Generic uniqueness and continuity of retionalizable strategies

For a finite set of actions and a rich set of fundamentals, consider the rationalizable actions on a universal type space, endowed with the usual product topology. (1) Generically, there exists a unique rationalizable action profile. (2) Every model can be approximately embedded in a dominance-solvable model. (3) A rationalizable strategy is continuous at a finite type if and only if there is a unique rationalizable action for that type. Keywords: higher-order uncertainty, rationalizability, universal type space, continuity. JEL Classifications: C72, C73.