Bayesian Stable States

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 stability can indeed be translated into our stability. Then we exemplify the usefulness of such an extension by (i) refining Liu’s Bayesian efficiency notion to define the Bayesian efficiency of a market state and (ii) generalizing his result—that Bayesian stable matching functions are Bayesian efficient—to an analogous one for market states. More importantly, we argue that a stability notion for market states facilitates the study of matching processes. Namely, our Bayesian stability notion for market states admits an algorithmic implementation via an adaptive matching process, which also serves as a foundation for Liu’s notion