Environmental-based defensive promotes cooperation in the prisoner's dilemma game

In real life, individuals tend to be self-interested. The defectors exploit the cooperators for high payoffs, and the cooperators take defensive measures to reduce their own losses. Since the defensive behavior of cooperators is affected by environmental factors, this paper proposes an environmental-based defensive game model in the well-mixed population. Theoretical analysis shows that when cooperators do not have the defensive awareness, all the individuals choose defection. When cooperators have defensive awareness, the cooperators can survive in the fierce competition, so as to realize the stable coexistence of cooperation and defection. If all the cooperators have defensive awareness, the system can reach an evolutionary stable state of full cooperation. Through abundant numerical calculations, it is found that when the temptation is small and the defensive probability is large, the cooperation fraction is significantly affected by the threshold. Furthermore, the stronger the defensive awareness, the higher the cooperation fraction. As long as there are cooperators in the population who take defensive measures, a state of full defection can be avoided. Reducing the defensive cost and increasing the defensive benefit as well as the defensive loss are conducive to enhance cooperation level. In a word, defensive behavior promotes cooperation, which provides a new perspective for understanding the emergence of cooperation. (C) 2021 Elsevier Inc. All rights reserved.