Apology and forgiveness evolve to resolve failures in cooperative agreements

Making agreements on how to behave has been shown to be an evolutionarily viable strategy in one-shot social dilemmas. However, in many situations agreements aim to establish long-term mutually beneficial interactions. Our analytical and numerical results reveal for the first time under which conditions revenge, apology and forgiveness can evolve and deal with mistakes within ongoing agreements in the context of the Iterated Prisoners Dilemma. We show that, when the agreement fails, participants prefer to take revenge by defecting in the subsisting encounters. Incorporating costly apology and forgiveness reveals that, even when mistakes are frequent, there exists a sincerity threshold for which mistakes will not lead to the destruction of the agreement, inducing even higher levels of cooperation. In short, even when to err is human, revenge, apology and forgiveness are evolutionarily viable strategies which play an important role in inducing cooperation in repeated dilemmas.