User:IssaRice/Aumann's agreement theorem

Hal Finney's example

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$E=\{\omega \in \Omega :\Pr(A\mid I(\omega ))=q_{1}{\text{ and }}\Pr(A\mid J(\omega ))=q_{2}\}$

What if we take $E'=\{\omega \in \Omega :\Pr(A\mid I(\omega ))=q_{1}\}$ and say that agent 1 knows $E'$ ?

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References

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

[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] ttps://math.stackexchange.com/questions/303834/common-knowledge-and-concept-of-coarsening-partition

[5] John Geanakoplos. "Common Knowledge".

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