Memory boosts turn taking in evolutionary dilemma games

Spontaneous turn taking phenomenon can be observed in many self-organized systems, and the mechanism is unclear. This paper tries to model it by evolutionary dilemma games with memory mechanism. Prisoner's dilemma, Snowdrift (including Leader and Hero) and Stag-hunt games are unified on an extended S-T plane. Agents play game with all the others and make decision by the last game histories. The experiments find that when agents remember last 2-step histories or more, a kind of cooperative turn taking (CAD) bursts at the area of Snowdrift game with restriction of S + T > 2R and S ≠ T, while the consistent strategy (DorC) gathers on the line of S + T > 2R and S = T. We also find that the system's fitness ratio greatly improved with 2-step memory.