In three-person envy games, an allocator, a responder, and a dummy player interact. Since agreement payoffs of responder and dummy are exogenously given, there is no tradeoff between allocator payoff and the payoffs of responder and dummy. Rather, the allocator chooses the size of the pie and...

We consider three-person envy games with a proposer, a responder, and a dummy player. In this class of games, the proposer, rather than allocating a constant pie, chooses the pie size which the responder can then accept or reject while the dummy player can only refuse his own share. While the...