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Hierarchies of belief and interim rationalizability

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  • , C.

    (Northwestern University)

  • ,

    (University of Chicago)

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 behavior. We specialize to two player games and the solution concept of interim rationalizability. We construct the universal type space for rationalizability and characterize the types in terms of their beliefs. Infinite hierarchies of beliefs over conditional beliefs , which 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.

Suggested Citation

  • , C. & ,, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
    • Handle: RePEc:the:publsh:163
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    Keywords

    Interim rationalizability; belief hierarchies;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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