Self-learning PD game with imperfect information on networks

In this paper, we discuss the prisoners´ dilemma (PD) game with imperfect information on complex networks. The players are assumed to know no information of the strategies of their opponents, and they have to make decisions only by learning from the limited history of their own. We present a self-learning rule for strategy update of the players and carry out numerical simulations for the evolution of the PD games on Barabasi-Albert (BA) scale-free networks and periodical boundary lattices (PBLs). The results show that the underlying network structures have a strong effect on the cooperation level and the wealth distribution of the players. It is also shown that making use of longer memory does not need to promote the cooperation frequency and wealth level in the game. This indicates that there should exists an optimal memory length for given parameters of the payoff matrix. Moreover, it is found that larger temptation of defection will tend to decreasing the cooperation frequency and increase the wealth.