Bargaining and reputation in search markets

In a two-sided search market agents are paired to bargain over a unit surplus. The matching market serves as an endogenous outside option for a bargaining agent. Behavioral agents are commitment types that demand a constant portion of the surplus. The frequency of behavioral types is determined in equilibrium. Even if the frequency of behavioral types is negligible, they affect the terms of trade and efficiency. In an unbalanced market where the entering flow of one side is short, there is one-sided reputation building in bargaining, and commitment types on the short side determine the terms of trade. In a balanced market where the entering flows are equal, there is twosided reputation building in bargaining, and reputation concerns lead to inefficiency. An equilibrium with persistent delays is constructed. The magnitude of inefficiency is determined by the demands of the commitment types and is independent of their frequency. Access to the market exacerbates bargaining inefficiencies caused by behavioral types, even at the frictionless limit of complete rationality.