Dynamic Matching and Bargaining Games: A General Approach

Dynamic matching and bargaining games provide models of decentralized trading with frictions. A central objective of the literature is to investigate how equilibrium outcomes depend on the level of the frictions. In particular, will the outcome become e¢ cient when frictions become small? Existing speci…cations of such games give di¤erent answers. To investigate what causes these di¤erence we identify four simple conditions on trading outcomes and their relation to the level of frictions. We show that for every game which satis…es these conditions, the equilibrium outcome becomes e¢ cient when frictions are small. We illustrate this approach with two games in which we show that our conditions hold, implying that the limiting outcome is e¢ cient. We then proceed to speci…cations of dynamic matching and bargaining games in which limiting equilibrium outcomes do not need to become e¢ cient. We show that our conditions do not hold in these games.