Roles of average degree for the networked game with generous tit-for-tat strategy

In this paper, we studied the evolution of reactive strategies (p,q) on the homogeneous regular networks with different average degrees, where p and q imply the probabilities to cooperate after a cooperative and defective opponent. Based on the prisoner´s dilemma game, we show that the proper density of regular networks can promote the emergence of generous tit-for-tat (GTFT) strategy and improve the individuals´ gains. However, the GTFT-like strategy is difficult to diffuse on the sparse network, whereas the defective strategy is easy to spread on the dense network. This work may provide some clues for understanding the emergence mechanism of cooperation in the multi-agent networked system.