Evolutionary dynamics of public goods game with tax-based rewarding cooperators

In public goods games, rewards have been demonstrated as an effective mechanism for sustaining cooperation among individuals. Rewarding cooperators are willing to incur personal costs to incentivize cooperative behavior. However, pure cooperators become second-order free-riders because they are not willing to bear these additional costs. To address this issue and ensure the effectiveness of the reward strategy, we propose the introduction of a tax mechanism. We examine the performance of strong altruistic rewarding cooperators and weak altruistic rewarding cooperators separately, with the support of the tax mechanism. Through theoretical analysis and numerical calculations, our study reveals that tax-based rewarding cooperators possess an evolutionary advantage in maintaining cooperation. In addition, we found that strong altruistic rewarding cooperators were more effective than weak altruistic rewarding cooperators in solving the second-order free-riders problem. Our findings contribute to the understanding of cooperative behavior in public goods games and provide insights into the design of mechanisms that promote sustained cooperation. The introduction of a tax mechanism in combination with strong altruistic reward strategies can offer an effective solution to the second-order free-riders problem.