The evolution of conventions in the presence of social competition

We study the long run convention emerging from stag hunt interactions when agents occasionally revise their action over time adopting a perturbed myopic best response rule, with the novelty of introducing social competition in the form of assignment of prizes to agents depending on the payoff ranking resulting from the stag hunt interaction. We find that social competition plays a crucial and articulated role in the selection of the long run convention: indeed, a high enough reward from competition selects the payoff-dominant convention when competition is harsh, and the maximin convention when competition is mild.