Impact of trajectory-dependent reputation dynamics on the spatial public goods game

In exploring the evolution of social cooperation, reputation mechanisms play a crucial role. To construct a model that more closely reflects reality, this paper proposes a reputation dynamics model based on multidimensional states and designs a dual-channel update rule that combines reputation and payoff. This framework enables players' decisions to no longer depend solely on short-term payoffs but to comprehensively evaluate richer, dynamic social reputation signals. This significantly enhances the competitiveness of cooperators in the public goods game dilemma and provides a possibility for their long-term survival. We find that the effect of the reputation mechanism on cooperative behavior is not a monotonic linear pattern. Although increasing the weight of reputation almost always systematically promotes cooperation, the designed reputation system (defined by the intensity of rewards and punishments and the strictness of social norms) is a double-edged sword. Whether increasing the punishment intensity alone or enhancing the strictness of norms, exceeding a critical point can trigger the negative effect of excessive punishment. That is, a severe punishment originally intended to promote cooperation can, when its intensity is too high, systematically destroy the cooperative order, leading to a "cooperation suppression regime." This paper profoundly clarifies the importance of avoiding excessive punishment and maintaining system resilience in reputation design, providing new insights into the evolution of cooperation in complex social systems.