Rigorous Punishment Promotes Cooperation in Prisoners' Dilemma Game

In this paper, we introduce a rigorous punishment mechanism into the prisoners’ dilemma game. In our model, the punisher punishes the defector with fine \(\beta \) at the cost of \(\gamma \). Monte-Carlo simulations show the evolution of system is jointly affected by \(\beta \), \(\gamma \) and system’s initial state. We find that when \(\gamma \) is small, the system can evolve into two steady states, i.e., coexisting of cooperators and defectors, and pure punishers. When \(\gamma \) is large, the system can evolve into the only steady state, i.e., coexisting of cooperators and defectors. However, in the middle value of \(\gamma \), the system can evolve into three steady states, i.e., coexisting of cooperators and defectors, a rock-paper-scissors type of cyclic dominance, and pure cooperators. These results are explained by average total payoff, transition possibility and evolutionary snapshot. We also find the heterogeneity of population distribution can affect cooperation as well.

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