Multi-agent bilateral bargaining and the Nash bargaining solution

This paper studies a bargaining model where n players negotiate how to share a pie through (n−1) bilateral bargaining sessions. In each session, two players bargain for a partial agreement that specifies who exits and who moves on to the next session (if there is any) via the alternating-proposal framework of Rubinstein [Rubinstein, A., 1982. Perfect equilibrium in a bargaining model. Econometrica 50, 97-109]. We consider two bargaining procedures under which the subgame perfect equilibrium outcomes converge to the Nash [Nash, J., 1950. The bargaining problem. Econometrica 18, 155-162] bargaining solution for the corresponding bargaining problem as the players' discount factor goes to one. Hence, the model studied here provides a non-cooperative foundation for the Nash cooperative bargaining solution in the multilateral case.