Why is it so hard to say sorry? Evolution of apology with commitments in the iterated Prisoner's Dilemma

When making a mistake, individuals can apologize to secure further cooperation, even if the apology is costly. Similarly, individuals arrange commitments to guarantee that an action such as a cooperative one is in the others' best interest, and thus will be carried out to avoid eventual penalties for commitment failure. Hence, both apology and commitment should go side by side in behavioral evolution. Here we provide a computational model showing that apologizing acts are rare in non-committed interactions, especially whenever cooperation is very costly, and that arranging prior commitments can considerably increase the frequency of such behavior. In addition, we show that in both cases, with or without commitments, apology works only if it is sincere, i.e. costly enough. Most interestingly, our model predicts that individuals tend to use much costlier apology in committed relationships than otherwise, because it helps better identify free-riders such as fake committers: 'commitments bring about sincerity'. Furthermore, we show that this strategy of apology supported by commitments outperforms the famous existent strategies of the iterated Prisoner's Dilemma.