Uniqueness of stationary equilibrium payoffs . . .

We study a model of sequential bargaining in which, in each period before an agreement is reached, a proposer is randomly selected, the proposer suggests a division of a pie of size one, each other agent either approves or rejects the proposal, and the proposal is implemented if the set of approving agents is a winning coalition for the proposer. We show that stationary equilibrium outcomes of a coalitional bargaining game are unique. This generalizes Eraslan (2002) insofar as: (a) there are no restrictions on the structure of sets of winning coalitions; (b) different proposers may have different sets of winning coalitions; (c) there may be a positive probability that no proposer is selected