In a weakly dominated strategy is strength: Evolution of optimality in stag hunt augmented with a punishment option

I explore the evolution of strategies in an Augmented Stag Hunt game that adds a pun-ishing strategy to the ordinary Stag Hunt strategies of cooperating, which aims for op-timality, and defecting, which “plays it safe.” Cooperating weakly dominates punishing and defecting is the unique evolutionarily stable strategy (ESS). Nevertheless, for a wide class of Augmented Stag Hunts, polymorphic strategies combining punishing and co-operating collectively have greater attracting power for replicator dynamics than that of the ESS. The analysis here lends theoretical support to the altruistic punishment hypoth-esis in the social sciences.