Imitation and aspiration update rules are frequently observed in human and animal populations. While the imitation process entails payoff comparisons with surroundings, the aspiration process refers to self-evaluation. This work explores the evolution of cooperation in dyadic games under the coexistence of these two dynamics in an infinitely large well-mixed population. Two situations have been explored: (i) individuals adopt either an imitation or aspiration update rule with a certain probability, and (ii) the entire population is divided into two groups where one group only uses imitative rules and the other obeys aspiration updating alone. Both premises have been modeled by taking an infinite approximation of the finite population. In particular, the second mixing principle follows an additive property: the outcome of the whole population is the weighted average of outcomes from imitators and aspiration-driven individuals. Our work progressively investigates several variants of aspiration dynamics under strong selection, encompassing symmetric, asymmetric, and adaptive aspirations, which then coalesce with imitative dynamics. We also demonstrate which of the update rules performs better, under different social dilemmas, by allowing the evolution of the preference of update rules besides strategies. Aspiration dynamics always outperform imitation dynamics in the prisoner's dilemma, however, in the chicken and stag-hunt games the predominance of either update rule depends on the level of aspirations as well as on the extent of greed and fear present in the system. Finally, we examine the coevolution of strategies, aspirations, and update rules which leads to a binary state of obeying either imitation or aspiration dynamics. In such a circumstance, when aspiration dynamics prevail over imitation dynamics, cooperators and defectors coexist to an equal extent.

中文翻译：

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志向与模仿机制并存的社会困境中合作的演变

模仿和愿望更新规则在人类和动物种群中经常被观察到。模仿过程需要与周围环境进行收益比较，而追求过程则是自我评估。这项工作探索了在无限大的充分混合人口中这两种动力并存的情况下二元游戏合作的演变。已经探讨了两种情况：（i）个人以一定的概率采用模仿或愿望更新规则，并且（ii）将整个人群分为两组，其中一组仅使用模仿规则，另一组仅遵循愿望更新。这两个前提都通过对有限人口进行无限逼近来建模。特别地，第二混合原理遵循加性：整个人群的结果是模仿者和志向驱动的个人结果的加权平均值。我们的工作逐步研究了强烈选择下的吸气动力学的多种变体，包括对称，不对称和自适应吸气，然后将它们与模拟动态融合在一起。我们还通过允许除策略之外的更新规则偏好的演变，证明了在不同的社会困境下，哪些更新规则的性能更好。在囚徒的困境中，愿望的动态总是胜过模仿的动态，但是，在鸡和鹿角游戏中，两种更新规则的优势都取决于愿望的水平以及系统中存在的贪婪和恐惧程度。最后，我们考察了各种策略，理想，并更新规则，导致遵循模仿或愿望动态的二元状态。在这种情况下，当愿望动态胜过模仿动态时，合作者和叛逃者在同等程度上共存。