Enhancement of cooperation in prisoner’s dilemma game on weighted lattices

We introduce the vertex weight into the spatial prisoners’ dilemma game to investigate the evolution of cooperation. Each player on a square lattice is assigned to a particular weight followed by three types of distributions, which include the exponential, power-law and uniform ones. Compared with the traditional version, we find that the cooperation level is markedly enhanced under the weighted square lattice. For most ranges of b, the highest cooperation level can be obtained under the uniform distribution, while power-law distribution usually leads to the lowest cooperation. The distributed weight can produce a heavy heterogeneity among the individuals’ payoff, some cooperators with higher weight will foster the cooperative clusters and even spread the cooperation strategy around the clusters, while defectors have no such advantages. In addition, we still investigate the impact of the amplitude of undulation of weight distribution on the cooperation, and the non-monotonic behavior about b is observed. Finally, the influence of noise on the cooperation is also studied for these types of distribution of weight. To some extent, our weighted scheme can characterize the difference or diversity of players, which will be beneficial to further understand the role of individuals during the evolution of cooperation.