Abstract
The extortion strategy is an important subset of the zero-determinant strategy, which ensures that the participant gets no less than its opponent’s payoff, attracting the attention of many scholars. Peer pressure has proved to be an effective mechanism for maintaining cooperation between selfish individuals in evolutionary game dynamics. Therefore, in this paper, we use punishment to imitate peer pressure to study the influence of peer pressure on the evolution of cooperation in the extortion strategy. Peer pressure can be simulated with punishment and use $$\alpha $$ to control the punishment intensity. The simulation results show that the punishment of the extortioner plays a key role in the evolution of the cooperative strategy. When $$\alpha $$ is small, the punishment of the extortioner will make the system enter a three-state cycle which similar to that of rock–scissor–paper, greatly promoting cooperation. When $$\alpha $$ is large, the extortioner will dominant the entire population by punishing cooperator and defector. In addition, proper punishment will make the cooperator dominant the entire population when b is small.
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