Impact of self-interaction on evolution of cooperation in voluntary prisoner's dilemma game

Voluntary participation, as a simple yet valid mechanism to promote cooperation in game theory, has been received a great deal of attention. In this paper, we introduce self-interaction into voluntary prisoner's dilemma game. In detail, cooperator will gain a fixed additional reward by having an interaction with itself, while defector will obtain nothing through self-interaction and loner don't participate in the game. It is shown that cooperative behavior is remarkably facilitated with increase of additional reward by forming huge clusters for low level of temptation to defect. While for large temptation, the system will fall into cycle dominance of three strategies and self-interaction hardly has impact on the evolution of cooperation compared with traditional version.