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 that
Ann believes that Bob’s assumption is wrong
This 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.
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Special Issue Ways of Worlds II. On Possible Worlds and Related Notions Edited by Vincent F. Hendricks and Stig Andur Pedersen
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Brandenburger, A., Keisler, H.J. An Impossibility Theorem on Beliefs in Games. Stud Logica 84, 211–240 (2006). https://doi.org/10.1007/s11225-006-9011-z
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DOI: https://doi.org/10.1007/s11225-006-9011-z