Memory-based stag hunt game on regular lattices

Memory normally plays an important role when people make a decision. Thus, it is reasonable and necessary to introduce the influence of memory in the evolutionary game theory. However, the previous work mainly focuses on prisoner’s dilemma, snowdrift game or public good game, but little on stag hunt game. In this paper, a memory-based stag hunt game is proposed. For each iteration, the players in the regular lattices will first choose its neighbor who has the largest accumulated payoff in the last M runs. Then, according to the Femi rule, the player will determine whether learning from the neighbor or not. It is found that the memory length M will promote the cooperation level. The larger the memory length is, the higher the cooperation level will be. Furthermore, when the payoff parameter is less than 0.75, cooperation will always spread the whole regular lattices. As the parameter is larger than 0.75, no matter how large the memory length is, the behavior of defection will always exist. Our work may shed some new light on the study of evolutionary games with memory effect.