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<p>We extend the Agreement Theorem of Aumann (Ann Stat 4(6):1236–1239, 1976) in two key directions. First, we introduce Knightian uncertainty by modeling beliefs as sets of probability measures, allowing for ambiguity in agents’ posterior beliefs. Second, we relax the assumption that agents observe perfectly each other’s posterior probabilities, replacing it with the assumption that they perceive only certain properties of their posterior probability sets. Our main result establishes that if agents share at least one common prior, they can only have common knowledge that their posterior probabilities satisfy a given property if these properties are mutually compatible. Furthermore, we explore economic implications in the context of trade under asymmetric information, deriving a No Trade result under ambiguity and highlighting conditions under which trade may still occur.</p>

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Weak agreement and the properties of beliefs under ambiguity

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Antoine Billot,
  • Vassili Vergopoulos

摘要

We extend the Agreement Theorem of Aumann (Ann Stat 4(6):1236–1239, 1976) in two key directions. First, we introduce Knightian uncertainty by modeling beliefs as sets of probability measures, allowing for ambiguity in agents’ posterior beliefs. Second, we relax the assumption that agents observe perfectly each other’s posterior probabilities, replacing it with the assumption that they perceive only certain properties of their posterior probability sets. Our main result establishes that if agents share at least one common prior, they can only have common knowledge that their posterior probabilities satisfy a given property if these properties are mutually compatible. Furthermore, we explore economic implications in the context of trade under asymmetric information, deriving a No Trade result under ambiguity and highlighting conditions under which trade may still occur.