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An Impossibility Theorem on Beliefs in Games

In: The Language of Game Theory Putting Epistemics into the Mathematics of Games

Author

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  • Adam Brandenburger
  • H. Jerome Keisler

Abstract

A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell's Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes thatAnn believes that Bob's assumption is wrongThis is formalized to show that any belief model of a certain kind must have a “hole.” An interpretation of the result is that if the analyst's tools are available to the players in a game, then there are statements that the players can think about but cannot assume. Connections are made to some questions in the foundations of game theory.

Suggested Citation

  • Adam Brandenburger & H. Jerome Keisler, 2014. "An Impossibility Theorem on Beliefs in Games," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 1, pages 1-30, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814513449_0001
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