The lack of cooperation can easily result in inequality among members of a society, which provides an increasing gap between individual incomes. To tackle this issue, we introduce an incentive mechanism based on individual strategies and incomes, wherein a portion of the income from defectors is allocated to reward low-income cooperators, aiming to enhance cooperation by improving the equitable distribution of wealth across the entire population. Moreover, previous research has typically employed network structures or game mechanisms characterized by homogeneity. In this study, we present a network framework that more accurately reflects real-world conditions, where agents are engaged in multiple games, including prisoner's dilemma games in the top-layer and public good games in the down-layer networks. Within this framework, we introduce the concept of ``external coupling'' which connects agents across different networks as acquaintances, thereby facilitating access to shared datasets. Our results indicate that the combined positive effects of external coupling and incentive mechanism lead to optimal cooperation rates and lower Gini coefficients, demonstrating a negative correlation between cooperation and inequality. From a micro-level perspective, this phenomenon primarily arises from the regular network, whereas suboptimal outcomes are observed within the scale-free network. These observations help to give a deeper insight into the interplay between cooperation and wealth disparity in evolutionary games in large populations.

翻译：合作缺失极易导致社会成员间的不平等，从而加剧个体收入差距。为应对此问题，我们提出一种基于个体策略与收入的激励机制：将背叛者部分收入重新分配给低收入合作者作为奖励，旨在通过改善整体财富分配的公平性来促进合作。此外，既往研究通常采用同质化的网络结构或博弈机制。本研究构建了一个更贴近现实条件的网络框架：智能体在顶层网络参与囚徒困境博弈，在底层网络参与公共物品博弈，形成多重博弈场景。在此框架中，我们引入"外部耦合"概念，通过跨网络连接智能体建立熟人关系，从而促进共享数据集的访问。研究结果表明，外部耦合与激励机制的协同正向效应能够实现最优合作率与较低的基尼系数，证明合作与不平等之间存在负相关关系。从微观层面看，该现象主要产生于规则网络，而在无标度网络中则观察到次优结果。这些发现有助于深入理解大规模群体演化博弈中合作与财富差距的相互作用机制。