Prisoner’s Dilemma Game with Nonlinear Attractive Effect on Regular Small-World Networks

We investigate a spatial Prisoner’s Dilemma game with nonlinear attractive effect on regular small-world networks. The players located on the sites of networks can either cooperate with their neighbours or defect. In every generation, each player updates its strategy by firstly choosing one of the neighbours with a probability proportional to A^α denoting the attractiveness of the neighbour, where A¹ is the collected payoff and α (≥0) is a free parameter characterizing the extent of nonlinear effect. Then each player adopts its strategy with a probability dependent on their payoff difference. Using Monte Carlo simulations, we investigate the density ρ_C of cooperators in the stationary state for various values of α and the rewiring probability q of the network. It is shown that the introduction of such attractive effect remarkably promotes the emergence and persistence of cooperation over a wide range of the temptation to defect for the same network structures. We also point out that long-range connections either enhance or inhibit the cooperation, which depends on the value of α and the payoff parameter b.