Role of reputation constraints in the spatial public goods game with second-order reputation evaluation

At present, the reputation evaluation problem caused by resource constraints significantly influences group cooperation behavior, and cannot be considered and solved in the traditional game model. In this paper, we consider the evolutionary behavior of a spatial public goods game with constraints on second-order reputation evaluation, which can be characterized by an evaluation variable. First, to achieve constraints on high-reputation individuals, an adaptive threshold adjustment function is introduced to dynamically regulate the individual's image, which is based on the evaluation variable. We discuss the impact of evaluation constraints on group evolutionary behavior under four classical second-order updating rules: shunning, stern judging, simple standing, and image scoring. For shunning and stern judging, the appropriate evaluation constraint maximizes the cooperation level; for the other rules, high cooperative behavior is promoted by a small constraint value. Finally, we also analyze the evolutionary behavior of some mechanisms in two other networks: random and small-world networks. In summary, the current results provide an opportunity to study the evolution of human behavior in a competitive situation and develop an effective mechanism to foster collective cooperation.