Robust multiplicity with a grain of naiveté

Rationalizability is a central concept in game theory. Since there may be many rationalizable strategies, applications commonly use refinements to obtain sharp predictions. In an important paper, Weinstein and Yildiz (2007) show that no refinement is robust to perturbations of high-order beliefs. We show that robust refinements do exist if we relax the assumption that all players are unlimited in their reasoning ability. In particular, for a class of models, every strict Bayesian–Nash equilibrium is robust. In these environments, a researcher interested in making sharp predictions can use refinements to select among the strict equilibria of the game, and these predictions will be robust.