Search theory, competitive equilibrium, and the Nash bargaining solution

We investigate a canonical search theoretic model of a society, à la Burdett and Wright (1998), in which two agents are randomly matched, facing a pair of nontransferable payoffs drawn randomly from a compact convex set, and choose whether or not to agree to form a partnership, which is formed if and only if both of them agree to do so, subject to a small probability of exogenous break down. As the discount factor converges to one, and the probability of exogenous break down vanishes, the Nash bargaining solution emerges as the unique undominated strategy equilibrium outcome, if the mass of each party is the same. Each agent in a society, without any centralized information processing institution, behaves as if he agreed upon the Nash bargaining solution. We also investigate the case where the size of one party is larger than the other to show that the short side extracts the entire gain from trading, in a sharp contrast to Rubinstein and Wolinsky (1985).