Research Summary
Research Summary
An Impossibility Theorem on Beliefs in Games (with H. Jerome Keisler)
Description
A 'paradox' of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to (a weak form of) Tarski's Theorem of mathematical logic. A rough interpretation of the theorem is that if a model of a game is available to the players themselves, then there must be a belief a player can have about the game that is not present in the model. In short, any model must have a 'hole' in it.