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Bayesian games with a continuum of states

By Ziv Hellman and Yehuda John Levy


We show that every Bayesian game with purely atomic\ud types has a measurable Bayesian equilibrium when the common knowl-\ud edge relation is smooth. Conversely, for any common knowledge rela-\ud tion that is not smooth, there exists a type space that yields this common\ud knowledge relation and payoffs such that the resulting Bayesian game\ud will not have any Bayesian equilibrium. We show that our smoothness\ud condition also rules out two paradoxes involving Bayesian games with\ud a continuum of types: the impossibility of having a common prior on\ud components when a common prior over the entire state space exists, and\ud the possibility of interim betting/trade even when no such trade can be\ud supported\ud ex ante

Publisher: Econometric Society
Year: 2017
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Provided by: Enlighten

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