Refinements of Rationalizability for Normal-Form Games: The Main Ideas

In normal-form games, rationalizability (Bernheim, 1984, Pearce, 1984) on its own fails to exclude some very implausible strategy choices. Three main refinements of rationalizability have been proposed in the literature: cautious, perfect, and proper rationalizability. Nevertheless, some of these refinements also fail to eliminate unreasonable outcomes and suffer from some drawbacks. Therefore, we introduce the trembling-hand rationalizability concept, where the players' actions have to be best responses also against perturbed conjectures. We also propose another refinement: "epsilon"-perfect rationalizability; and we show that every proper rationalizable strategy profile is also "epsilon"-perfect rationalizable. The differences between the various refinements are illustrated by means of examples.