Promotion of cooperation in aspiration-based spatial prisoner's dilemma game

We introduce a deterministic aspiration-based learning mechanism into the prisoner's dilemma game on regular lattices and then investigate the evolution of cooperation for different values of aspiration level A. It is found that the cooperation level exhibits discontinuous phase transition with A and there is a moderate aspiration level that can best favor the cooperative behavior. Besides, the evolution time series show the so-called "ping-pong effect" for both high and low aspiration levels. The evolution of spatial patterns is also investigated. It is found that the cooperator frequency is not sensitive to the initial condition but the evolutionary patterns can be quite different.