Uniqueness in Random-Proposer Multilateral Bargaining

Solution uniqueness is an important property for a bargaining model. Rubinstein’s (1982) seminal 2-person alternating-offer bargaining game has a unique Subgame Perfect Equilibrium outcome. Is it possible to obtain uniqueness results in the much enlarged setting of multilateral bargaining with a characteristic function? In an exploratory effort, this paper investigates a model first proposed in Okada (1993) in which each period players have equal probabilities of being selected to make a proposal and bargaining ends after one coalition forms. Focusing on transferable utility environments and Stationary Subgame Perfect Equilibria (SSPE), we find ex ante SSPE payoff uniqueness for large classes of characteristic functions. This study includes as a special case a variant of the legislative bargaining model in Baron and Ferejohn (1989), and our results imply (unrestricted) SSPE payoff uniqueness in this case.