In recent years, mechanisms favoring fair split in the ultimatum game have attracted growing interests because of its practical implications for international bargains. In this game, two players are randomly assigned two different roles respectively to split an offer: the proposer suggests how to split and the responder decides whether or not to accept it. Only when both agree is the offer successfully split; otherwise both get nothing. It is of importance and interest to break the symmetry in role assignment especially when the game is repeatedly played in a heterogeneous population. Here we consider an adaptive role assignment: whenever the split fails, the two players switch their roles probabilistically. The results show that this simple feedback mechanism proves much more effective at promoting fairness than other alternatives (where, for example, the role assignment is based on the number of neighbors).
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