User:IssaRice/Aumann's agreement theorem: Difference between revisions

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<math>E = \{\omega \in \Omega : \Pr(A \mid I(\omega)) = q_1 \text{ and } \Pr(A \mid J(\omega)) = q_2\}</math>
<math>E = \{\omega \in \Omega : \Pr(A \mid I(\omega)) = q_1 \text{ and } \Pr(A \mid J(\omega)) = q_2\}</math>
What if we take <math>E' = \{\omega \in \Omega : \Pr(A \mid I(\omega)) = q_1\}</math> and say that agent 1 knows <math>E'</math>?


<ref>Tyrrell McAllister. [https://web.archive.org/web/20110725162431/http://dl.dropbox.com/u/34639481/Aumann_agreement_theorem.pdf "Aumann's agreement theorem"]. July 7, 2011.</ref>
<ref>Tyrrell McAllister. [https://web.archive.org/web/20110725162431/http://dl.dropbox.com/u/34639481/Aumann_agreement_theorem.pdf "Aumann's agreement theorem"]. July 7, 2011.</ref>

Revision as of 21:43, 24 August 2018

Hal Finney's example

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E={ω∈Ω:Pr(A∣I(ω))=q1 and Pr(A∣J(ω))=q2}

What if we take E′={ω∈Ω:Pr(A∣I(ω))=q1} and say that agent 1 knows E′?

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References

  1. ↑ Tyrrell McAllister. "Aumann's agreement theorem". July 7, 2011.
  2. ↑ Wei Dai. "Probability Space & Aumann Agreement". December 10, 2009.
  3. ↑ Robert J. Aumann. "Agreeing to Disagree". November 1976.
  4. ↑ https://math.stackexchange.com/questions/303834/common-knowledge-and-concept-of-coarsening-partition
  5. ↑ John Geanakoplos. "Common Knowledge".
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