Adaptive persistence based on environment comparison enhances cooperation in evolutionary games

Switching strategy is generally accompanied by material cost or mental pressure to players in reality. An efficient solution is to hold the current strategy for a period time before the next updating. In evolutionary games, it has been reported that strategy persistence or strategy inertia could promote cooperation. There arises a question that how players determine the duration of their strategy persistence time, which is also called the persistence level. Here, we consider the evolutionary prisoner’s dilemma games in which players can adapt their persistence levels based on the comparison between the local and global environments. We assume that, the players who have better local environments tend to preserve their current strategies longer and increase the persistence levels. In contrast, those whose local environments are worse than the global environment tend to decrease their persistence levels. The results show that network reciprocity can get greatly enhanced by such an adaptive strategy persistence, especially in hostile environments to cooperation. Moreover, by comparing with the fixed and randomly adaptive persistence level cases, we emphasize the importance of the environment comparison in enlarging the persistence levels of cooperators, which could be further enhanced by a larger upper limit or a smaller increment of persistence level. Our results provide insights into the promotion of cooperation by the adaptive strategy persistence when players can perceive both the local and global environments in evolutionary games.