Competitive equilibria in decentralized matching with incomplete information

This paper shows that all perfect Bayesian equilibria of a dynamic matching game with two-sided incomplete information of independent private values variety converge to competitive equilibria. Buyers purchase a bundle of heterogeneous, indivisible goods and sellers own one unit of an indivisible good. Buyer preferences and endowments as well as seller costs are private information. Agents engage in costly search and meet randomly. The terms of trade are determined through bilateral bargaining between buyers and sellers. The paper considers a market in steady state. It is shown that as frictions disappear, i.e., as discounting and the fixed cost of search become small, all equilibria of the market game converge to perfectly competitive equilibria.