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

Aspiration-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. (C) 2020 The Authors. Published by Elsevier Inc.

Automated summary

The study found that the effectiveness of the average payoff-driven update rule for promoting cooperation depends on whether a reciprocity mechanism exists, and under certain conditions, the imitation update rule is more effective.