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.
CITATION STYLE
Brandenburger, A., & Keisler, H. J. (2023). An impossibility theorem on beliefs in games. In World Scientific Series in Economic Theory (Vol. 5, pp. 1–30). World Scientific. https://doi.org/10.1142/9789814513449_0001
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