An evolutionary game analysis of a dynamically switching zero-determinant strategy

In evolutionary game theory, zero-determinant (ZD) strategies have become a breakthrough in the study of the Prisoner’s Dilemma due to their ability to unilaterally control payoffs. However, traditional ZD strategies—such as extortion (E) and generosity (G) strategies—suffer from imbalanced interests and limited adaptability. This paper proposes a dynamically switching PERG strategy (Poverty-Extortion, Richness-Generosity), which adaptively switches between E and G based on state-dependent mechanisms to balance the payoffs of both parties. By constructing a seven-strategy model including PERG, TFT, WSLS, E, G, C, and D, we systematically reveal the evolutionary dynamics in well-mixed populations, synthetic networks, and real-world networks. Computational simulations show that in well-mixed populations, benevolent strategies like PERG have evolutionary advantages. Smaller extortion and generosity factors can suppress the spread of the D strategy, and lower cooperation costs may weaken the incentive effect of payoffs on cooperation. In synthetic networks and real-world networks, PERG, WSLS, and G strategies rapidly invade other strategies. The benefit parameter has little impact on the distribution of dominant strategies in synthetic networks, and in BA scale-free networks, the proportion of the PERG strategy shows an upward or downward trend as specific parameters change.