Bargaining with nanonymous disagreement: nondecomposable rules

Abstract

We analyze bargaining situations where the agents’ payos from disagreement depend on who among them breaks down the negotiations. We model such problems as a superset of the standard domain of Nash (1950). We first show that this domain extension creates a very large number of new rules that could not have been analyzed under the standard domain. Particularly, the rules associated with the Nash domain constitute a nowhere dense subset of all possible rules. Next, we analyze monotone path rules on our domain and show that they are characterized by a set of properties that are not jointly compatible on the Nash domain. We also analyze and characterize a Proportional rule on our domain.