The evolution of punishment in n-player public goods games: a volunteer's dilemma

The evolution of punishment to stabilize cooperation in n-player games has been treated as a second-order social dilemma, where contributions to punishment of free-riders are altruistic. Hence it may only evolve under highly restricted conditions. Here, we build on recent insights using the volunteer's dilemma as an alternative payoff matrix for the evolution of cooperation. The key feature of a volunteer's dilemma is that the benefits of cooperation are a nonlinear function of the number of contributors, meaning that cooperation is negatively frequency dependent. We propose that nonlinear returns are also an inherent feature of punishment and that this insight allows for a simple and novel explanation of how punishment evolves in groups.