A Theory of Stability in Matching with Incomplete Information

We provide a framework for studying two-sided matching markets with incomplete information. The framework accommodates two-sided incomplete information as well as heterogeneous information among the agents. We propose a notion called stability for a market state, which, based upon agents' information structure, requires (i) individual rationality, (ii) no blocking and (iii) information stability. The novelty of our stability notion lies in how the agents evaluate a blocking prospect, in the presence of general two-sided incomplete information. We show that a stable state exists; moreover, if a state is stable, then coarsening agents' information leads to another stable state