Asymmetry of individual activity promotes cooperation in the spatial prisoner's dilemma game

We consider an aspiration-based asymmetric individual activity co-evolutionary prisoner's dilemma game model on the square lattice. In detail, each player has an individual weight that evolves with its strategy. We introduce an asymmetric setting that only μ fractions of players in the network chosen to be active can update their individual weights according to whether their payoffs satisfy their aspirations. Therefore, our individual weights can be regarded as a type of intrinsic motivation satisfaction. Through Monte Carlo simulations on the square lattice, our co-evolution mechanism has been proven to significantly promote cooperation. Furthermore, we find that the moderate μ leads to the highest cooperation level. By dividing the players into four types according to their strategies and weights, we prove that the inversion of the dominant relationship between cooperators and defectors with low weights leads to a conversion cycle of the four types of players, which enhances spatial reciprocity to promote cooperation. Moderate μ results in an appropriate number of low-weight players in this cycle. Interestingly, our results show that higher weight heterogeneity does not lead to higher levels of cooperation, which is contrary to the intuition formed in the previous work.