Hinderance of cooperation by individual solutions: Evolutionary dynamics of three-strategy games combining the prisoner's dilemma and stag hunt (2502.06624v1)

Abstract: We considered a three-strategy game with the characteristics of the prisoner's dilemma and stag hunt games. This game was inspired by recent experimental studies that elucidated the role of individual solutions. People who adopt individual solutions do not free-ride on the cooperative efforts of others, but instead attempt to solve the problem only to the extent necessary to prevent an impact on themselves. We argue that individual solutions play a role similar to that of defection in the stag hunt game, and this study examined the effects of orthodox free-riding and the individual solution on the evolution of cooperation. Our analysis revealed that a state in which all of the agents adopt the individual solution is the only stable equilibrium in the well-mixed population. Interactions on a square lattice led to modest improvements in cooperation levels, which were mainly sustained by cyclic dominance. Payoff values favorable to cooperation resulted in full cooperation, but rare mutations could hamper the cooperative equilibrium and support the dominance of the individual solution. Our analysis echoed experimental observations and illustrated that overcoming the reliance on individual solutions is critical in understanding the evolution of cooperation.