The existence of fence-sitters relaxes the spatial prisoner's dilemma and enhances network reciprocity

We introduce a new spatial prisoner's dilemma (SPD) model in which the so-called network reciprocity is enhanced more than in the conventional model. In addition to the usual binary strategies—perfect cooperator and perfect defector—we introduce “fence-sitters”, who either cooperate or defect with equal probability, as a third strategy. In regions with larger Stag-Hunt-type dilemmas but smaller Chicken-type dilemmas, the existence of the fence-sitters works as a buffer, hampering the exploitation of cooperators by neighboring defectors and significantly enhancing the cooperative phase. Conversely, in regions with larger Chicken-type dilemmas but smaller Stag-Hunt-type dilemmas, the existence of the fence-sitters expands the critical dilemma strength for the survival of cooperation, but it reduces the cooperating fraction more than in the conventional model. What we have found may justify the conclusion that the existence of people with neutral opinions—often regarded betwixt and between—absorbs the severe competition between two extreme groups, bringing a more accommodationist situation to our society, backed with greater cooperation.