In real life, a good reputation generally brings positive returns to individuals. For example, merchants with numerous good reviews usually gain higher profits. Considering this in the ultimatum game, we propose a reputation-based reward mechanism to investigate the evolution of fairness. Specifically, individuals' reputations evolve dynamically based on the outcomes of games. At the same time, we set a reputation threshold in the population. When individuals' reputations exceed the reputation threshold, they are considered excellent. Otherwise, they are ordinary. The excellent individuals can receive extra rewards compared to the ordinary ones. Finally, individuals' total payoffs determine their fitness within the population. Based on these settings, this paper mainly explores how reputation threshold, weight factor and reward strength affect the evolution of fairness. Through a series of simulations, the reputation-based rewards mechanism is proved to effectively promote the fairness in the population. To be specific, we find that higher reputation thresholds and smaller values of weight factor significantly enhance the promotion effect of reward on fairness. Simultaneously, there is a specific correspondence between the reputation threshold and the weight factor. When reward strength is fixed, for different reputation thresholds, the optimal value of weight factor to achieve maximum fairness levels also varies. Additionally, increasing reward strength can significantly promote fairness.

中文翻译：

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基于声誉的奖励机制促进了公平性的进化


在现实生活中，良好的声誉通常会给个人带来积极的回报。例如，拥有众多好评的商家通常会获得更高的利润。考虑到这一点，在最后通牒游戏中，我们提出了一种基于声誉的奖励机制来研究公平性的演变。具体来说，个人的声誉会根据游戏的结果动态变化。同时，我们在总体中设置了声誉阈值。当个人的声誉超过声誉阈值时，他们被视为优秀。否则，他们就是普通的。与普通人相比，优秀的个人可以获得额外的奖励。最后，个体的总收益决定了他们在种群中的健康状况。基于这些设置，本文主要探讨了声誉阈值、权重因子和奖励强度如何影响公平性的演变。通过一系列仿真，证明了基于声誉的奖励机制可以有效地促进人口的公平性。具体来说，我们发现较高的声誉阈值和较小的权重因子值会显著增强奖励对公平性的提升效果。同时，声誉阈值和权重因子之间存在特定的对应关系。当奖励强度固定时，对于不同的声誉阈值，实现最大公平性水平的最佳权重系数值也会有所不同。此外，增加奖励强度可以显着促进公平性。