Dynamic incentives and environmental feedback in public goods games: Promoting cooperation through critical thresholds

Understanding the emergence and maintenance of cooperation in multiplayer games is a significant challenge across various theoretical disciplines. In this paper, we introduce an innovative model to study the impacts of environmental feedback in systems with critical thresholds. Different from prior studies on public goods games with environmental feedback, we propose that the system holds expectations for collective behavior, and the dynamic incentives are equal for all group members. Our findings reveal that dynamic incentives driven by environmental feedback significantly enhance cooperation, particularly in scenarios with low synergy factors. As incentives increase, the system shifts from the non-cooperative to cooperative state. Moreover, a faster rate of incentive growth leads to a higher level of cooperation, demonstrating a strong positive correlation between dynamic incentive levels and overall cooperation within the system. Counterintuitively, our study finds that introducing dynamic incentives from environmental feedback not only effectively promotes cooperation under high expectation levels but also surprisingly increases the success rate of cooperation as expectations rise.