Hybrid reward-punishment in feedback-evolving game for common resource governance

How to maintain the sustainability of common resources is a persistent challenge, as overexploiters often undermine collective efforts by prioritizing personal gain. To mitigate the overexploitation of resources by violators, previous theoretical studies have revealed that the introduction of additional incentives, whether to reward rule-abiding cooperators or to punish those who overexploit, can be beneficial for the sustainability of common resources when the resource growth rate is not particularly low. However, these studies have typically considered rewarding and punishing in isolation, thus overlooking the role of their combination in common resource governance. Here, we introduce a hybrid incentive strategy based on reward and punishment within a feedback-evolving game, in which there is a complex interaction between human decision making and resource quantity. Our coevolutionary dynamics reveal that resources will be depleted entirely, even with cooperative strategies for prudent exploitation, when resource growth is slow. When the rate of resource growth is not particularly low, we find that the coupled system can generate a state where resource sustainability and cooperation can be maintained. Furthermore, when the rate of resource growth is moderate, we find that achieving this state cannot simply allocate all incentive budgets to reward. In addition, the increase in per capita incentives significantly promotes the stability of this state.