Two-Stage Bargaining with Reversible Coalitions: The Case of Apex Games

This paper studies coalition formation and payoff division in apex games under the following assumptions: first, payoff division can only be agreed upon after the coalition has formed (two-stage bargaining); second, negotiations in the coalition can break down, in which case a new coalition may be formed (reversible coalitions).In contrast with the results of other two-stage models, all minimal winning coalitions may form and expected payoffs coincide with the per capita nucleolus.These results are robust to the details of the bargaining procedure.Surprisingly, having a two-stage process (rather than a one-stage process with simultaneous coalition formation and payoff division) benefits the apex player.