Critical Types

Abstract

How can we know in advance whether simplifying assumptions about beliefs will make a difference in the conclusions of game-theoretic models? We define <it>critical types</it> to be types whose rationalizable correspondence is sensitive to assumptions about arbitrarily high-order beliefs. We show that a type is critical if and only if it exhibits common belief in some non-trivial event. We use this characterization to show that all types in commonly used type spaces are critical. On the other hand, we show that <it>regular</it> types (types that are not critical) are generic, although perhaps inconvenient to use in applications.