The effect of heterogeneous perceptions with environmental feedback on spatial social dilemmas

Heterogeneity as an effective factor influencing cooperation typically stems from the differences between individuals' subjective characteristics and external objective conditions. However, the interplay between subjective and objective heterogeneity is often overlooked in the evolutionary game. Therefore, we study the evolution of cooperative behavior in populations when external objective environments influence subjective perceptions. Considering that individuals may have different perceptions when facing the same social dilemma and individuals' perceptions are influenced by the environment, we use the prisoner's dilemma game and the snowdrift game to build a multigame model in which players' payoffs are affected by the local environment, i.e., the number of players' cooperative neighbors. The experimental results suggest that higher levels of perceived heterogeneity and stronger environmental feedback are more conducive to enhancing cooperation levels, but full cooperation still cannot be achieved. Through the analysis of state transition probabilities, we further explain the limitations of environmental feedback on enhancing cooperation. Additionally, we find that the subpopulation playing the snowdrift game is more sensitive to environmental changes. We also perform sensitivity analysis and verify the robustness of our mechanism. Our explorations may help to understand how heterogeneity may affect the survival and maintenance of cooperation.