Aumann's agreement theorem, roughly speaking, says that two agents acting rationally (in a certain precise sense) and with common knowledge of each other's beliefs cannot agree to disagree. More specifically, if two people are genuine Bayesians, share common priors,priors, and have common knowledge of each other's current probability assignments, then they must have equal probability assignments.
Related tags and wikis: Disagreement, Modesty, Modesty argument, Aumann agreement, The Aumann Game
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