Effects of strategy-updating cost on evolutionary spatial prisoner’s dilemma game

•We study the evolutionary spatial prisoner’s dilemma game with strategy updating cost.•There exist sudden increases of cooperation level with the increase of temptation to defect.•The critical threshold of strategy-updating cost has a nontrivial effect on the persistence of cooperation on networks. Strategy-updating rules play fundamental roles for the persistence of cooperation in groups composed by selfish individuals. In this paper, we study the spatial evolutionary prisoner’s dilemma game with the introduction of the strategy-updating cost for players, where each player is able to update its strategy if its payoffs is greater than a critical threshold. We show that there exist sudden increases of cooperation level as the temptation to defect increases for a fixed strategy-updating cost, which means a larger temptation to defect cannot always inveigle players into defection, but sometimes promote players to cooperate. This striking phenomenon is in contradiction with the previous wide cognition that a larger temptation to defect always gives rise to a lower cooperation level. This abnormal phenomenon can be explained by a systematic analysis of the payoffs earned by cooperators and defectors and the strategy-transition probabilities between cooperation and defection, respectively. In some cases, the strategy-updating cost can prevent some defectors from becoming cooperators and the increase of temptation to defect enable their payoffs to exceed the threshold of strategy-updating cost. Our results prove that the temptation to defect may have facilitation to the emergence of cooperation in the existence of strategy-updating cost, and thus provide a new understanding of the previously hidden roles of the temptation to defect for the social cooperation.