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Impact of reputation-based switching strategy between punishment and social exclusion on the evolution of cooperation in the spatial public goods game

The historical behavior of a defector in a group is usually considered in the determination of the intensity of the punishment to be applied to the defector. Because exclusion is a more severe form of punishment, we introduce a conditional punishment that allows punishers to choose between traditional punishment and exclusion. The specific form of punishment is chosen to fit the specific reputation of the defector. A good reputation garners a traditional milder punishment, such as a fine, whereas a bad reputation merits exclusion. The historical behaviors of the individuals in a group are recorded to evaluate their reputations. Those whose reputations fall below a designated threshold are regarded as bad. We study the effects of reputation thresholds, fines, enhancement factors, and exclusion costs on the evolution of cooperation in spatial public goods games. Simulations show that higher thresholds are more conducive to the evolution of cooperation. An extremely small enhancement factor can induce individuals to cooperate when the threshold is relatively high. Cooperation also appears with smaller enhancement factors for higher fines or lower exclusion costs. These results may expand our understanding of how these two strategies of punishment promote cooperation.