The Weinstein-Yildiz Critique and Robust Predictions with Arbitrary Payoff Uncertainty ∗

Weinstein and Yildiz (2007b) show that under a richness assumption which relaxes all common-knowledge restrictions on payoffs, every rationalizable action of every (finite) type can be selected as a uniquely rationalizable action by perturbing the higher-order beliefs (the structure theorem). Consequently, types with uniquely rationalizable actions are generic in the universal type space (generic uniqueness). This WY critique implies that (i) a prediction for a given type is robust (for a neighborhood of the type) if and only if it consists of all rationalizable actions for that type; (ii) selecting a prediction from the rationalizable actions is either ad hoc or unnecessary. However, their richness assumption rules out prominent applications in economic models and thus undermines their critique. In this paper, we provide an algorithm that characterizes all selections from and all robust predictions of rationalizable actions without relying on any richness assumption. By invoking the characterization, we delineate the boundary of the WY critique by further characterizing the structure theorem as well as generic uniqueness from the primitives. We also use economic examples such as Cournot competition and auctions to illustrate our approach.