NDLI: An Impossibility Theorem on Beliefs in Games

Content Provider	Springer Nature Link
Author	Brandenburger, Adam Keisler, H. Jerome
Copyright Year	2006
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.
Starting Page	211
Ending Page	240
Page Count	30
File Format	PDF
ISSN	00393215
Journal	Studia Logica
Volume Number	84
Issue Number	2
e-ISSN	15728730
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2006-11-09
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	belief model complete belief model game first order logic modal logic paradox Computational Linguistics Mathematical Logic and Foundations Logic
Content Type	Text
Resource Type	Article
Subject	Logic History and Philosophy of Science

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An Impossibility Theorem on Beliefs in Games