The Structure of Bayesian Stable Matchings

Abstract

Stability is a central concept in matching theory. We investigate the set of stable matchings in a general environment that can accommodate both complete and incomplete information. We first exemplify how two fundamental structural results, i.e., the celebrated lone wolf theorem and lattice theorem, may fail. Then for each of them, we study the conditions that restore positive results. Our key condition called common information encompasses complete information as a special case, thereby reshaping our understanding of the two structural properties.

Keywords: matching, incomplete information, the lone wolf theorem, the lattice theorem