Theoretical and empirical studies have generally weighed the effect of peer punishment and pool punishment for sanctioning free riders separately. However, these sanctioning mechanisms often pose a puzzling tradeoff between efficiency and stability in detecting and punishing free riders. Here, we combine the key aspects of these qualitatively different mechanisms in terms of evolutionary game theory. Based on the dilemmatic donation game, we introduce a strategy of commitment to both cooperation and peer punishment. To make the commitment credible, we assume that those willing to commit have to make a certain deposit. The deposit will be refunded as long as the committers faithfully cooperate in the donation game and punish free riders and non-committers. It turns out that the deposit-based commitment offers both the efficiency of peer punishment and the stability of pool punishment and that the replicator dynamics lead to transitions of different systems: pool punishment to commitment to peer punishment.
evolution of cooperation peer punishment pool punishment commitment refundable deposit