This paper studies coalition formation and payoff division in a class of majority games (apex games) assuming that payoff division can only be agreed upon after forming the coalition (two-stage bargaining) and that negotiations in the coalition can break down and a new coalition be formed...

I propose a normal form game of agreement formation in which each player's strategy is to say for each size of agreement whether it is acceptable or not. I propose a refinement, which guarantees that each one of these choices is self-enforcing. For general payoff functions, which exhibit...