We consider two-sided matching markets in which agents have private information on a state of nature which determines the agents' utilities of matching. Monetary transfers are allowed and utility functions are quasi-linear. The model thus extends the assignment game introduced by Shapley and...

This paper studies the set of equilibria that can be achieved by adding general communication systems to Bayesian games in which some information can be certified or, equivalently, in which players’ types are partially verifiable. Certifiability of information is formalized by a set of...