Learning Algorithm and the Cooperation Behavior of Continuous Prisoner's Dilemma Game on Complex Networks ⋆

The standard evolutionary Prisoner’s Dilemma Game (PDG), which is the most widely used model for investigating the evolution of cooperation, does not allow for changeable degrees of cooperation and the players can either cooperate or defect in each time. In this paper, we study Continuous Prisoner’s Dilemma Games (CPDG) on complex networks (or Spatial Continuous Prisoner’s Dilemma Games (SCPDG)); in which each agent locates on a vertex of the network and interacts with all his neighboring agents by making an investment. Each agent’s investment will benefit all its neighbors and incur a cost to the focus agent. The investment which can be varied continuously exhibits variable degrees of cooperation. The cooperative level of the group is characterized by the average investment of the population. Unlike the imitation of the best neighbors learning rule, the probability based imitation learning rule and the Moran process based learning rule that usually used in the standard evolutionary SPDG, we propose a new learning algorithm in the continuous condition. Three parameters to describe the imitation ability of the best neighbors, the memory length of the individual and uncertainty effect of the environment are introduced. We investigate the co-effect of these parameters on the cooperation level of the population on the Barabasi-Albert (BA) scale-free networks, the nearest-neighbor coupled networks and the Newman-Watts (NW) small-world networks. Our results may provide some new conclusion on the study of evolutionary games on networks.