A Framework for Robustness to Ambiguity of Higher-Order Beliefs

This paper defines simple procedures to construct ambiguous perturbations of belief structures associated to standard type spaces with precise beliefs, based on ambiguous type spaces whose induced belief hierarchies approximate the belief hierarchies corresponding to the initial type space. Two alternative procedures to construct such perturbations are introduced, and are shown to yield a simple and intuitive characterization of convergence of the resulting approximations to the initial unperturbed environment. The perturbations arising from one of these procedures include the set of all finite perturbations as a special case. The introduced perturbations and their convergence properties provide a foundation for the analysis of robustness to ambiguity of various solutions concepts, and for various decision rules under ambiguity.