Core equivalence in collective-choice bargaining under minimal assumptions

We investigate a collective-choice bargaining model under minimal assumptions. In this model, the set of alternatives is arbitrary; each player’s utility function is nonnegative-valued; the decision rule is monotonic; the probability of each player’s being recognized as a proposer depends only on the tuple of actions in the previous round; any player is perfectly patient. We show that for any alternative, it is in the core if and only if there exists a stationary subgame perfect equilibrium (SSPE) such that it is proposed by every player and implemented with certainty.