Abstract
We present a new solution concept for strategic games called comprehensive rationalizability that embodies a new version of “common cautious belief in rationality” based on a sound epistemic characterization in a universal type space. Differently from existing iterative strategy elimination procedures in the literature, it should rather be viewed as an iterative strategy demotion procedure as it requires some memory of previously discarded strategies. It refines rationalizability, but it neither refines nor is refined by iterated admissibility. Nevertheless, it coincides with iterated admissibility in many relevant economic applications.