School of Mathematical Sciences, Beijing Normal University, Beijing, P.R. China.
PLoS One. 2013 Sep 4;8(9):e74540. doi: 10.1371/journal.pone.0074540. eCollection 2013.
In the ultimatum game, two players divide a sum of money. The proposer suggests how to split and the responder can accept or reject. If the suggestion is rejected, both players get nothing. The rational solution is that the responder accepts even the smallest offer but humans prefer fair share. In this paper, we study the ultimatum game by a learning-mutation process based on quantal response equilibrium, where players are assumed boundedly rational and make mistakes when estimating the payoffs of strategies. Social learning is never stabilized at the fair outcome or the rational outcome, but leads to oscillations from offering 40 percent to 50 percent. To be precise, there is a clear tendency to increase the mean offer if it is lower than 40 percent, but will decrease when it reaches the fair offer. If mutations occur rarely, fair behavior is favored in the limit of local mutation. If mutation rate is sufficiently high, fairness can evolve for both local mutation and global mutation.
在最后通牒博弈中，两名参与者分配一笔钱。提议者建议如何分割，回应者可以接受或拒绝。如果提议被拒绝，双方都将一无所有。理性的解决方案是，即使是最小的提议，回应者也会接受，但人类更喜欢公平的份额。在本文中，我们通过基于量子反应均衡的学习-突变过程来研究最后通牒博弈，其中假设参与者是有限理性的，并在估计策略的收益时会犯错。社会学习从未在公平结果或理性结果处稳定下来，而是导致从提供 40%到 50%的波动。更准确地说，如果低于 40%，提供的平均值有明显的增加趋势，但达到公平报价时会下降。如果突变很少发生，那么在局部突变的极限中，公平行为就会受到青睐。如果突变率足够高，那么公平性就可以在局部突变和全局突变中同时进化。
