This paper shows that all perfect Bayesian equilibria of a dynamic matching game with two-sided incomplete information of independent private values variety are asymptotically Walrasian. 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 a Bayesian mechanism proposal game. The paper considers a market in steady state. As discounting and the fixed cost of search become small, all trade takes place at a Walrasian price. However, a robust example is presented where the limit price vector is a Walrasian price for an economy where only a strict subsets of the goods in the original economy are traded, i.e, markets are missing at the limit. Nevertheless, there exists a sequence of equilibria that converge to a Walrasian equilibria for the whole economy where all markets are open.
Matching and Bargaining Search Foundations for Perfect Competition Two-sided Incomplete Information