Bargaining, voting, and value

Resumen

This paper addresses the following issue: If a set of agents bargain on a set of feasible alternatives 'in the shadow' of a voting rule, that is, any agreement can be enforced if a 'winning coalition' supports it, what general agreements are likely to arise? In other words: What influence can the voting rule used to settle (possibly non-unanimous) agreements have on the outcome of negotiations? To give an answer we model the situation as an extension of the Nash bargaining problem in which an arbitrary voting rule replaces unanimity to settle agreements by n players. This provides a setting in which a natural extension of Nash's solution is obtained axiomatically. Two extensions admitting randomization on voting rules based on two informational scenarios are considered.