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Impact of multi-step punishment on the spatial prisoner’s dilemma game. (English) Zbl 1503.91029

Summary: Punishment has been proved to be an effective means for sustaining and promoting the evolution of cooperation. However, most works only consider one-off punishment, that is, the effect of each punishment only acts at one time step, it is often inconsistent with real-world scenarios. Therefore, different from previous works, we propose a new punishment model, which extends the punishment from one step to multiple ones. In particular, we assume that individuals will change their reputation scores according to their own behaviors, and begin to accept the punishment with intensity \(w\) when their reputation is below the reputation threshold. Through plenty of Monte Carlo simulations, it is found that there exists an optimal punishment time window to foster the cooperative behaviors, which indicates that the multi-step punishment is a double-edged sword, and too long or too short punishment is not conductive to sustain the collective cooperation.

MSC:

91A22 Evolutionary games
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