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.

中文翻译：

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两面市场的稳定性和贝叶斯一致性

我们提出了信息不对称的双向市场的稳定性准则。一个中心思想是制定以反事实成对偏差为条件的偏离路径的信念，以及在不存在这种偏离的情况下制定偏离路径的信念。如果匹配相对于路径上的信念系统是个别合理的，并且相对于路径上的信念系统而言没有被阻塞，则匹配信念配置是稳定的。该表述提供了一种语言，用于根据其支持的信念评估匹配的结果，并为进一步基于信念的改进打开了大门。本文分析的主要改进要求路径上和路径外信念与先前信念的贝叶斯一致性。我们定义了贝叶斯效率，理性预期，竞争均衡和核心概念。