Stability and Bayesian Consistency in Two-Sided Markets

Abstract

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)

Centralized Matching with Incomplete Information

“…In the decentralized, cooperative setting, there has been a long-standing quest for a natural stability notion allowing for incomplete information. Liu et al (2014) and Liu (2020) offer such a notion for matching markets with transfers and one-sided incomplete information, similar to ours. Bikhchandani (2017) suggests such a notion for similar markets that do not allow transfers.…”

Stable Outcomes and Information in Games: An Empirical Framework

“…First, our solution concept adopts the idea of rational expectations equilibrium pioneered by Radner (1979) to capture how players refine their information based on market observables in equilibrium situations. Our approach closely follows the logic in Liu (2020) who used the same idea to define the notion of stability in two-sided markets with incomplete information. Compared to other 4 The empirical literature has been aware that the Nash framework is subject to ex-post regret.…”

“…First, we argue that rational expectations equilibrium, appropriately defined for our setting, provides a simple approach to rationalizing stable outcomes under incomplete information. We define rational expectations equilibrium by adopting the "outcome function" approach of Liu (2020), who uses a similar approach to define the notion of stability in two-sided markets with incomplete information. Next, we show that Bayes stable equilibrium characterizes the implications of rational expectations equilibria when the analyst can only specify the minimal information available to the players.…”

A Dynamic Contest Model of Platform Competition in Two-Sided Markets

“…Ref. [27] studies a two-sided market where agents on one side of the market have private information about their payoff-related attributes. Based on concepts of Bayesian efficiency, the rational expectations' competitive equilibrium and the core, the author proposes a criterion of stability for two-sided markets with asymmetric information.…”