Aumann's Agreement Theorem states that two individuals who share the same prior beliefs, and whose current beliefs about some event are common knowledge between them, cannot rationally continue to disagree about the probability of that event, even without having exchanged any information about the reasons behind their beliefs. Named for Robert Aumann, it is a foundational result in the game-theoretic study of knowledge and belief.
Facts
StatementTwo agents who begin with the same prior probability, and whose current beliefs about the probability of some event are common knowledge between them, cannot rationally continue to disagree about that probability, even without ever exchanging the reasons behind their beliefs. 1 Classification
Statement Form Connections
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Aumann's Agreement Theorem (Wikipedia)
Wikimedia FoundationLead section, statement of the theorem
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.
Lead section, on the 1976 paper
The theorem was proved by Robert Aumann in his 1976 paper "Agreeing to Disagree", which also introduced the formal, set-theoretic definition of common knowledge.
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