Strategies Memorizing More Rounds May Promote the Emergence of Cooperation in Stochastic Games

In this paper, we study the evolution of cooperation in a stochastic game model where agents evolve in terms of some famous and important memory-two strategies, such as AllC, AllD, TFT and W SLS strategies. Comparing with memory-one strategies, it is found that the cooperation is easier to emerge in stochastic games with memory-two strategies. When agents remember more rounds of outcomes, cooperation can boost in noisy environment when some efficient transition rules work to reward mutual cooperation and punish defection. This may provide some potential clues to seek for efficient methods that maintain cooperation in multi-agent games.