Robustness of cooperation in memory-based prisoner’s dilemma game on a square lattice

• We introduce the accumulative payoff in all time steps.
• Cooperation can be significantly promoted by introducing the accumulative payoff.
• We introduce random defective mutations into cooperative clusters.
• Robustness of cooperation is analyzed in such an invasive noise.

Cooperation in prisoner’s dilemma game can be promoted significantly by introducing memory effects. In this work, we assume that the changing probability of strategy is determined by the agents’ accumulative payoff in all time steps. We have numerically investigated robustness of cooperation by introducing an attack probability, with which an individual in cooperation clusters becomes a defector. It is found that the density of cooperators at stable states decreases with the attack probability in traditional memoryless models. However, in the memory-based model, the density of cooperators cannot reach a stable state even if the attack probability is very small. The more the increase of the attack probability, the faster the vanishment of the cooperators. Our work could be helpful to understand the emergence of cooperation in systems consisting of selfish individuals. It suggests a new method to study whether cooperation can be maintained in noisy environments.