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MENTAL MODEL · M3974

Aumann's Agreement Theorem

Aumann's Agreement Theorem
DecideHigh supportGame Theory
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Version 1.0.0 · Updated 2026-07-28

CORE DEFINITION

Aumann's agreement theorem states that two Bayesian agents with the same prior beliefs cannot "agree to disagree" about the probability of an event if their individual beliefs are common knowledge. In other words, if it is commonly known what each agent believes about some event, and both agents are rational and update their beliefs using Bayes' rule, then their updated (posterior) beliefs must be

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Aumann's agreement theorem states that two Bayesian agents with the same prior beliefs cannot "agree to disagree" about the probability of an event if their individual beliefs are common knowledge. In

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Robert Aumann: Two rational agents with the same prior beliefs cannot "agree to disagree" after sharing all relevant private information—that is, their posterior probabilities for the same event must coincide. The mechanism is that common knowledge plus Bayesian updating eliminates divergence.

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Source support: Explicit

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    en.wikipedia.orghttps://en.wikipedia.org/wiki/Aumann%27s_agreement_theoremZH · Explicit
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