Information Sharing in Oligopoly: Sharing Groups and Core-Periphery Architectures

The trade-off between the costs and benefits of disclosing a firm’s private information has been the object of a vast literature. The absence of incentives to share information on a common market demand prior to competition has been advocated to interpret information sharing as evidence of collusion. Recent contributions have looked at bilateral information sharing, showing that information sharing is consistent with pairwise stability, This paper studies the networked pattern of bilateral information sharing on market demand, focusing on the role of heterogeneous information (firms’ signals have different variances). We show that while pairwise stability predicts that i.i.d. signals are always shared in groups with a symmetric internal structure (both with and without side-payment and linking costs), heterogeneous signals are shared in asymmetric core-periphery architectures, in which “core” firms have more valuable information than periphery firms.

Chain stability in trading networks

In a general model of trading networks with bilateral contracts, we propose a suitably adapted chain stability concept that plays the same role as pairwise stability in two‐sided settings. We show that chain stability is equivalent to stability if all agents' preferences are jointly fully substitutable and satisfy the Laws of Aggregate Supply and Demand. In the special case of trading networks with transferable utility, an outcome is consistent with competitive equilibrium if and only if it is chain stable.

On the Existence of Pairwise Stable Weighted Networks

In network theory, Jackson and Wolinsky introduced a now widely used notion of stability for unweighted network formation called pairwise stability. We prove the existence of pairwise stable weighted networks under assumptions on payoffs that are similar to those in Nash's and Glicksberg’s existence theorem (continuity and quasi concavity). Then, we extend our result, allowing payoffs to depend not only on the network, but also on some game-theoretic strategies. The proof is not a standard application of tools from game theory, the difficulty coming from the fact that the pairwise stability notion has both cooperative and noncooperative features. Last, some examples are given and illustrate how our results may open new paths in the literature on network formation.

Stability and Bayesian Consistency in Two-Sided Markets

We propose a criterion of stability for two-sided markets with asymmetric information. A central idea is to formulate off-path beliefs conditional on counterfactual pairwise deviations and on-path beliefs in the absence of such deviations. A matching-belief configuration is stable if the matching is individually rational with respect to the system of on-path beliefs and is not blocked with respect to the system of off-path beliefs. The formulation provides a language for assessing matching outcomes with respect to their supporting beliefs and opens the door to further belief-based refinements. The main refinement analyzed in the paper requires the Bayesian consistency of on-path and off-path beliefs with prior beliefs. We define concepts of Bayesian efficiency, the rational expectations competitive equilibrium, and the core. Their contrast with pairwise stability manifests the role of information asymmetry in matching formation. (JEL C78, D40, D82, D83)

Weighted Matching Markets with Budget Constraints

We investigate markets with a set of students on one side and a set of colleges on the other. A student and college can be linked by a weighted contract that defines the student's wage, while a college's budget for hiring students is limited. Stability is a crucial requirement for matching mechanisms to be applied in the real world. A standard stability requirement is coalitional stability, i.e., no pair of a college and group of students has any incentive to deviate. We find that a coalitionally stable matching is not guaranteed to exist, verifying the coalitional stability for a given matching is coNP-complete, and the problem of finding whether a coalitionally stable matching exists in a given market, is SigmaP2-complete: NPNP-complete. Other negative results also hold when blocking coalitions contain at most two students and one college. Given these computational hardness results, we pursue a weaker stability requirement called pairwise stability, where no pair of a college and single student has an incentive to deviate. Unfortunately, a pairwise stable matching is not guaranteed to exist either. Thus, we consider a restricted market called a typed weighted market, in which students are partitioned into types that induce their possible wages. We then design a strategy-proof and Pareto efficient mechanism that works in polynomial-time for computing a pairwise stable matching in typed weighted markets.

Specifying a Structural Matching Game of Trading Networks with Transferable Utility

Structural estimation of matching games with transferable utility, including matching games of trading networks and many-to-many matching, is increasingly popular in empirical work. I explore several modeling decisions that need to be made when specifying a structural model for a matching game. One decision is the choice of a game theoretic solution concept to impose in the structural model. I discuss pairwise stability, competitive equilibrium, and noncooperative games such as auctions. Another decision is whether to work with a continuum of agents or a finite number of agents. I explore other issues as well.

An Empirical Model of the Medical Match

This paper develops a framework for estimating preferences in a many-to-one matching market using only observed matches. I use pairwise stability and a vertical preference restriction on one side to identify preferences on both sides of the market. Counterfactual simulations are used to analyze the antitrust allegation that the centralized medical residency match is responsible for salary depression. Due to residents' willingness to pay for desirable programs and capacity constraints, salaries in any competitive equilibrium would remain, on average, at least $23,000 below the marginal product of labor. Therefore, the match is not the likely cause of low salaries. (JEL C78, I11, J31, J44, K21, L44)

The Stability and Efficiency of Network Structure with Joining Costs

This paper aim to study the stability and efficiency of a social and economic network in which the various elements are closely related by the network structure, while self-interested individuals can form or sever links with the network by incurring joining costs. Our novel feature is that we consider joining costs in network formation. Firstly, We also propose the concept of a stable network that is similar to the pairwise stability of Jackson and Wolinsky (1996) based on joining costs. We examine changes in the stability, efficiency and network structure. For a link model, we identify the main characteristics of stable and efficient networks. It is important to note that a stable network is not always efficient. Next, we show that the range of stable networks has been extended through the evolutionary process of developing networks with joining costs. Moreover, consistency, stability and efficiency also enhance the networks structure.

Measuring the Efficiency of an FCC Spectrum Auction

We propose a method to structurally estimate the deterministic component of bidder valuations in FCC spectrum auctions, and apply it to the 1995–1996 C block auction. We base estimation on a pairwise stability condition: two bidders cannot exchange two licenses in a way that increases the sum of their valuations. Pairwise stability holds in some theoretical models of simultaneous ascending auctions under intimidatory collusion and demand reduction. Pairwise stability results in a matching game approach to estimation. We find that a system of four large regional licenses would raise the allocative efficiency of the C block outcome by 48 percent. (JEL D44, D45, H82, L82)