The Efficient Interaction of Costly Punishment and Commitment

To ensure cooperation in the Prisoner's Dilemma, agents may require prior commitments from others, subject to compensations when defecting after agreeing to commit. Alternatively, agents 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 instigate cooperation. In this work, using Evolutionary Game Theory, we describe a computational model showing that there is a wide range of parameters where the combined strategy is better than either strategy by itself, leading to a significantly higher level 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 strategies.