Effects of defensive cooperation strategy on the evolution of cooperation in social dilemma

Punishment and reward are effective ways to sustain cooperation among selfish groups. Researches show that the ultimate result of selflessness is self-interest. This paper considers that individuals take defensive measures to reduce losses in the face of unknown risks. Defensive cooperators need to pay the defensive cost. When they interact with unconditional defectors, the defensive cooperators gain benefit due to defensive behavior, while the unconditional defectors lose some benefit due to the defense of defensive cooperators. Results show that in the well-mixed population, reducing defensive cost and improving defensive benefit can promote cooperation, and maintain a higher cooperation level unchanged within a larger range of temptation. In the structured population, the three strategies perform the phenomenon of cyclic dominance, that is unconditional cooperators dominate defensive cooperators who dominate unconditional defectors who dominate unconditional cooperators. It is worth noting that both in the well-mixed population and structured population, three strategies have obvious phased advantages with regard to defensive benefit. Lower defensive benefit leads to an advantage for unconditional defectors. If defensive benefit is moderate, the weakened competitiveness of unconditional defectors leads defensive cooperators dominate. And excessive defensive benefit results in the second-order free-rider phenomenon of the unconditional cooperation strategy. In addition, structured population do not always support cooperation better than well-mixed population. When the defensive cost is small and defensive benefit is high, the spatial effect can enhance network reciprocity. More generally, our results prove that defensive self-interested behavior leads to the maintenance of cooperation, which provides a new perspective for understanding the cooperation evolutionary.