Bargaining , Voting and Value ∗

This paper addresses the following issue: If a set of agents bargain on a set of feasible alternatives ’under the shadow’ of a voting rule, that is, any agreement can be enforced if a ’winning coalition’ supports it, which general agreements are likely to arise? In other terms: Which is the influence that the voting rule used to settle agreements can project on the outcome? To give an answer we model the situation as an extension of Nash bargaining problem in which an arbitrary voting rule replaces the unanimity to settle agreements by n players. This provides a setting in which a natural extension of Nash’s solution (consistent with Shapley’s value) is obtained axiomatically by, basically, integrating into a single system Nash’s and Shapley’s characterizing systems.