On the Neutrality of Coalition Formation in a Pure Bargaining Problem

We show the nuetrality of coalition formation in the sequential bargaining game a la Stahl-Binmore-Rubinstein with random proposers. To that end, we juxtapose an ex-ante coalition formation stage to their bargaining game. Based on the expected outcomes in the negotiation over how to split a dollar, players can form coalitions in a sequential manner, within each of which they can redistribute their payoffs. We find that the grand coalition forms, and that each player receives his discounted expected payoff that is obtained by playing as a single player in the negotiation. In this sense, the neutrality holds in terms of payoffs, although there could be many equilibria in the bargaining stage. We also examine the neutrality from other criteria.