Limits of Exact Equilibria for Capacity Constrained Sellers with Costly Search

It is shown that the distribution of prices offered by sellers in both the exact and rational expectations equilibrium converge weakly to the same limit as the number of buyers and sellers grows large.

Abstract

This paper studies finite versions of competitive matching models in which sellers announce prices and buyers understand the relationship between price and probability of trade. Two equilibrium concepts are studied for finite games, subgame perfect equilibrium and rational expectations equilibrium. It is shown that the distribution of prices offered by sellers under both equilibrium concepts converges weakly to the same competitive equilibrium distribution of prices. Furthermore, the payoffs that sellers face in both kinds of equilibrium have the market utility property in the limit. Journal of Economic Literature Classification Numbers: C78, D41, D45.