Convergence to Bayesian Stable States without Assuming Observability

Abstract

Chen and Hu (2024) proposes a concept of Bayesian stability for matching with incomplete information. They also invoke the result of Chen and Hu (2020) to provide a foundation for their solution concept. Particularly, assuming in job matching that firms can observe the type of their employees, then starting from an arbitrary market state, a random learning-blocking path converges to a Bayesian stable state with probability one. In this companion note, we document how one could prove the following result without assuming observability, which strengthens Corollary 1 in Chen and Hu (2024).

Keywords: two-sided matching, Bayesian stability, convergence, observability

JEL Classification: C78, D40, D82, D83