We study the robustness of interim correlated rationalizability to perturbations of higher-order beliefs. We introduce a new metric topology on the universal type space, called uniform weak topology, under which two types are close if they have similar first-order beliefs, attach similar...

For different purposes, economists may use different topologies on types. We characterize the relationship among these various topologies. First, we show that for any general types, convergence in the uniform-weak topology implies convergence in both the strategic topology and the uniform...