Effect of memory on the prisoner's dilemma game in a square lattice

We have studied the effect of memory on the evolution of the prisoner's dilemma game in square lattice networks. Based on extensive simulations, we found that the density of cooperators was enhanced by an increasing memory effect for most parameters. However, we also observed that the density of cooperators decreased with an increased memory effect in the case of a large memory and moderate temptation. It is interesting to note that memory makes cooperators immune from temptation. The strength of protection reaches its maximal value only for a moderate memory effect.