Bargaining and matching in small markets

The present paper focuses on markets where trade is carried out through matching and bargaining and where at each date t = 0,1, ... a finite and exogenously given number of agents enters. Such markets are "small" in the sense that whether a match ends with trade influences matching probabilities at subsequent dates. For a small market we show that as the market becomes large, the equilibrium of the small market converges to the equilibrium of a limit market with a continuum of agents. Nonetheless, for any small market there exists a matching process such that the equilibrium of the small market significantly differs from the equilibrium of the associated large market with a continuum of agents, although equilibrium-path matching probabilities are the same in both markets. Therefore, matching models with a continuum of agents are not always a good approximation of small markets