title: Punishment does not promote cooperation under exploration dynamics when anti-social punishment is possible.
abstract: It has been argued that punishment promotes the evolution of cooperation when mutation rates are high (i.e. when agents engage in 'exploration dynamics'). Mutations maintain a steady supply of agents that punish free-riders, and thus free-riders are at a disadvantage. Recent experiments, however, have demonstrated that free-riders sometimes also pay to punish cooperators. Inspired by these empirical results, theoretical work has explored evolutionary dynamics where mutants are rare, and found that punishment does not promote the evolution of cooperation when this 'anti-social punishment' is allowed. Here we extend previous theory by studying the effect of anti-social punishment on the evolution of cooperation across higher mutation rates, and by studying voluntary as well as compulsory Public Goods Games. We find that for intermediate and high mutation rates, adding punishment does not promote cooperation in either compulsory or voluntary public goods games if anti-social punishment is possible. This is because mutations generate agents that punish cooperators just as frequently as agents that punish defectors, and these two effects cancel each other out. These results raise questions about the effectiveness of punishment for promoting cooperation when mutations are common, and highlight how decisions about which strategies to include in the strategy set can have profound effects on the resulting dynamics.
authors.affiliation: Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA; Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA.
authors.forename: Oliver
authors.initials: O
authors.lastname: P Hauser
authors.affiliation: Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA; Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA; Department of Mathematics, Harvard University, Cambridge, MA, USA.
authors.forename: Martin
authors.initials: M
authors.lastname: A Nowak
authors.affiliation: Department of Psychology, Yale University, New Haven, CT, USA; Department of Economics, Yale University, New Haven, CT, USA; Program in Cognitive Science, Yale University, New Haven, CT, USA; School of Management, Yale University, New Haven, CT, USA. Electronic address: david.rand@yale.edu.
authors.forename: David
authors.initials: D
authors.lastname: G Rand
mesh_terms: D005075:Biological Evolution; D003198:Computer Simulation; D003299:Cooperative Behavior; D005716:Game Theory; D006801:Humans; D008960:Models, Psychological; D059645:Mutation Rate; D011678:Punishment / Q000523:psychology*
keywords: Anti-social punishment; Cooperation; Evolutionary dynamics; Mutation rates