The secret behind cooperation with the present profit-pursuing nature has been unveiled via the Evolutionary Game Theory and models. However, the payoff equality is not sufficiently explored. This paper proposes a simple but efficient way to focus on the synergetic behaviors of payoff equality and cooperation improvement. Herein, the classical Evolutional Game model is re-evaluated from the perspective of payoff equality. By assuming the similarity between the value function in “mental accounting effect” and the inverse of the Lorenz curve, the “rank strategy” is introduced in the form of a slightly alternated Fermi strategy which focuses on the rank difference on the wealth (payoff) distribution curve along the calculation of the Gini coefficient. Such introduction opens up a new perspective to the cross section between economics and the evolutionary game theory. Compared with the original Fermi strategy adoption (named payoff strategy), the rank strategy significantly aids the system to survive a higher benefit with a faster recovery after the enduring period. The reason behind this can be discussed from the formation of giant clusters, which also indicates a spillover effect in both cooperation and payoff equality improvement. A further breakdown in the population also suggests the leading role of rich players who help poor players in improving the payoff equality among them. The rank strategy is further evaluated in a broad parameter range with different combinations of the ratio of initial cooperators, the benefit (b) and the fitness (K). In most cases, the rank strategy shows a better performance in both the fraction of cooperators and the Gini coefficient, which concludes that the mental accounting effect could be the more realistic factor that may be critical to consider. The resolution in the cooperative mechanism may also be linked to wealth equality. Simulation results in this work suggest a close relationship between cooperation improvement and the payoff equality which is not extensively explored in earlier works. Simulations with Gini distribution explain “A good deed is never lost” in a numerical way.

中文翻译：

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进化博弈的回报平等视角：心理账户与合作促进


与当前逐利本质合作的秘密已通过进化博弈论和模型揭开。然而，收益相等性没有得到充分的探索。本文提出了一种简单而有效的方法来关注收益平等和合作改进的协同行为。在此，从收益相等的角度重新评估了经典的进化博弈模型。通过假设“心理核算效应”中的价值函数与洛伦兹曲线的倒数相似性，“等级策略”以略微交替的费米策略的形式引入，该策略侧重于沿基尼系数计算的财富（收益）分配曲线上的等级差异。这样的介绍为经济学和进化博弈论之间的交叉领域开辟了一个新的视角。与最初的费米策略采用（称为 payoff strategy）相比，秩策略显着帮助系统在持久期后以更快的恢复速度生存下来。这背后的原因可以从巨型集群的形成中讨论出来，这也表明合作和收益平等改善都存在溢出效应。人口的进一步细分也表明，富人在帮助穷人提高他们之间的收益平等方面发挥着主导作用。使用初始合作者比率、收益 （b） 和适应度 （K） 的不同组合，在广泛的参数范围内进一步评估排名策略。 在大多数情况下，排名策略在合作者比例和基尼系数方面都显示出更好的表现，这得出的结论是，心理核算效应可能是更现实的因素，可能值得考虑。合作机制中的决议也可能与财富平等有关。这项工作的仿真结果表明，合作改进与收益平等之间存在密切关系，这在早期的工作中没有得到广泛探讨。基尼分布的模拟以数字方式解释“善行永远不会丢失”。