Hinderance of cooperation by individual solutions: Evolutionary dynamics of three-strategy games combining the prisoner’s dilemma and stag hunt

Abstract

This study analyzes a three-strategy game that integrates elements of the prisoner’s dilemma and stag hunt. The framework builds upon recent research that determines the impact of individual solutions. Individuals adopting such solutions do not free ride on the cooperative efforts of others; rather, they act just sufficiently to prevent adverse consequences for themselves. We hypothesize that individual solutions function analogously to the defection strategy in the stag hunt game. This study examines the effects of orthodox free riding and individual solutions on the evolution of cooperation. Our analysis reveals that in well-mixed populations, the only stable rest point is the one in which all players opt for individual solutions. When interactions are structured on a square lattice, cooperation levels exhibit modest improvements, primarily sustained through cyclic dominance. Payoff values favorable to cooperation result in full cooperation; however, rare mutations can disrupt the cooperative equilibrium, promoting the adoption of individual solutions. Our analysis aligns with experimental observations and illustrates the importance of overcoming reliance on individual solutions to better understand the emergence of cooperation.