A noncooperative foundation of the asymmetric Nash bargaining solution

We consider a noncooperative multilateral bargaining model with heterogeneous time preferences in which the first rejector of a proposal in the current round becomes the proposer in the next round. We show the existence of a stationary subgame perfect equilibrium (SSPE), characterize SSPEs and show the efficiency of SSPEs. We show that any sequence of SSPE payoff profiles converges to the asymmetric Nash bargaining solution weighted by the inverses of discount rates as the bargaining friction vanishes.