Evolutionary games with different time scales of strategy updating

Variation in learning rates within populations suggests that evolutionary game theory may not necessarily be restricted to uniform time scales associated with the game interaction and strategy adaption evolution. Using agent-based evolutionary simulation in the framework of prisoner's dilemma game, we demonstrate the sustainability of cooperation and the emergence of different macro-effects, when equipping agents with non-uniform time scale preferences. We employ a spatial random regular grid to describe the social interactions among agents. We conclude that the cooperation level has a strong dependence on the population composition, and the suitable fraction of the fast-updating players in the system which is associated with the maximal cooperation frequency has been found out. Besides, the extent of the promotive effect of diversifying time scales is also closely related with the payoff adoption rules in strategy updating, especially when we invent a past history for each agent. Summing up the gained results, a general conclusion can be drawn, saying that the combination of these factors (e.g. time scales and memory) gives rise to rich dynamic behavior of the system.