When apology is sincere, cooperation evolves, even when mistakes occur frequently

Evolutionary psychologists have argued that revenge, apology and forgiveness are moral sentiments that humans acquired to establish and maintain long-term mutually beneficial relationships, especially since misapprehensions, intentional or not, can always occur that could lead to worse outcomes. Their argument assumes an evolutionary advantage to such emotional thinking, for which no explicit model was available. Using the iterated prisoners dilemma as context, we provided analytical and numerical results that show that these three behaviours emerge spontaneously, ensuring lasting cooperation [16]. Concretely our work revealed that apology and forgiveness are efficient even in a very noisy environment. Yet in order for apology to work, it needs to be sufficiently costly as otherwise exploiting the system by defecting and apologising is the most profitable behaviour.