An intermediate number of neighbors promotes the emergence of generous tit-for-tat players on homogeneous networks

This paper investigates the evolution of reactive strategies (p,qp,q) on the homogeneous regular and random networks with different network densities. Here p and q mean the probabilities to cooperate after a cooperative and defective opponent. Through the prisoner’s dilemma model, we show that the intermediate number of neighbors of both regular and random networks can promote the emergence of generous tit-for-tat (GTFT) strategy and improve the individuals’ gains. The sparse network inhibits the diffusion of the GTFT-like strategy, while the dense network promotes the spread of the defective strategy. Moreover, our investigation shows that compared with the regular ring, the individuals on the random network with proper number of neighbors can obtain higher gains, whereas the cooperative behavior is inhibited for the denser random network.