Robust refinement of rationalizability with arbitrary payoff uncertainty

Following Fudenberg et al. (1988) and Dekel and Fudenberg (1990), we say that a refinement of (interim correlated) rationalizability is robust if it is prescribed by a solution correspondence that is upper hemicontinuous with respect to perturbations of higher-order beliefs. We characterize robust refinements of rationalizability subject to arbitrary common knowledge restrictions on payoffs. We demonstrate how the characterization pins down a novel family of robust refinements of rationalizability in arbitrary finite games as well as in specific economic examples such as first-price auctions and the Cournot competition. We also apply our characterization to study the critique raised by Weinstein and Yildiz (2007b) to the global-game equilibrium refinement approach. In terms of the model primitives, we provide a necessary and sufficient condition under which the Weinstein-Yildiz critique remains valid.