Non-cooperative Support for the Asymmetric Nash Bargaining Solution

Our work contributes to the game-theoretic analysis of bargaining by providing additional non-cooperative support to the well-known Nash bargaining solution. In particular, in the present paper we study a model of non-cooperative multilateral bargaining with a very general proposer selection protocol and set of feasible payo s. In each period of the bargaining game, one out of n players is recognized as the proposer according to an irreducible Markov process. The proposer o ers a particular element of the convex set of feasible payo s. If all players accept the o er, it is implemented. If a player rejects the o er, with some probability the negotiations break down and with the remaining probability the next period starts. We show that subgame perfect equilibria in stationary strategies exist and we fully characterize the set of such equilibria. Our main result is that in the limit, as the exogenous risk of breakdown goes to zero, stationary subgame perfect equilibrium payo s converge to the weighted Nash bargaining solution with the stationary distribution of the Markov proposer selection process as the weight vector.