Generic Uniqueness and Continuity of Rationalizable Strategies

Abstract

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) For any given rationalizable strategy of any finite model, there exists a nearby finite model with common prior such that the given rationalizable strategy is uniquely rationalizable for nearby types.