Reputation for Toughness

Abstract

We study reputation for toughness in finitely repeated contests. Players are rational (payoff-maximizing), or "tough" (always exerting an exogenous high "tough effort"). In the unique symmetric equilibrium, a rational player has strictly positive payoff only if she is monopolizing reputation. In a reputational oligopoly, a fierce war of attrition to become the reputational monopolist may yield overdissipation. In a reputational monopolist, overdissipation never happens and the monopolist mixes between a non-tough effort to cash in on her reputation today and the tough effort to boost her reputation. In our main application, criminal groups build reputation for toughness in illegal markets