Cooperation in spatial evolutionary games with historical payoffs

• We introduce a strategy adoption mechanism induced by memory-based weighted average payoff.
• It is interesting that cooperators update their strategies according to more payoff information than that of defectors.
• We find that excessive attention of past payoffs is not beneficial to the spreading of cooperation.

The most common of strategy adoption in evolutionary games relies on players' payoffs of the last round. While a rational player usually fixes the coming strategy by comprehensively considering certain amount of payoff information within its memory length. Here, we explore several measures of historical payoffs in getting the weighted average payoff. Then, player sets the strategy by comparing the weighted average payoff of neighbour's and itself. We show that, cooperators can resist the invasion by referring to the most payoff information, when strategy and measure coevolve. In contrast, strategy adoption of defectors only relies on the nearest one round. Especially, our results suggest that, excessive attention of past payoffs is not favorable to spread cooperative behaviors.