Fairness in bargaining

We consider new three player games to test existing models of fairness. Our games consist of a proposer who offers an allocation of $10 between two players, either himself and the responder or the responder and a third party. In each case, the responder either accepts or rejects this allocation. In case of a rejection, the player who was not part of the initial division (the third party and the proposer, respectively) receives a rejection payoff (of $0, $5 or $10, depending on the game). Our results cast some doubt on existing fairness theories.