Effect of migration based on strategy and cost on the evolution of cooperation

• Propose a migration based on strategy and cost in the Prisoner’s Dilemma Game.
• The level of cooperation without mutation is higher than that with mutation.
• Increased costs have no effect on the level of cooperation without mutation.
• The level of cooperation decreases with the increase in cost with mutation.
• An optimal density value ρ resulting in the maximum level of cooperation exists.

Humans consider not only their own ability but also the environment around them during the process of migration. Based on this fact, we introduce migration based on strategy and cost into the Spatial Prisoner’s Dilemma Game on a two-dimensional grid. The migration means that agents cannot move when all of the neighbors are cooperators; otherwise, agents move with a probability related to payoff and cost. The result obtained by the computer simulation shows that the moving mechanism based on strategy and cost improves the level of cooperation in a wide parameter space. This occurs because movement based on strategy effectively keeps the cooperative clusters and because movement based on cost effectively regulates the rate of movement. Both types of movement provide a favorable guarantee for the evolution of stable cooperation under the mutation rate q = 0.0. In addition, we discuss the effectiveness of the migration mechanism in the evolution of cooperation under the mutation rate q = 0.001. The result indicates that a higher level of cooperation is obtained at a lower migration cost, whereas cooperation is suppressed at a higher migration cost. Our work may provide an effective method for understanding the emergence of cooperation in our society.