Social viscosity with zealots

Abstract

Cooperation delivers collective benefits but faces evolutionary challenges due to the advantage of selfish defection. Evolutionary game theory explains how cooperation can emerge through various social viscosity mechanisms: direct reciprocity, indirect reciprocity, kin selection, group selection and network reciprocity. This study extends these mechanisms by introducing zealots—individuals who never change their strategy—as either unconditional cooperators or unconditional defectors. Using mathematical analysis, we derive conditions under which zealous players influence cooperative outcomes. Without zealots, known conditions govern cooperation under each mechanism. With zealous cooperators, systems tend towards full cooperation or become destabilized. In contrast, zealous defectors stabilize mixed equilibria in direct and indirect reciprocity while promoting either coexistence or full defection in kin selection, group selection and network reciprocity. These results show that inflexible individuals can critically reshape the evolutionary stability of cooperation and offer novel insights into how social viscosity interacts with committed players to influence collective behaviour.