From eligibility to suitability: Regulation and restriction of reputation-based access system on free-riding behavior in spatial public goods game

In spatial public goods games (SPGG), social exclusion is regarded as a strategy more efficient than punishment for mitigating first-order free-riding behaviors. In the traditional exclusion model, exclusion actions are often taken after the game has concluded, by modifying the payoff structure to ensure that defection strategies do not yield benefits. However, this implies that defectors are still allowed to participate throughout the entirety of the game. We propose the establishment of an access system based on reputation, purposefully filtering players to preclude low-reputation individuals prone to free-riding from participating in the game, thus circumventing exploitative strategies, minimizing risks, and enhancing cooperative efficiency. In our study, we have established two models governing exclusionary behaviors within the reputation-based access system, using homogeneous exclusion probability and heterogeneous exclusion probability respectively. Experimental results demonstrate that both models significantly foster cooperation and effectively address the problem of second-order free-riding. The homogeneous exclusion probability model approximates the exclusion efficiency of traditional exclusion strategies under higher exclusion probabilities, whereas the heterogeneous model, influenced by varying intensities of exclusion, surpasses traditional strategies in efficacy at higher levels of exclusion intensity. This research aids in better understanding the impact of reputation-based access systems on free-riding behavior in real-world scenarios.