Bargaining Micro-foundations of Decentralized Markets, Competition, and Reputation

Abstract

Existing literature shows that it is possible for rational players to establish one-sided and two-sided reputation in a bilateral bargaining environment by mimicking irrational, r-insistent players, and that this reputation build-up can drastically change the Rubinstein (1982) outcome, by causing delay in reaching agreement. Furthermore, the literature on outside options in bilateral bargaining suggests that unless outside options are very large, they do not affect these bargaining outcomes. We are interested in the impact on the bargaining outcome from endogenizing outside options|namely, bargaining in markets. In the presence of competition in decentralized search markets, can rational agents mimic irrationality to build reputation, when can irrational types on both sides of the market trade in equilibrium, and what are the consequences for delay and efficiency? We develop discrete, hybrid and continuous-time models of bargaining in markets with and without irrational types by combining reputational bargaining of Abreu and Gul (2000) with a continuous-time version of the Rubinstein and Wolinsky (1985) model of bargaining in markets. Applications include decentralized search markets for labor, exotic assets, over-the-counter securities, venture capital funding, and repurchase agreements.