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Chapter 1: An Impossibility Theorem on Beliefs in Games
Originally published in Studia Logica, 84, 211–240.
https://doi.org/10.1142/9789814513449_0001Cited by:0 (Source: Crossref)
Abstract: 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.
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
