A synergy of costly punishment and commitment in cooperation dilemmas

To ensure cooperation in the Prisoner's Dilemma, individuals may require prior commitments from others, subject to compensations when agreements to cooperate are violated. Alternatively, individuals may prefer to behave reactively, without arranging prior commitments, by simply punishing those who misbehave. These two mechanisms have been shown to promote the emergence of cooperation, yet are complementary in the way they aim to promote cooperation. Although both mechanisms have their specific limitations, either one of them can overcome the problems of the other. On one hand, costly punishment requires an excessive effect-to-cost ratio to be successful, and this ratio can be significantly reduced by arranging a prior commitment with a more limited compensation. On the other hand, commitment-proposing strategies can be suppressed by free-riding strategies that commit only when someone else is paying the cost to arrange the deal, whom in turn can be dealt with more effectively by reactive punishers. Using methods from Evolutionary Game Theory, we present here an analytical model showing that there is a wide range of settings for which the combined strategy outperforms either strategy by itself, leading to significantly higher levels of cooperation. Interestingly, the improvement is most significant when the cost of arranging commitments is sufficiently high and the penalty reaches a certain threshold, thereby overcoming the weaknesses of both mechanisms.