The Influence of Fine Distribution and Compensation on Cooperation in Public Goods Game

In spatial public goods games, groups consisting solely of defectors do not benefit. Consequently, intelligent defectors are inclined to incur the cost of punishing other defectors to enable cooperators to flourish within the group, thereby safeguarding their own advantages. Drawing from real-world observations where early preparation often dictates future success, we integrated probabilistic punishment into the public goods game and analyzed two scenarios. In the first scenario, a probabilistic punishment mechanism was established, wherein the higher the cost was of monitoring and enforcement, the greater was the probability of punishment. In the second scenario, a compensation and fine distribution mechanism was introduced alongside probabilistic punishment, where the outcome of the punishment determined whether the smart defector recovered part of the fine or rewarded cooperators with additional benefits. This incentivized smart defectors to judiciously assess the punishment cost required to effectively protect their interests. The study demonstrated that both mechanisms significantly enhanced cooperation, with the probabilistic punishment model involving fine distribution and compensation proving more effective than simple probabilistic punishment alone. These results offer novel insights into the dynamics of probabilistic punishment and the role of fine distribution in fostering cooperation.