Riskless versus Risky Bargaining Procedures: the Aumann-Roth Controversy Revisited

In a series of papers, Aumann and Roth discussed a game in which players can cooperate in pairs and two of them prefer to form a coalition with each other. Roth argued that the only rational outcome is that the players who prefer each other form a coalition; Aumann argued that all three coalitions are possible because the players have a problem of expectation coordination. A noncooperative analysis provides additional support for Aumann's arguments and shows that the difference between Aumann's and Roth's views can be traced back to a difference (risky versus riskless) in the bargaining procedure.