HIERARCHIES OF BELIEF AND INTERIM RATIONALIZABILITY

Jeffrey Ely and Marcin Peski

No 1388, Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science

Abstract: In games with incomplete information, conventional hierarchies of belief are incomplete as descriptions of the players’ information for the purposes of determining a player’s behavior. We show by example that this is true for a variety of solution concepts. We then investigate what is essential about a player’s information to identify rationalizable behavior in any game. We do this by constructing the universal type space for rationalizability and characterizing the types in terms of their beliefs. Infinite hierarchies of beliefs over conditional beliefs, what we call delta-hierarchies, are what turn out to matter. We show that any two types in any two type spaces have the same rationalizable sets in all games if and only if they have the same delta-hierarchies.

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Related works:
Working Paper: Hierarchies of Belief and Interim Rationalizability (2005)
Journal Article: Hierarchies of belief and interim rationalizability (2006)
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