Cooperation dynamics in spatial public goods games with graded punishment mechanism

Punishment, as an incentive mechanism, was normally carried out with a certain fixed probability in previous studies. But in a real legal society, recidivists are punished more than first offenders. Learning from this idea, we introduce a new form of graded punishment in the spatial public goods game, in which the punishment probability changes dynamically according to the number of consecutive defections in the games. Our logic is that the more times a player defects continuously, the greater the probability that he will be punished. To demonstrate the effect of the graded punishment mechanism, we serve the traditional fixed probability punishment as the reference model. By comparing the simulation results of the two models, we find that graded punishment can solve social dilemmas, and in most cases, it is more conducive to cooperation than traditional probabilistic punishment. However, with the increase in the punishment cost or the decline of the fine, the advantage of graded punishment weakens. Additionally, if the initial punishment probability is small enough and the punishment cost is close to the fine, the effect of the graded punishment is not as good as the traditional punishment. Therefore, it has pros and cons in promoting cooperation. These results provide a new perspective on the punishment mechanism in promoting cooperation and establish a basis for choosing more effective incentives.

Automated summary

In previous studies, punishment as an incentive mechanism was typically carried out with a fixed probability. However, in a real legal society, recidivists are punished more than first offenders. To address this, we introduce a new form of graded punishment in the spatial public goods game, where the punishment probability changes dynamically based on consecutive defections. Our findings show that graded punishment can effectively solve social dilemmas and promote cooperation better than traditional probabilistic punishment in most cases.