In this paper, we extend the stability notion and Bayesian efficiency notion of Liu (2020) to local ones, as well as his result—that under certain intuitive conditions, stable matchings are Bayesian efficient—to an analogous one for local notions. Furthermore, the extended stability notion,...

This paper extends the Bayesian stability notion of Liu (2020) to define the Bayesian stability of a market state , which consists of a matching outcome and an information structure. Here, the information structure can be arbitrarily heterogeneous among agents. We first establish that Liu’s...