Average payoff-driven or imitation? A new evidence from evolutionary game theory in finite populations

AbstractHighlights •We combined the imitation-driven update rule and the average payoff-driven update rule in the finite populations with positive assortment.•We studied the evolution of cooperative behavior in one-shot and iterated Prisoner ’s dilemma game.•The results show that the effectiveness of the average payoff-driven update rule for the promotion of cooperation depends on the reciprocity mechanism. AbstractAspiration-driven or imitation? Which one is most effective for the promotion of cooperation? There is a lot of interest that being brought to this issue. In this paper, we investigate the evolutionary outcomes with a stochastic evolutionary game dynamic that combined the imitation update rule and the average payoff-driven update rule in finite populations, in which both one-shot and iterated Prisoner’s dilemma game with positive assortment are implemented. The average abundance of cooperators is obtained through the transition probabilities and the properties of Markov chain. Both numerical and analytical results show that the effectiveness of the average payoff-driven update rule for the promotion of cooperation depends on whether there is a reciprocity mechanism in the system. In detail, average payoff-driven update rule is better than imitation update rule only when our model has one of the following three conditions: (1) small probability of the positive assortment; (2) small probability to the next round; (3) small probability of knowing one’s reputation. If the above conditions are not satisfied, then imitation update rule is most effective for the promotion of cooperation. We thus provide a deeper understanding for the effectiveness of these rules regarding the promotion of cooperation.