Elsevier

Games and Economic Behavior

Volume 119, January 2020, Pages 172-188
Games and Economic Behavior

Entry-deterring agency

https://doi.org/10.1016/j.geb.2019.09.012Get rights and content

Abstract

We provide a model in which an intermediary can choose between wholesale or agency. The possibility that buyers and sellers transact directly limits his market power and, thus, creates incentives for him to deter the emergence of bilateral exchanges. In equilibrium, the intermediary chooses agency and thereby pre-empts the emergence of a competing bilateral exchange if the matching technology of the competing exchange is sufficiently efficient. For symmetric Pareto distributions, whenever agency is chosen in equilibrium, consumer and social surplus decrease while listing and transaction prices tend to increase. The predictions of our model are broadly consistent with empirical evidence.

Introduction

Merchants, middlemen, and market makers have always assumed important economic roles. For just as long, they have been viewed with suspicion for doing so.1 Traditional examples of these intermediaries are real estate brokers, employment agencies, and used car dealers. Following the entry into the 21st century, the emergence of the Internet and e-commerce has witnessed the creation of intermediaries such as Amazon, eBay, Apple with its i-products and services, AirBnB, Expedia, Uber, and Booking.com. Resonating with traditional suspicions, these Internet platforms are viewed as controversial by policy makers and the public, with a major concern being that they extract excessive rents from the two sides of the market.2,3

Unlike monopoly producers, an intermediary faces the competitive threat of being circumvented by its customers even if it is a monopoly: in principle, buyers and sellers can always trade directly with each other. From a consumer surplus perspective, this competitive threat is welcome because, all else being equal, it reduces the intermediary's market power.4 However, it also provides the intermediary with incentives to (potentially inefficiently) deter the emergence of a competing bilateral exchange.

In this paper, we focus on two widely used models of intermediation, called wholesale and agency, which feature prominently in recent antitrust debates and cases (see, e.g., Johnson, 2017). We show that a monopoly intermediary optimally uses agency if and only if the competitive threat is sufficiently strong. He does so to pre-empt the emergence of a bilateral exchange. For symmetric Pareto distributions, this reduces both social and consumer surplus while increasing the listing prices buyers face.

A sketch of our model and the forces at work is as follows. We assume a continuum of buyers and sellers with heterogeneous valuations and costs for a homogeneous good. Buyers have single-unit demand and sellers have single-unit capacities. This implies that, in the absence of a bilateral exchange, wholesale with appropriately chosen prices for buyers and sellers is the optimal mechanism for the intermediary. However, because it induces a spread between buyers' and sellers' prices, traders with values and costs in between these prices cannot trade with the intermediary but can, to their mutual benefit, trade with each other. Wholesale is thus associated with an active bilateral exchange that improves the outside option of not trading with the intermediary even for traders who in equilibrium join the intermediary. Consequently, the bilateral exchange puts downward pressure on the spread the intermediary can charge, and the more so, the more efficient is the bilateral exchange. In contrast, under agency the intermediary does not take a position but rather has the sellers set prices, randomly matching them to buyers and charging a percentage fee on the price whenever a transaction occurs. Because sellers are heterogeneous with respect to their costs, agency is associated with a non-degenerate distribution of transaction prices, and more importantly, with overlapping supports in the valuations and costs of buyers and sellers who join the intermediary. Because of this overlap, no buyers and sellers are left who could trade to their mutual benefit in a bilateral exchange.5 Consequently, the intermediary can use agency to deter the emergence of the bilateral exchange.

In the main model, where we assume that transactions in the bilateral exchange occur at a fixed price while buyers and sellers draw their types from general distributions satisfying Myerson's regularity assumptions, we show that entry deterrence via agency is always possible, and profitable if and only if the competing exchange would be sufficiently efficient if it emerged. For symmetric Pareto distributions, we also show that whenever entry deterrence pays off, social surplus and consumer surplus (defined as the aggregate of buyers' and sellers' surplus) decrease, and buyers' prices tend to increase. We also show these findings are robust to alternative bargaining protocols such as take-it-or-leave-it offers, double-auctions, and Nash bargaining for which we can solve for the equilibrium outcomes in closed form when both distributions are uniform.

As usual in models of trade, there is a multiplicity of equilibria both for wholesale and for agency. For wholesale, there is always an equilibrium in which the intermediary and the bilateral exchange coexist. Agency does not exhibit equilibria where both the intermediary and the bilateral exchange coexist. Further, equilibria where the intermediary alone is active are the most “reasonable” (in a sense we will discuss in detail later) under agency.

A policy implication of our results is that banning the agency model can in some cases be welfare improving. This has indeed been the court's decision in the Apple e-books case, where the ban on agency led to a wholesale model. In other instances, for example, in real estate brokerage, mandating the wholesale model may not be practical or feasible. An alternative solution is to require flat fees paid independent of whether there is a transaction, which can be shown to be equivalent to a wholesale model of intermediation.6 The Department of Justice's 2007 settlement with the Realtor's Association was a milder form of this alternative: while the agency model was not banned, the Realtor's Association was required to abandon practices that discriminated against flat-fee agents.

To the best of our knowledge, ours is the first paper to analyze an intermediary's incentives and options to deter entry by an alternative exchange. The emergence of the Internet and e-commerce has led to new intermediaries and to an upsurge of research on two-sided markets. Starting with the pioneering work by Caillaud and Jullien, 2001, Caillaud and Jullien, 2003, Rochet and Tirole, 2003, Rochet and Tirole, 2006, Anderson and Coate (2005) and Armstrong (2006), this literature has primarily focused on monopoly platforms or competition between platforms, abstracting from the exact mechanisms the platforms employ to generate surplus, from traders' options to circumvent the platform, and the platform's incentives to prevent them from so doing.7 Two notable exceptions that explicitly analyze the platform's trading mechanism are Gomes (2014) and Niedermayer and Shneyerov (2014). Competition between wholesale intermediaries and alternative exchanges fares prominently in the works of Rubinstein and Wolinsky (1987), Stahl (1988), Gehrig (1993), Spulber (1996), Bloch and Ryder (2000), Rust and Hall (2003), Loertscher (2007) and Neeman and Vulkan (2010), which, however, do not address intermediaries' incentives and options to drive out the competing exchanges.

Our paper builds on the existing literature. Participation fees, which are equivalent to the wholesale model, have been analyzed by Niedermayer and Shneyerov (2014), while Loertscher and Niedermayer, 2017a, Loertscher and Niedermayer, 2017b analyze brokers' fee structures from an optimal pricing perspective for the agency model. These papers assume that there is no competing bilateral exchange.8

Our paper also shares features with the Industrial Organization literature on predation, in particular with the strand of literature where predatory pricing is made credible, without invoking differential access to financing, by the presence of learning-by-doing as analyzed by Cabral and Riordan, 1994, Cabral and Riordan, 1997, Besanko et al. (2010), and Besanko et al. (2014). In this strand of literature, the cumulative effects of learning-by-doing render predatory pricing credible. In our model it is the threat of the emergence of an alternative exchange between buyers and sellers that makes agency credible for deterring entry. However, the incentives and methods used for entry deterrence in the literature mentioned above and the present paper are different and complementary. A novel feature of our model is that a strategic player, the intermediary, may predate the emergence of an alternative exchange who is not a player.

Recently, Edelman and Wright (2015) developed a model that exhibits excessive intermediation in that more agents are active than would be under Walrasian conditions, but the mechanisms in the two papers are quite different. In their paper, it is price coherence that induces inefficient outcomes whereas in our model it is the opposite – the freedom of sellers to set prices and the non-degenerate price distributions this induces. The two papers thus complement each other. In settings with one-sided incomplete information, Bourguignon et al. (2019) and Gomes and Tirole (2018) analyze alternative regulatory interventions for credit card fees and the pricing of ancillary goods, respectively. Biglaiser and Li (2018) study a moral hazard model in which the presence of a middleman who uses (in our terminology) wholesale can increase or decrease welfare. In contrast, we study an adverse selection model in which the intermediary is always present but in equilibrium chooses an inefficient mechanism to reduce traders' outside options. While the themes of our paper and theirs are similar, the setups, mechanisms, and outcomes are thus quite different, which renders the papers complementary. Our analysis has a similar flavor as Johnson (2017) because both analyze agency versus wholesale. However, the setup and the question are very different: our focus is on the entry deterrence effect of the agency model, which is an effect that cannot occur in Johnson (2017) because in his setup it is, by assumption, impossible for the supplier to circumvent the retailer.

Our paper also contributes to the literature on intermediation and specifically on real estate brokerage such as the papers by Yavas (1996), Hsieh and Moretti (2003), Rutherford et al. (2005), Levitt and Syverson (2008), Hendel et al. (2009) and Loertscher and Niedermayer, 2017a, Loertscher and Niedermayer, 2017b. The agency model is difficult to reconcile with a principal-agent perspective, but consistent with an optimal pricing perspective.9 In the companion paper (Loertscher and Niedermayer, 2017b), we also take the theory to the data and estimate demand and supply under the assumption that payoffs from a bilateral exchange market are exogenous (or that no bilateral exchange market exists). Yavas (1996) has investigated whether real-estate brokers have an incentive to induce inefficiently many trades by matching buyers and sellers “horizontally” rather than “vertically” (i.e. high-cost sellers to high-value buyers rather than inducing trades among the most efficient pairs) because brokers earn commissions that depend on the price and not on the surplus trades generate. While the specifics of the models and mechanisms are different, we obtain a similar result: that under agency horizontal matchings occur with positive probability. This contrasts with the wholesale model, which induces trade among the most efficient buyers and sellers with probability 1. In a wider sense, this paper also relates to Fudenberg and Tirole (2000)'s results of entry deterrence in a dynamic market with network externalities.10

The remainder of this paper is organized as follows. Section 2 describes the setup. In Section 3, we derive the equilibrium under wholesale and agency and equilibrium entry deterrence for general distributions assuming fixed-price bargaining. In Section 4, we derive normative implications of our model for social and consumer surplus and predictions for equilibrium prices, assuming symmetric Pareto distributions for buyers and sellers. In Section 5, we analyze multiplicity and uniqueness of equilibrium. We show that under agency there is no equilibrium in which both the intermediary and the bilateral exchange are active, and we provide conditions that ensure that the equilibrium under agency we focus on is unique. Section 6 shows that our results are robust insofar as the key insights—entry deterrence via agency if the competing exchange is sufficiently efficient, reduction of social and consumer surplus and price increases when entry deterrence occurs—also hold for the alternative bargaining protocols of take-it-or-leave-it offers, Nash bargaining and double-auctions. For tractability, this section assumes uniform distributions. Section 7 discusses extensions and policy implications, and Section 8 concludes the paper. The Online Appendix contains omitted proofs and derivations, including auxiliary mechanism design results; robustness checks and generalizations, and an alternative model with binary types and dynamic random matching.

Section snippets

Setup

We consider a one-period model with a continuum of buyers and a continuum of sellers, each with mass 1. Buyers have single-unit demand and sellers have single-unit capacities. All agents are risk neutral, have quasilinear preferences, and outside options with value 0. Buyers draw their valuations v independently from the distribution F(v) with support [0,1] and density f(v)>0 for all v[0,1] and sellers draw their costs c independently from the distribution G(c) with support [0,1] and density g(

Equilibrium

We now analyze the model laid out above, beginning with equilibrium under wholesale, where our focus will be on the equilibrium in which for λ>0 the bilateral exchange is active, which seems to be the plausible equilibrium.18

Welfare and price effects

We now consider the effects of agency on social surplus, consumer surplus, and on equilibrium prices and price distributions. In this analysis, we focus on (symmetric) Pareto distributions because of tractability.

Multiplicity and uniqueness of equilibrium

As is well known, models of market making are prone to exhibit multiple equilibria simply because not joining a given platform or exchange is often a best response if no one else joins it. For example, in our setup there is always an equilibrium under wholesale in which no one joins the bilateral exchange.

Similarly, under wholesale a multiplicity of equilibria can occur that differ with respect to the mass of buyers and sellers who join the intermediary as noted, for example, by Gehrig (1993).

Take-it-or-leave-it offers and other bargaining protocols

We now demonstrate that our insights based on the assumption of fixed-price bargaining are robust. Specifically, we now assume that the bilateral exchange has one of three alternative, widely used bargaining protocols—random proposer take-it-or-leave-it offers, Nash bargaining, and double-auctions—while assuming that the distributions F and G are uniform.34

Discussion

We now discuss an extension in which agency is chosen to deter Bertrand competition and policy implications. Discussions of additional extensions and aspects of our model are deferred to Online Appendix C for space constraints.

Conclusions

In this paper, we present a model in which the operator of one market can successfully deter the emergence of a competing exchange. Entry deterrence is the more profitable the more efficient is the matching technology in the competing exchange whose emergence is deterred. The paper thus brings to light a relevant and novel possibility of entry deterrence. For symmetric Pareto distributions, entry deterrence is always harmful to social welfare, and when it occurs in equilibrium, to consumer

References (51)

  • P. Belleflamme et al.

    Industrial Organization: Markets and Strategies

    (2015)
  • D. Besanko et al.

    The economics of predation: what drives pricing when there is learning-by-doing?

    Am. Econ. Rev.

    (2014)
  • D. Besanko et al.

    Learning-by-doing, organizational forgetting, and industry dynamics

    Econometrica

    (2010)
  • G. Biglaiser et al.

    Middlemen: the good, the bad, and the ugly

    Rand J. Econ.

    (2018)
  • F. Bloch et al.

    Two-sided search, marriages, and matchmakers

    Int. Econ. Rev.

    (2000)
  • L.M.B. Cabral et al.

    The learning curve, market dominance, and predatory pricing

    Econometrica

    (1994)
  • L.M.B. Cabral et al.

    The learning curve, predation, antitrust, and welfare

    J. Ind. Econ.

    (1997)
  • B. Caillaud et al.

    Chicken and egg: competition among intermediation service providers

    Rand J. Econ.

    (2003)
  • K. Chatterjee et al.

    Bargaining under asymmetric information

    Oper. Res.

    (1983)
  • CT, 2011. The Toronto Real Estate Board. Case...
  • E. Damiano et al.

    Price discrimination and efficient matching

    Econ. Theory

    (2007)
  • B. De Los Santos et al.

    E-book pricing and vertical restraints

    Quant. Mark. Econ.

    (2017)
  • DOJ

    Competition in the Real Estate Brokerage Industry

    (2007)
  • B. Edelman et al.

    Price coherence and excessive intermediation

    Q. J. Econ.

    (2015)
  • P.S. Foner

    History of the Labor Movement in the United States: The Industrial Workers of the World, 1905-1917, vol. 4

    (1965)
  • Cited by (5)

    • The pricing of ancillary goods when selling on a platform

      2022, International Journal of Industrial Organization
      Citation Excerpt :

      It contrasts with the traditional wholesale model in which retailers set final prices. A large body of literature has explored the optimality of agency pricing (Gans, 2012; Gaudin and White, 2014; Tan et al., 2016; Foros et al., 2017; Johnson 2017; Loertscher and Niedermayer, 2020). In contrast to these papers, we take intermediaries’ use of agency pricing as given but instead focus on its implications for downstream firms’ pricing behavior.

    • Monopoly Pricing, Optimal Randomization, and Resale

      2022, Journal of Political Economy

    The comments and suggestions of three anonymous referees and an Associate Editor of this journal have helped us improve the paper. This paper has also benefited from comments by and discussions with Luis Cabral, Arthur Campbell, Edwin Chan, Renato Gomes, Stephen King, Stephan Lauermann, Joao Montez, Martin Peitz, Patrick Rey, Michael Riordan, Larry Samuelson, Artyom Shneyerov and seminar audiences at the University of Mannheim. We also thank participants of AETW 2013 at UQ, EARIE 2013 in Evora, SAET 2013 in Paris, the CLEEN Workshop in 2013, IIOC 2013 in Boston, the MaCCI Annual Conference in 2013 in Mannheim, the SFB TR 15 meeting 2013 in Bonn, the 2015 ATE Symposium in Auckland, the Multi-Sided Platforms Workshop in 2015 in Singapore, the 2018 Melbourne IO and Theory Day, the 2015 Workshop on Consumer Search in Bad Homburg, the 2018 CRESSE/JUFE Workshop in Nanchang, the 2018 ZJU International Conference on Industrial Economics in Hangzhou, the 2018 Annual Meeting of the Verein für Socialpolitik in Freiburg, and the Conference in memoria of Artyom Shneyerov at Paris-Dauphine PSL in 2018 for helpful comments. The second author gratefully acknowledges funding by the Deutsche Forschungsgemeinschaft through SFB TR 15 and project PE 813/2-2. Financial support via a visiting research scholar grant from the Faculty of Business and Economics at the University of Melbourne and from the Samuel and June Hordern Endowment is also gratefully acknowledged. A previous version of the paper circulated under the title “Predatory Platforms”.

    View full text