Bargaining with Mechanisms

Two players bargain over a single indivisible good and a transfer, with one-sided incomplete information about preferences. Both players can offer arbitrary mechanisms to determine the allocation. We show that there is a unique perfect Bayesian equilibrium outcome. In the equilibrium, one of the players proposes a menu that is optimal for the uninformed player among all menus, such that each type of the informed player receives at least her payoff under complete information. The optimal menu can be implemented with at most three allocations. Under a natural assumption on the uninformed player’s beliefs, the optimal menu coincides with the Myerson’s neutral solution to the bargaining problem in this environment. (JEL C78, D82, D83)