Three-player repeated games with an opt-out option.

The existence of cooperation is problematic for those who view the world through an evolutionary lens. Although natural selection disfavors unconditional cooperation, cooperators who can distinguish cooperators from defectors and discontinue their interactions with the latter can be favored. Economic experiments have indicated that human beings indeed adopt such strategies when they detect defectors. Experiments have also shown that human beings also use those strategies in interactions involving more than two individuals as both cooperators and defectors may be present among opponent players. In such cases, it is not obvious whether it is better to continue or stop the interaction. In this study, I analyzed three-player prisoner's dilemma games. My findings algebraically reveal that both tolerant cooperators, who want to continue interacting with their current partners comprising one cooperator and one defector, and intolerant cooperators, who choose to discontinue such interactions, can survive when the cost of cooperation is small. In addition, my numerical analysis indicates that the coexistence of tolerant and intolerant cooperators cannot be an evolutionary outcome.