independently. Platform A can extract the whole consumer surplus (sM ) from product M , but platforms compete for subscribers on both sides of the tied good market. From (1), combined with nH + nK = 1, the demand of each group agent must satisfy i i the following condition. 0 vi pH i 0 ti nH + i nH = vi i j pK i ti (1 nH ) + i (1 i nH ) j where i; j = 1; 2 (i 6= j) and H; K = A; B (H 6= K). Consequently, the number of group-i agents subscribing to platform H is given by K i (pj 1 nH = + i 2 pH ) + tj (pK j i 2 (t1 t2 pH ) i 1 2) where i; j = 1; 2 (i 6= j) and H; K = A; B (H 6= K). The …rst order condition of each platform’ maximization problem is given by s pH = i 1 2 pK + ci i H Ii + ti j tj i H cj + Ij + 1 + i j pH j i K pj j (3.2) where i; j = 1; 2 (i 6= j) and H; K = A; B (H 6= K). The symmetric equilibrium price is reduced to pi = ci where pi pA = pB ; pj i i Ii + ti pA = pB ; Ii j j j tj i cj + Ij + pj A B Ii = Ii ; Ij (3.3) A B Ij = Ij and i; j = 1; 2 (i 6= j). Due to inter-group externalities, subscription fees are adjusted downward to represent the marginal external bene…t from attracting an extra group-1 agent which is measured by the last term in (3.3).16 In the general case, the equilibrium prices are determined as in Appendix A. 16 See Section 4 of Armstrong (2006) for details. 83 Tying. Now consider the case where platform A ties its product with product M: Tying prevents group-1 agents from purchasing product M separately. Accordingly, group-1 agents’ choice is essentially between consuming the bundled product by subscribing to platform A and consuming the unbundled product by subscribing to platform B with foregoing the consumption of product M . In this case, the equilibria are no longer symmetric. The demand of each group agent must satisfy the following conditions. 0 vM + v1 0 v2 0 ~2 t1 nA + 1 nA = v1 ~1 ~ P1 pB ~1 t1 (1 nA ) + 1 (1 ~1 nA ) ~2 0 = v2 pB ~2 t2 (1 nA ) + 2 (1 ~2 nA ) ~1 ~1 t2 nA + 2 nA ~2 pA ~2 ~ where P1 denotes the price for the bundled product. Consequently, the number of group-1 and group-2 agents subscribing to platform A are given by nA ~1 ~ pA ) + t2 (~B P1 + vM ) ~2 p1 2(t1 t2 1 2) ~1 + vM ) + t1 (~B pA ) P p ~ pB 1 1 (~2 = + 2 nA = ~2 pB 1 2 (~1 + 2 2 2(t1 t2 2 1 2) Note that the number of group-i agents subscribing to platform B can be derived from nB = 1 ~i nA . ~i ~ P1 De…ne a …ctitious price pA ~1 vM which measures the implicit subscription fee for platform A separated from the price of bundled product. The …rst order conditions of each platform’ maximization problem are given by s 1 2 1 pA = ~2 2 1 pB = ~i 2 pA = ~1 pB + c1 ~1 ~A I1 pB + c2 + t2 ~2 pA + ci ~i 2 sM + t1 1 t1 2 ~B Ii + ti j tj 1 t2 ~A c2 + I2 + 1 + 1 2 ~A c1 + I2 + sM + 1 + 2 1 i ~B cj + Ij + 1 + i j pA ~1 pB ~j pA ~2 1 B p2 ~ 2 2 B p1 ~ 1 i A pj ~ j ; ; : (3.4) where i; j = 1; 2 (i 6= j). Comparing (3.2) and (3.4), we can observe that tying intensi…es 84 the price competition on both sides of the market. Tying shifts platform A’ reaction curves s for both group-1 and group-2 agents inward because platform A behaves as if its costs on the group-i side were ci ~A Ii sM with tying. The intuition of this result is the following. With tying, platform A can realize the monopoly surplus (sM ) only with the sale of bundled product. Because of inter-group externalities, tying on the group-1 side makes platforms to determine their prices more aggressively on the group-2 side as well as the group-1 side. The equilibrium prices in the tying case are determined as in Appendix B. 3.3.2 R&D decision In the R&D stage, each platform maximizes its own pro…t given price decision. Graphically, the equilibrium R&D investments are decided at the intersection of each platform’ reaction s curves. The e¤ect of tying on R&D incentives is determined by the change of reaction curves from tying arrangements. Proposition 10 characterizes the e¤ect of tying on R&D incentives. Proposition 10 In the two-sided singlehoming model, tying raises tying platform’ R&D s investments but reduces rival platform’ R&D investments on both sides of the market (i.e., s A B ~A ~B Ii > Ii and Ii < Ii , i = 1; 2). Proof. Suppose that reaction curves have negative slopes and satisfy stability conditions.17 H The reaction curves under no tying and tying can be de…ned as @ H =@Ii ~H @ ~ H =@ Ii H C 0 (Ii ) = 0 and H ~H ~H C 0 (Ii ) = 0 (i = 1; 2 and H = A; B). For any given Ii = Ii , the di¤erences 17 Given the second order conditions of maximization problems, the negative slope and sta! ! 2 H bility conditions are written as @H K < 0 and @Ii @Ii @2 H H K @Ii @Ii H C 00 (Ii ) @2 K K H ; i = 1; 2 and H; K = A; B (H 6= K). @Ii @Ii 85 @2 H H2 @ Ii K C 00 (Ii ) @2 K K2 @ Ii > I iB ~ RiA RiA A* B* ( Ii , Ii ) ~ * ~ * ( I i A , I iB ) ∆I iB RiB I iA ~ RiB ∆I iA Figure 3.2: E¤ects of tying on R&D investments between reaction curves under tying and no tying are given by @ ~A ~A @ I1 @ ~A ~A @ I2 where @ A A @I1 @ A A @I2 2( 1 = = @ ~B ~B @ I1 @ ~B ~B @ I2 2 2 ) + 9 (t1 t2 @ B B @I1 @ B B @I2 ! ! = = 6t2 h 2 + 4( 1 3 ( 1 + 2) h 4 2) i sM ; 2 + 4( 1 4 2) i sM : (3.5) 1 2 ). Both equations in (3.5) are positive under As- sumption (5.1).18 This implies that tying shifts platform A’ reaction curves outward and s platform B’ reaction curves inward on both sides of the market. Figure 3.2 shows that s A B ~B ~A Ii > Ii and Ii < Ii (i = 1; 2).19 The intuition behind this result is as follows. Tying allows the tying platform to capture a larger market share on both sides of the market as the platform determines its price more 18 Both the numerator and the denominator of (3.5) are positive if t t 1 2 1 2 > 0 (Assumption (5.1)). 19 In Figure 3.2, the shifts of reaction curves are parallel because the di¤erence between the slopes of reaction curves under tying and no tying does not rely on R&D investment levels. 86 aggressively on both sides of the market with tying. This implies that the cost reduction from R&D investments translates into a larger pro…t with tying through the larger market share e¤ect. That is, tying plays a role as a commitment to more aggressive R&D investments and raises tying platform’ R&D investments. Tying also reduces rival’ R&D investments s s from the substitutability of R&D investments.20 Note that this result only depends on Assumption (5.1) with a few regular conditions such as the negative slope and stability conditions of reaction curves. This implies that tying distorts R&D incentives of competing platforms for any parameter values satisfying the two-sided singlehoming conditions. In addition, the e¤ect of tying on R&D investments might be asymmetric between the tying side and non-tying side. Lemma 8 explores the relative size of R&D e¤ects on both sides of the market. Lemma 8 For the parameter values satisfying Assumption 5, @ ~H ~H @ I1 Proof. From (3.5), @ ~H ~H @ I1 @ H H @I1 8 > @ H < > @I H > : 1 @ ~H ~H @ I2 9 > = @ ~H > @I H ; ~2 3 [t2 @ H = H @I2 @ H H @I2 if t2 > 1+ 2 2 otherwise. 2 ( 1 + 2 )] h 4 2) 2 + 4( 1 i sM and so @ ~H ~H @ I1 @ H H @I1 @ ~H ~H @ I2 @ H > 0 i¤ t2 > H @I2 1+ 2 2 . Lemma 8 shows that the relative size of R&D e¤ects of tying depends on the product di¤erentiation on the non-tying side (t2 ) and inter-group externalities ( 1 ; 2 ). Tying may have larger R&D e¤ects on the tying side than on the non-tying side if t2 is larger than 20 See Bulow, Geanakoplos and Klemperer (1985) and Tirole (1988) for the strategic sub- stitutes of R&D investments. 87 ( 1 + 2 )=2. However, the relative size of e¤ects can be reversed for a su¢ ciently small t2 compared to 1 and 2 . The result is intuitive in the sense that platforms may have incentives to compete aggressively for R&D investments on the non-tying side for a relatively large inter-group externalities ( 1 ; 2 ) given the product di¤erentiation on that side (t2 ). This lemma is closely related to the optimal pricing structure. In the two-sided singlehoming model, platforms target one group more aggressively than the other if the group causes larger bene…ts to the other group and/or is more competitive side of the market. From the interaction between the price and R&D game, the intense price competition reinforces the R&D competition. Thus, R&D e¤ect is likely to be smaller on the non-tying side than on the tying side for a small inter-group externalities (small inter-group bene…ts) or for a large product di¤erentiation on the non-tying side (less competition on the non-tying side). With symmetric parameter values, R&D e¤ects are determined unambiguously as R&D e¤ect is always larger on the tying side than on the non-tying side. Corollary 1 For 1 = 2 and t1 = t2 , @ ~H ~H @ I1 @ ~H @ H > H ~H @I1 @ I2 @ H H @I2 This corollary follows from Lemma 8 since t2 > ( 1 + 2 )=2 holds for 1 = 2 under Assumption (5.1). The analyses in this subsection show that tying forecloses rival’ R&D investments even s without exclusion of rival platform. This implies that the anti-competitive e¤ect of tying may occur through two di¤erent channels: i.e., (i) exclusion of rival platform and (ii) distortion of R&D incentives. In the following subsection, I explore if tying can be pro…table for the tying platform even without exclusion of rival platform from the product market (i.e., the analysis focuses on the second channel). 88 3.3.3 Tying decision This subsection examines the pro…tability of tying. Speci…cally, I assume the symmetric parameter values and a speci…c investment cost function to explore if there exist parameter speci…cations such that tying is pro…table for the tying platform. Suppose t1 = t2 = 1 and 1 = 2 = ; < 1 which satisfy Assumption 1. I further assume C(I) = k I 2 to obtain 2 a closed form solution for the optimal R&D investment levels. 1 H The symmetric equilibrium R&D investments without tying are given by Ii = 3k where i = 1; 2 and H = A; B. On the other hand, the equilibrium R&D investments with tying are given by 1 + 3k 9k 9k(1 1 = 3k 9k 9k(1 1 + = 3k 9k 9k(1 1 = 3k 9k 9k(1 ~A I1 (9k 2) (9k 2) 9k 2) 9k 2) = ~B I1 ~A I2 ~B I2 2) 2 2) 2 2(9k 2) 2(9k 2) 2 2(9k 2) 2 2(9k 2) sM sM sM sM The pro…tability condition is given by21 sM > 2 [9k (1 ) 2] [9k (1 + ) 2]2 [18k (1 ) 3k (9k 1)(9k 2)2 243k 2 (3k 1) 2 5] (3.6) For a graphical analysis, I additionally assume the stability condition of reaction curves and no exit condition to focus on the case where tying does not induce the rival platform to exit. With a stability condition, the cost e¢ ciency parameter (k) should satisfy Proposition 21 Platform A’ pro…t change from tying is given by s A= 324k 2 (1 6f9k 9k(1 2 ) + 18k(9 + 2) 2 2(9k k(9k 1)(9k ) sM + 2)g 2f9k 9k(1 A A; A A A ~A where C(I1 ) A > 0. Thus, tying is pro…table if 89 2)2 243k 3 (3k 1) 2 sM 2 2) 2 2 2(9k 2)g A C(I2 ) + sM ; ~ A ~A ~A C(I1 ) ~A C(I2 ). 1, which is given by22 k> 2 9(1 (3.7) ) In addition, no exit condition (i.e., 0 < nA < 1) is given by23 ~i 0 < sM < 2 9k 1 2 3k(9k 2(9k 2) (3.8) 2) Graphically, tying is pro…table without exclusion of rival platform for the parameter values of k; sM satisfying (3.6) (3.8). Figure 3.3 illustrates the tying incentives for = 0:5.24 The shaded area represent the parameter values in which tying is pro…table without exclusion of rival platform. The main insights for the general case can be obtained from this …gure. Proposition 11 characterizes the pro…tability of tying. Proposition 11 Suppose 1 = 2 = ; t1 = t2 = 1 and 0 < < 1. In the two-sided singlehoming model, there exist the investment cost e¢ ciency (k) and the monopoly surplus (sM ) such that tying is pro…table for the tying platform even without exclusion of rival platform. Proof. Denote k and k to represent two intersection points of the pro…tability and no exit conditions. One can show that the set of (k; sM ) satisfying (3.6) (3.8) is not empty, because (k; sM ) with k 2 (k; k) and sM 2 (0; sM ) satisfy (3.6) (3.8) where k = 2= [9(1 k > k and sM = 9k 1 2 2 2(9k 2) = 3k(9k 2) )] ; > 0. Therefore, there exist (k; sM ) such that the conditions (3.6) (3.8) are satis…ed for any 0 < < 1. 22 The condition is derived from the comparison of equilibrium investment levels. 0 < For < 1; this condition is stricter than the stability condition itself which is given by 2 . The stability condition is derived from @ 2 H = 1 (1 2 ) and C 00 (I H ) = k. i 9 H2 @ Ii 2 H 2 ) < 0 for In addition, the negative slope condition is satis…ed since @H K = 1 (1 9 @Ii @Ii k>2 1 9 < 1 (see Footnote 17 for details). 23 Only nA < 1 is binding under the condition (3.7). ~1 24 For = 0:5, the conditions (3.6) (3.8) are given by s 3(27k 8) 4 k > 9 and 0 < sM < 4k(9k 2) 2 3k . 90 (9k 4)(9k 5)(27k 4)2 M > 12k(9k 1)(9k 2)2 729k 2 (3k 1) ; sM 7 4 k= 9 sM = (9k − 4)(9k − 5)(27 k − 4) 2 12k (9k − 1)(9k − 2) 2 − 729k 2 (3k − 1) 6 5 4 3 2 sM = 1 0 1 2 3(27k − 8) 2 − 4(9k − 2) 3k 3 k Figure 3.3: Tying incentives in the two-sided singlehoming model ( =0.5) This result shows that tying can be a pro…table strategy for the tying platform even without exclusion of rival platform for certain parameter con…gurations. The intuition behind this result is as follows. In a dynamic model with R&D competition, tying has a tradeo¤ on tying platform’ pro…t: (i) pro…t loss from intense price competition and (ii) pro…t gain s from foreclosure of rival’ R&D investments. Proposition 11 con…rms that there always exist s certain parameter con…gurations such that the pro…t gain from tying outweighs the pro…t loss. More speci…cally, tying is more likely to be pro…table for a small k (i.e., more e¢ cient in R&D investments) or a large sM (i.e., larger monopoly surplus). Intuitively, the platform, which is more e¢ cient in investments or has larger monopoly surplus, can easily obtain pro…ts from tying. 3.3.4 Welfare analysis Welfare e¤ects of tying may have important policy implications. In the two-sided singlehoming model, tying may have potential welfare e¤ects through two di¤erent channels: i.e., (i) exclusion of rival platform and (ii) distortion of R&D investments. As the …rst channel leads 91 to the welfare reduction obviously, I focus on the second channel to discuss the potential welfare implications of tying without exclusion of rival platform. In my model, there are several channels through which tying a¤ects the social welfare. First, tying causes the asymmetry in R&D incentives and results in socially suboptimal R&D investments (tying platform invests too much and rival platform invests too little). Second, tying increases transportation costs as it induces the asymmetry in market shares. Third, some group-1 agents must forego the consumption of product M under tying. All three channels lead to welfare reduction in my model. Proposition 12 In the two-sided singlehoming model, tying reduces the social welfare even without exclusion of rival platform. Proof. See Appendix C. The result implies that tying may have anti-competitive e¤ects even without exclusion of rival platform from the product market. Proposition 11 and 12 con…rm that the main results of Choi (2004) in one-sided markets carry over to the two-sided singlehoming model and provide a new rationale for the regulation on Microsoft’ tying practice in the media s software markets. In two-sided markets, tying practice may have anti-competitive e¤ects through the foreclosure of rival’ R&D investments as well as the exclusion of rival platform s from the product market. Moreover, as the foreclosure of R&D investments occurs on both sides of the market in two-sided markets, the anti-competitive e¤ect may be reinforced via inter-group externalities. Welfare implications of this paper are signi…cantly di¤erent from the existing literature. The existing literature on tying in two-sided markets has focused on the welfare-enhancing e¤ect of tying from inter-group externalities (Amelio and Jullien, 2007; Rochet and Tirole, 2008; Choi, 2010). In contrast, my model stresses the welfare-reducing e¤ect from the distortion of R&D incentives. Their papers and mine are complementary in the sense that my paper presents the potential welfare-reducing e¤ect of tying which has not been considered in the other papers. 92 0 1 A B n2 = n2 = 1 M B A n1A B n1 1 0 Figure 3.4: Platform competition in the competitive bottlenecks model 3.4 Competitive Bottlenecks This section analyzes the e¤ects of tying in the competitive bottlenecks model. The model of Section 3 is modi…ed to allow group-2 agents to subscribe to both platforms (multihome). Figure 3.4 summarizes the platform competition structure in the competitive bottlenecks model. The analyses on tying in the competitive bottlenecks model are meaningful in several respects. First, there are several examples which are well characterized by the competitive bottlenecks model.25 Moreover, the optimal pricing structure in this model di¤ers from the two-sided singlehoming model. In the competitive bottlenecks model, platforms compete more aggressively on the singlehoming side and leave zero surplus on the multihoming side. Platforms behave as though they do not compete directly for the multihoming side, instead compete indirectly by attracting the singlehoming side to subscribe. This section explores how the di¤erence in pricing structure a¤ects the impacts of tying on R&D incentives, pro…tability and social welfare. The model in this section follows Section 4.2 in Armstrong and Wright (2007) in which 25 Armstrong (2006) presents several examples of the competitive bottlenecks framework, such as mobile telecommunications networks, newspapers, shopping malls, supermarkets and airline reservation system. 93 only one side cares about the platform performance on the other side (i.e., 1 = 0).26 The utility of group-1 agent located at x1 2 [0; 1] from the platform H is written as 0 uH = v1 1 pH 1 t1 x1 (3.9) 0 where H = A; B: v1 is su¢ ciently large such that all group-1 agents are willing to subscribe 0 at least one platform in equilibrium and v2 is assumed at 0. Furthermore, I assume the following restrictions on the parameter values throughout this section. Assumption 6 (Competitive bottlenecks conditions) Parameter values satisfy the following conditions. (6.1) 2 > 1 = 0; t1 > t2 = 0 (6.2) c2 min ft1 =2; (6.3) c1 + t1 2 =4g 2 In the unique and symmetric equilibrium, group-1 agents choose singlehoming and group-2 agents choose multihoming under Assumption 6. Speci…cally, Assumption (6.1) ensures the uniqueness of equilibrium.27 Platforms serve group-2 agents in equilibrium with nonnegative pro…ts under Assumption (6.2). Finally, Assumption (6.3) guarantees the nonnegative equilibrium prices. Additionally, I assume that cost-reducing R&D investments are feasible only on the group-1 side. In the competitive bottlenecks model, platforms have no incentive to engage in R&D competition on the group-2 side because all group-2 agents have already subscribed to both platforms. After R&D decision is made, platform H’ cost on the group-1 side is s given by c1 H I1 but the cost on the group-2 side remains at c2 . 26 Armstrong and Wright (2007) pointed out that many of insights in more general models can be seen in this simpli…ed setup. 27 The assumption is adopted to focus on the unique equilibrium without concerning about the equilibrium selection among multiple equilibria. 94 3.4.1 Price decision No tying. Without tying, platform A can extract the whole consumer surplus (sM ) from product M. From the multihoming assumption, the numbers of group-2 agents subscribing to platform A and B are both equal to 1 (i.e., nA = nB = 1). From (3.9), combined with 1 1 nB = 1 1 nA , the demand of group-1 agents must satisfy the following condition. 1 pH 1 0 v1 0 t1 nH = v1 1 pK 1 t1 1 nH 1 where H; K = A; B (H 6= K): The number of group-1 agents subscribing to platform H is given by nH = 1 1 pK pH 1 + 1 2 2t1 where H; K = A; B (H 6= K): I also assume that if group-2 agents subscribe to a platform if they are indi¤erent between subscribing and unsubscribing to the platform. In this case, it is optimal for platforms to charge the maximum willingness to pay for group-2 agents. Thus, each platform charges pH = 2 nH for group-2 agents: 2 1 The …rst order condition of each platform’ maximization problem is given by s 1 pH = (pK + c1 1 2 1 H I1 + t1 2) (3.10) where H; K = A; B (H 6= K). The symmetric equilibrium price for group-1 agents is reduced to p1 = c1 where p1 pA = pB and I1 1 1 I1 + t1 2 (3.11) A B I1 = I1 . The interpretation for the equilibrium price is similar to the two-sided singlehoming model (Section 3). Platforms have incentives to adjust subscription fees downward to utilize the external bene…t from attracting an extra group-1 agent. In the competitive bottlenecks model, the marginal external bene…t from an extra group-1 agent is equal to 2 as the price for group-2 agents is determined at pH = 2 nH . 2 1 95 Tying. With tying, group-1 agents’choice is essentially between consuming the bundled product by subscribing to platform A and consuming the unbundled product by subscribing to platform B with foregoing the consumption of product M . While all group-2 agents ~2 subscribe to both platforms (i.e., nA = nB = 1), the demand of group-1 agents must satisfy ~2 the following condition. 0 vM + v1 ~ P1 0 t1 nA = v1 ~1 pB ~1 t1 (1 nA ) ~1 ~ where P1 denotes the price for the bundled product. The number of group-1 agents subscribing to platform A is written as nA = ~1 ~1 1 vM + pB + 2 2t1 ~ P1 The number of group-1 agents subscribing to platform B can be derived from nB = 1 ~i ~ P1 Let us de…ne pA ~1 nA . ~i vM which measures the implicit subscription fee for platform A separated from the price of bundled product. The …rst order conditions of each platform’ s maximization problem are given by pA = ~1 1 B p + c1 ~ 2 1 ~A I1 sM + t1 1 ~B 2 ; p1 = 2 pA + c1 ~1 ~B I1 + t1 2 (3.12) Comparing (3.10) and (3.12), platform A behaves as if its cost on the group-1 side were c1 ~A I1 sM under tying. This implies that tying shifts platform A’ reaction curve inward s on the group-1 side. Solving (3.12), the equilibrium prices for group-1 agents are given by pA = c1 + t1 ~1 2 ~A ~B 2I1 + I1 + 2sM ; pB = c1 + t1 ~1 3 96 2 ~A ~B I1 + 2I1 + sM 3 (3.13) 3.4.2 R&D decision No tying. The maximization problem of each platform is written as max H H C(I1 ) = H I1 t1 2+ c2 H I1 K I1 ! H K I1 1 I1 + 2 6t1 ! H K I1 1 I1 + 2 6t1 ! H C(I1 ) 3 + 2 where H; K = A; B (H 6= K). The equilibrium investments are decided by K H I1 1 I1 H + = C 0 (I1 ) 3 9t1 (3.14) where H; K = A; B (H 6= K): I assume that reaction curves satisfy the negative slope A B I1 = I1 ), the negative slope and stability conditions: In a symmetric equilibrium (I1 condition is satis…ed from the second order conditions of maximization problem and the H stability condition is given by C 00 (I1 ) > 2 t1 . 9 Tying. The maximization problem of each platform is written as max ~ H ~H I1 ~H C(I1 ) = t1 + 2 ~H I1 ~K I1 + sM 3 ~H 1 I1 + 2 ~K I1 + sM 6t1 2+ ! ! ~H 1 I1 + 2 c2 ~K I1 + sM 6t1 ! ~H C(I1 ) where H; K = A; B (H 6= K). The equilibrium investments are decided by ~A 1 I1 + 3 ~B ~B I1 + sM 1 I1 ~A = C 0 (I1 ); + 9t1 3 ~A I1 9t1 sM ~B = C 0 (I1 ) (3.15) Thus, the equilibrium R&D investment levels are decided at the intersection of platform A and B’ reaction curves. Comparing (3.14) and (3.15), we can observe that tying shifts s platform A’ reaction curve outward but platform B’ reaction curve inward on the groups s 1 side. Therefore, tying raises platform A’ R&D investments but reduces platform B’ s s 97 investments (see Figure 3.2 for a graphical illustration). Proposition 13 In the competitive bottlenecks model, tying raises tying platform’ R&D s ~A investments but reduces rival platform’ R&D investments on the group-1 side (i.e., I1 > s ~ I A and I B < I B ): 1 1 1 The proof and intuition for this proposition are similar to Proposition 10. Tying forecloses R&D investments of rival platform because it acts as a commitment to more aggressive R&D investments. 3.4.3 Tying decision Suppose 1 = 2 = ; t1 = 1; t2 = 0 and < 1 which satisfy Assumption 6. In addition, R&D investment cost function is assumed as C(I) = k I 2 . 2 1 Without tying, the symmetric equilibrium R&D investments are decided by I1 = 3k from (3.14). With tying, the equilibrium R&D investments are decided by (3.15) and they are given by 1 1 1 ~A ~B I1 = + sM ; I1 = 3k 9k 2 3k 1 9k s 2 M Graphically, tying is optimal for the tying platform for parameter values (k; sM ) satisfying the pro…tability, stability and no exit conditions, which are respectively given by28 sM > 2 (9k 2) (18k 5) ; 3k (9k 1) 2 k> ; 9 0 < sM < 3 2 3k (3.16) In Figure 3.5, the shaded area represent the parameter values satisfying the conditions in (3.16). For any 0 < < 1, there exist parameter values (k; sM ) where tying is pro…table for the tying platform even without exclusion of rival platform. 28 Platform A’ pro…t change from tying is given by s where A > 0. A ~A A; A A A C(I1 ) + sM ; ~ A 98 A = 5 18k s + k(9k 1) s 2 ; 3(9k 2) M 2(9k 2)2 M A C(I A ): Tying is pro…table if ~ ~ 1 sM k= 2 9 sM = 2(9k − 2)(18k − 5) 3k (9k − 1) 8 6 4 sM = 3 − 2 0 0.5 1 2 3k 1.5 2 k Figure 3.5: Tying incentives in the competitive bottlenecks model Proposition 14 Suppose 1 = 2 = ; t1 = 1; t2 = 0 and 0 < < 1. In the competitive bottlenecks model, there exist the investment cost e¢ ciency (k) and the monopoly surplus (sM ) such that tying is pro…table for the tying platform. Proposition 14 implies that the one-sided leverage theory of tying translates into the competitive bottlenecks model. In other words, tying can be used as a tool to leverage monopoly power in one market to gain pro…ts in the tied product markets through the distortion of R&D investments. 3.4.4 Welfare analysis Welfare implications in the two-sided singlehoming model also apply to the competitive bottlenecks model. Tying can be socially ine¢ cient through (i) the distortion of R&D incentives, (ii) the increase of transportation costs and (iii) the reduction in the consumption of product M . Proposition 15 In the competitive bottlenecks model, tying reduces the social welfare even without exclusion of rival platform. 99 Proof. See Appendix C. 3.5 Concluding Remarks This paper studies the e¤ects of tying on the price and R&D competition when there exist inter-group externalities between agents on both sides of the market. My paper contributes to the literature by extending the leverage theory of tying to two-sided markets. The paper formalizes the mechanism how tying a¤ects the interaction between the price and R&D competition in two-sided markets. In the two-sided Hotelling model, tying with a monopolistic product leads to the distortion of R&D incentives as well as the exclusion of rival platform. Moreover, this tying practice can be pro…table and welfare-reducing through foreclosing rival’ R&D investments even without exclusion of rival platform. The analyses of this paper s are relevant to Microsoft’ tying case and implies that tying between Windows Operating s System and Windows Media Player may have anti-competitive e¤ects through distorting platforms’R&D incentives. In my paper, agents’ homing decision has been given exogenously. I assume the parameter values to satisfy the two-sided singlehoming or competitive bottlenecks conditions in each model. However, agents’homing decision itself can be also a¤ected by tying decision. Considering the endogenous homing decision complicates the analysis considerably, but it may be more realistic in some tying cases in two-sided markets. For example, tying on the consumer side may raise sellers’multihoming incentives (see Choi (2010) for a model of endogenous homing decision). 100 APPENDIX 101 Appendix A. Equilibrium prices without tying in the two-sided singlehoming model pH i = [ 2 i2 j 5 i j2 2 j 3 + 2 i 2 ti + 5 i j ti + 2 j 2 ti + 9 j ti tj +2 i 2 ci + 5 i j ci + 2 j 2 ci H +6ti tj Ii 2 K j Ii H 2 i 2 Ii 9ti tj ci K K 2 i j Ii + 3ti tj Ii =(2 1 2 + 5 1 2 + 2 2 2 2 H j Ii H 3 i j Ii H j )(Ij ti ( i 9 ti 2 tj K Ij )] 9t1 t2 ); where i; j = 1; 2 (i 6= j) and H; K = A; B (H 6= K): B. Equilibrium prices with tying in the two-sided singlehoming model pA ~1 = [ 2 12 2 5 1 22 2 2 3 + 2 1 2 t1 + 5 1 2 t1 + 2 2 2 t1 + 9 2 t1 t2 9 t1 2 t2 + 2 1 2 c1 + 5 1 2 c1 + 2 2 2 c1 f( 1 + 2 )(2 1 + 2 ) 2 ~B 2 I1 6t1 t2 gsM ~B ~B 2 1 2 I1 + 3t1 t2 I1 /(2 1 2 + 5 1 2 + 2 2 2 pB ~1 = [ 2 12 2 5 1 22 9t1 t2 c1 ~A ~A ( 1 + 2 )(2 1 + 2 )I1 + 6t1 t2 I1 ~A 2 )(I2 t1 ( 1 9t1 t2 ); 2 2 3 + 2 1 2 t1 + 5 1 2 t1 + 2 2 2 t1 + 9 2 t1 t2 9 t1 2 t2 + 2 1 2 c1 + 5 1 2 c1 + 2 2 2 c1 f 2 (2 1 + 2 ) 3t1 t2 gsM 9t1 t2 c1 ~A 2 1 2 I1 2 ~A ~A 2 I1 + 3t1 t2 I1 ~B ~B ( 1 + 2 )(2 1 + 2 )I1 + 6t1 t2 I1 + t1 ( 1 /(2 1 2 + 5 1 2 + 2 2 2 pH ~2 = [ 2 13 5 12 2 2 ~K 1 I2 H 2 )(I2 A 2 )(I2 B I2 )] 9t1 t2 ); 2 1 2 2 + 2 1 2 t2 + 5 1 2 t2 + 2 2 2 t2 + 9 1 t1 t2 9t1 t2 2 + 2 1 2 c2 + 5 1 2 c2 + 2 2 2 c2 +t2 ( 1 ~B I2 )] K I2 + sM ) 2 ~H 1 I2 9t1 t2 c2 ~H 3 1 2 I2 ~H ~H 2 2 2 I2 + 6t1 t2 I2 ~K ~K 2 1 2 I2 + 3t1 t2 I2 ] /(2 1 2 + 5 1 2 + 2 2 2 9t1 t2 ); where H; K = A; B (H 6= K): 102 C. Proofs omitted in the text Denote group-i agents’consumer surplus of as si Proof of Proposition 12. ci . vi The social welfare without tying can be written as nA 2 B A B A 1 1 nA + I2 nA + I2 W = sM + s1 + s2 + [I1 nA + I1 2 1 1 | {z k A 2 + IB 2 + IA 2 + IB 2 ] I1 1 2 2 2 | {z } DR 2 3 Z nA Z 1 Z nA Z 1 2 4 1 t1 xdx + t2 xdx + t1 xdx + t2 xdx5 A n1 0 | nA 2 0 {z } TC The social welfare with tying can be written as ~ ~A ~ ~B 1 W = sM nA + s1 + s2 + [I1 nA + I1 ~1 1 | 2 2 2 2 k ~A ~B + I A + I B )] ~ ~ ( I1 + I1 2 2 | 2 {z } 0 @ | Z nA ~ 1 0 g DR t1 xdx + Z 1 nA ~1 t1 xdx + {z Z nA ~ 2 0 nA ~1 ~A ~ ~B + I2 nA + I2 2 {z t2 xdx + Z 1 g TC nA ~2 } 1 nA ~2 } 1 t2 xdxA } The social welfare change from tying can be decided by W g (i) DR ~ W g T C < DR W = sM (~ A n1 h g 1) + (DR g T C) (DR i T C) T C: The following maximization problem can be considered to 103 g compare (DR max A B ;I1 ;I1 g T C) and (DR H K H T C) from Ii + Ii = 2=3k with Ii = 1=3k. B 1 A 1 = I1 ( + 1 ) + I1 ( 2 2 A 1 B 1 1 ) + I2 ( + 2 ) + I2 ( 2 k A2 B2 A2 (I1 + I1 + I2 + 2 Z 1+ Z 1 2 1 t1 xdx+ 2 2 B I2 ) Z 1+ 2 2 t1 xdx+ 1+ 0 1 2 0 2) t2 xdx+ Z 1 t2 xdx 1+ 2 2 ! 2 B A B A : subject to I1 + I1 = I2 + I2 = 3k H g is maximized at i = 0; Ii = 1=3k which implies DR (ii) sM (~ A n1 Therefore, 1) < 0 from nA < 1. ~1 g T C < DR T C. W < 0 follows from (i) and (ii). Proof of Proposition 15. The social welfare without tying can be written as A B W = sM + s1 + s2 + I1 nA + I1 1 1 | 0 1 Z nA Z 1 1 @ t1 xdx + t1 xdxA nA 1 0 | {z TC The social welfare with tying can be written as 0 | {z g TC nA ~1 } 104 DR } } ~ ~A ~ ~B W = sM nA + s1 + s2 + I1 nA + I1 ~1 1 | 0 1 Z nA Z 1 ~1 @ t1 xdx + t1 xdxA k A 2 B 2 + I1 ) (I1 2 nA 1 {z 1 nA ~1 {z g DR k ~A 2 ~B 2 (I + I1 ) 2 1 } The social welfare change from tying can be decided by W g (i) DR W = sM (~ A n1 ~ W g T C < DR g to compare (DR h g 1) + (DR g T C) (DR i T C) T C : The following maximization problem can be considered g T C) and (DR A B ~A ~B T C) from I1 + I1 = I1 + I1 = 2=3k with B A ~B ~A I1 = I1 = 1=3k and I1 = 1=3k + sM =(9k 2); I1 = 1=3k sM =(9k 2). max A B ;I1 ;I1 A 1 B 1 = I1 ( + ) + I1 ( 2 2 ) k A2 A2 (I1 + I1 ) 2 Z 1+ 2 0 t1 xdx+ Z 1 1+ 2 t1 xdx 2 A B subject to I1 + I1 = : 3k is maximized at (ii) sM (~ A n1 Therefore, A B g = 0; I1 = I1 = 1=3k which implies DR 1) < 0 from nA < 1. ~1 W < 0 follows from (i) and (ii). 105 g T C < DR T C: ! 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