An Improved Fitness Evaluation Mechanism with Memory in Spatial Prisoner's Dilemma Game on Regular Lattices

To deeply understand the emergence of cooperation in natural, social and economical systems, we present an improved fitness evaluation mechanism with memory in spatial prisoner's dilemma game on regular lattices. In our model, the individual fitness is not only determined by the payoff in the current game round, but also by the payoffs in previous round bins. A tunable parameter, termed as the memory strength (μ), which lies between 0 and 1, is introduced into the model to regulate the ratio of payoffs of current and previous game rounds in the individual fitness calculation. When μ=0, our model is reduced to the standard prisoner's dilemma game; while μ=1 represents the case in which the payoff is totally determined by the initial strategies and thus it is far from the realistic ones. Extensive numerical simulations indicate that the memory effect can substantially promote the evolution of cooperation. For μ<1, the stronger the memory effect, the higher the cooperation level, but μ=1 leads to a pathological state of cooperation, but can partially enhance the cooperation in the very large temptation parameter. The current results are of great significance for us to account for the role of memory effect during the evolution of cooperation among selfish players.