Evolution of co-operation among mobile agents with different influence

Co-operation is a key factor in understanding the evolution of our society. Inspired by this issue, the individual mobility in game theory has been proved to be a very useful scenario. However, it is not realistic, as described in previous studies, that each agent has the same influence on its neighbour's movement trait. In this work, we mainly focus on the weighted influence on the mobility of agents in the prisoner's dilemma game. Here the weight is proportional to its degree with power exponent of λ, where λ is the adjustable parameter to control the level of heterogeneity among individuals in the network. Through numerous simulations we find that co-operation level is promoted when the heterogeneous influence factor is considered. In particular, there is an intermediate value λopt≈10 to guarantee the optimal evolution of co-operation. Moreover, we also prove that the effect of influence weight on the enhancement of co-operation is only valid when the agent's interaction radius is within a threshold value. We thus present a viable method of understanding the ubiquitous co-operative behaviour in nature and hope that it will inspire further studies to resolve social dilemmas.