Equalizing payoffs of a structured population in repeated Prisoner’s Dilemma game

Through the zero-determinant theory in the infinite repeated Prisoner’s Dilemma game, this paper explores a novel method to equalize the average payoff of individuals in a regular graph, where individuals turn their strategies in terms of a uniform updating vector. Through designing three parameters about the transition probability for all defective state (starting point of the vector), the ratio coefficient and the probability difference, these elements in this strategy updating vector can form two arithmetic sequences respectively corresponding to focal cooperators and focal defectors, and the expected average payoff of population may fall into the region between mutual cooperation and mutual defection. Simulations in the ring with two degrees and the square lattice with four degrees validate the effectiveness of these theoretical results, and show the ratio coefficient can not only decide the converge rate, but also affect the divergence of individuals’ payoffs. This work may give some clues for designing protocols to adjust utility of structured populations in multi-agent systems.