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> | ||
One of the assumptions in the agreement theorem is that <math>E</math> is common knowledge. This seems like a pretty strange requirement, since it seems like the posterior probability of <math>A</math> can never change no matter what else the agents condition on in addition to <math>E</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>? | 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>? | ||
Revision as of 21:45, 24 August 2018
Hal Finney's example
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One of the assumptions in the agreement theorem is that is common knowledge. This seems like a pretty strange requirement, since it seems like the posterior probability of can never change no matter what else the agents condition on in addition to .
What if we take and say that agent 1 knows ?
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".