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We study price competition and entry of platforms in multi-sided markets. Utilizing the simplicity of the equilibrium pricing formula in our setting with heterogeneity of customers’ membership benefits, we demonstrate that in the presence of externalities, the standard effects of competition can be reversed: as platform competition increases, prices, and platform profits can go up and consumer surplus can go down. We identify economic forces that jointly determine the social inefficiency of the free-entry equilibrium and provide conditions under which free entry is socially excessive as well as an example in which free entry is socially insufficient.

In this paper, we provide an alternative explanation for why auctioneers often keep the reserve price hidden or secret. We consider a standard independent private values environment in which the buyers are risk-averse and the seller has private information about her valuation of the object to be auctioned. The seller uses a first-price sealed-bid auction mechanism combined with either an announced reserve price or a hidden reserve price. We compare the seller＇s ex ante expected profits under these two policies and find that the optimal hidden reserve price policy generates higher expected profits for the seller when the buyers are fairly risk-averse under particular restrictions on buyers＇ preferences and the distributions of private values. As the number of the buyers increases, the hidden reserve price is more likely to dominate. Numerical methods are used to demonstrate the generality of our main results.

In this paper, we analyze a recent antitrust case of abuse of dominance that was decided by a Chinese administrative enforcement agency under China’s Anti-Monopoly Law (“AML”). A key issue in this case involved the impact of loyalty rebate programs used by a dominant firm. We provide an overview of the case, highlight the main points of the decision, and focus on the assessment of loyalty rebates. As the first antitrust ruling in China involving loyalty discounts, we expect that the decision will serve as an important reference in antitrust enforcement in China.

We develop models of bilateral oligopoly with traffic exchanges to study the competition and regulatory policies in the international telephone markets. Under the requirement of uniform settlement rates, the proportional return rule (PRR) inflates the rates and hence neutralizes PRR's effect on calling prices. Retail competition and PRR increase net settlement payments. Market efficiency is improved when there are multiple channels for traffic exchanges. Using a panel of 47 countries that exchanged traffic with the United States between 1992 and 2004, we test the effects of bilateral market structures and the U.S. policies. The empirical results support our theoretical findings.

We investigate the strategic effects of all-units discounts (AUDs) used by a dominant firm in the presence of a capacity-constrained rival. Due to the limited capacity of the rival, the dominant firm has a captive portion of the buyer's demand for the single product. As compared to linear pricing, the dominant firm can use AUDs to go beyond its captive portion by tying its captive demand with part of the competitive demand and partially foreclose its small rival. When the rival's capacity level is well below relevant demand, AUDs reduce the buyer's surplus.

We consider a nonlinear pricing problem faced by a dominant firm competing with a minor firm. The dominant firm offers a general tariff first, and then the minor firm responds with a per-unit price, followed by a buyer choosing her purchases. By developing a mechanism-design approach to solve the subgame perfect equilibrium, we characterize the dominant firm’s optimal nonlinear tariff, which exhibits convexity and yet can display quantity discounts. In equilibrium the dominant firm uses a continuum of unchosen offers to constrain its rival’s potential deviations and extract more surplus from the buyer. Antitrust implications are also discussed.

We study a model in which two carriers choose networks to connect cities and compete for customers. We show that if carriers compete aggressively (e.g., Bertrand-like behavior), one carrier operating a single hub-spoke network is an equilibrium outcome. Competing hub-spoke networks are not an equilibrium outcome, although duopoly equilibria in nonhub networks can exist. If carriers do not compete aggressively, an equilibrium with competing hub-spoke networks exists as long as the number of cities is not too small. We provide conditions under which all equilibria consist of hub-spoke networks.

We study equilibria in second-price auctions where bidders are independently and privately informed about both their values and participation costs, and where the joint distributions of these values and costs across bidders are not necessarily identical. We show that there always exists an equilibrium in this general setting with two-dimensional types of ex ante heterogeneous bidders. When bidders are ex ante homogeneous, there is a unique symmetric equilibrium, but asymmetric equilibria may also exist. We provide conditions under which the equilibrium is unique (not only among symmetric ones). We find that the marginal density of participation costs and the concentration of values matter for the uniqueness. The presence of private information on participation costs tends to reduce multiplicity of participation equilibria, although multiplicity still persists.

This paper studies endogenous coalition formation in a rivalry environment where continuing conflict exists. A group of heterogeneous players compete for a prize with the probability of winning for a player depending on his strength as well as the distribution of strengths among his rivals. Players can pool their strengths together to increase their probabilities of winning as a group through coalition formation. The players in the winning coalition will compete further until one individual winner is left. We show that in any equilibrium there are only two coalitions in the initial stage of the contest. In the case of three players, the equilibrium often has a coalition of the two weaker players against the strongest. The equilibrium coalition structure with four players mainly takes one of the two forms: a coalition of the three weaker players against the strongest or a coalition of the weakest and strongest players against a coalition of the remaining two. Our findings imply that the rivalry with the possibility of coalition formation in our model exhibits a pattern of two-sidedness and a balance of power. We further study the impact of binding agreements by coalition members on equilibrium coalition structures. Our analysis sheds some light on problems of temporary cooperation among individuals who are rivals by nature.