Optimally Stubborn

Models on reputational bargaining have introduced a perturbation with simple be-havioral types as a way of refining payo˙ predictions for the rational type. I show that this outcome refinement is not robust to the specification of the behavioral type. More specifically, I consider a slight relaxation of the strategy restriction on behavioral types relative to the literature, allowing behavioral types to choose their initial demands. I show that with this relaxation any feasible payo˙ can be achieved in equilibrium for the rational type when the probability of facing a behavioral type is small. My results highlight the implications of di˙erent perturbations for economic applications