Dynamic Matching and Bargaining Games: A General Approach

Dynamic matching and bargaining games provide models of decentralized markets with trading frictions. A central objective of the literature is to investigate how equilibrium outcomes depend on the size of the frictions. In particular, will the outcome become efficient when frictions become small? Existing specifications of such games give different answers. To investigate what causes these differences, we identify four simple conditions on trading outcomes. We show that for every game which satisfies these conditions, the equilibrium outcome must become efficient when frictions are small. We demonstrate that our conditions hold under several specifications in the literature, suggesting a common cause behind their convergence results. These specifications include, for example, the recent contribution by Satterthwaite and Shneyerov (Econometrica, 2007). For those specifications in the literature for which outcomes do not become efficient, we show exactly which of our conditions do not hold. These specifications include, for example, Serrano (2002, JME) and DeFraja and Sakovics (2001, JPE).