Play Like Me Or Else! Supporting Conformity in Stag Hunt Problems With Costly Punishment

The Stag Hunt problem is sometimes proposed as a model of the social contract, where each member of a community can choose either to perform by contributing at some personal cost towards completing a mutually beneficial project or to defect by withholding one’s contribution. I explore the evolution of strategies in Augmented Stag Hunt games that add punishing strategies to the performing and defecting strategies in ordinary Stag Hunt. I consider how the members of a population might tend to adopt norms requiring conforming behavior in Stag Hunts that they enforce via costly pro-social and anti-social punishing behavior. I argue that the effects of pro-social and anti-social punishments depend crucially upon the ability of community members to execute punishment strategies correctly. I also argue that the analysis here lends support to the hypothesis that altruistic punishment can contribute to the formation and maintenance of norms of cooperation in a social contract.

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