The impact of memory reputation-induced tax and reward allocation on spatial public goods games

In spatial public goods games (SPGG), the use of rewards serves as an effective strategy to enhance cooperation among group members. In this scenario, the rewarder incurs a cost to incentivize altruistic behavior. However, many individuals who are willing to cooperate are unwilling to bear the cost of incentives and thus become second-order free-riders. To address this issue, we propose a tax allocation mechanism that levies a specific tax from all participants in the public goods games to subsidize the rewarders. The introduction of a reputation system can significantly elevate the level of cooperation among individuals within the framework. To further enhance cooperation, we suggest implementing a memory-based reputation allocation mechanism. This mechanism distributes taxes and rewards to group members based on the magnitude of individual reputations of the cooperators and the rewarders. Through comprehensive numerical analyses, we demonstrate that the memory-based allocation of taxes and rewards typically fosters an increase in cooperation levels within the system and clarifies the origins of the rewards, thereby rendering the model more realistic compared to traditional reward systems.