Effect of distribution of fines on evolution of cooperation in spatial public goods game

In the realm of public goods game, punishment, as a potent tool, stands out for fostering cooperation. While it effectively addresses the first-order free-rider problem, the associated costs can be substantial. Punishers incur expenses in imposing sanctions, while defectors face fines. Unfortunately, these monetary elements seemingly vanish into thin air, representing a loss to the system itself. However, by virtue of the redistribution of fines to cooperators and punishers, not only can we mitigate this loss, but the rewards for these cooperative individuals can be enhanced. Based upon this premise, this paper introduces a fine distribution mechanism to the traditional pool punishment model. Under identical parameter settings, by conducting a comparative experiment with the conventional punishment model, the paper aims to investigate the impact of fine distribution on the evolution of cooperation in spatial public goods game. The experimental results clearly demonstrate that, in instances where the punishment cost is prohibitively high, the cooperative strategies of the traditional pool punishment model may completely collapse. However, the model enriched with fine distribution manages to sustain a considerable number of cooperative strategies, thus highlighting its effectiveness in promoting and preserving cooperation, even in the face of substantial punishment cost.