Difference between revisions of "Talk:Common priors"

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I strongly suspect that "common priors" means priors that are [[Wikipedia:common knowledge (logic)]], not just same priors. Please research it better. --[[User:Vladimir Nesov|Vladimir Nesov]] 20:05, 10 September 2009 (UTC)
 
I strongly suspect that "common priors" means priors that are [[Wikipedia:common knowledge (logic)]], not just same priors. Please research it better. --[[User:Vladimir Nesov|Vladimir Nesov]] 20:05, 10 September 2009 (UTC)
 
:I had been given to understand that ''common priors'' and ''common knowledge'' are distinct concepts and that the original Aumann result required both. "Agreeing to Disagree" opens: "If two people have the ''same priors'', and their posteriors for a given event A are ''common knowledge'', then these posteriors must be equal" (emphasis mine). But I'm by no means really up to speed on this literature, so I could be wrong. ---[[User:Z. M. Davis|Z. M. Davis]] 03:30, 11 September 2009 (UTC)
 
:I had been given to understand that ''common priors'' and ''common knowledge'' are distinct concepts and that the original Aumann result required both. "Agreeing to Disagree" opens: "If two people have the ''same priors'', and their posteriors for a given event A are ''common knowledge'', then these posteriors must be equal" (emphasis mine). But I'm by no means really up to speed on this literature, so I could be wrong. ---[[User:Z. M. Davis|Z. M. Davis]] 03:30, 11 September 2009 (UTC)
 
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::From Hanson's paper http://hanson.gmu.edu/prior.pdf and intuition it does seem clear that Aumann's result uses common knowledge of the same priors; but when people say it requires "priors are the same" they're probably just leaving common knowledge as an unstated background fact, just like they're leaving out the fact that it's common knowledge that the agents do Bayesian updating; and so I'm not sure "common priors" actually *means* "common knowledge of the same priors", rather than "the same priors" with the common knowledge part being taken for granted. (Is there any other foo where "common foo" means "common knowledge of the same foo"?) --steven0461
From Hanson's paper http://hanson.gmu.edu/prior.pdf and intuition it does seem clear that Aumann's result uses common knowledge of priors; but when people say it requires "priors are the same" they're probably just leaving common knowledge as an unstated background fact, just like they're leaving out the fact that it's common knowledge that the agents do Bayesian updating; and so I'm not sure "common priors" actually *means* "common knowledge of the same priors", rather than "the same priors" with the common knowledge part being taken for granted. --steven0461
 

Latest revision as of 04:18, 12 September 2009

I strongly suspect that "common priors" means priors that are Wikipedia:common knowledge (logic), not just same priors. Please research it better. --Vladimir Nesov 20:05, 10 September 2009 (UTC)

I had been given to understand that common priors and common knowledge are distinct concepts and that the original Aumann result required both. "Agreeing to Disagree" opens: "If two people have the same priors, and their posteriors for a given event A are common knowledge, then these posteriors must be equal" (emphasis mine). But I'm by no means really up to speed on this literature, so I could be wrong. ---Z. M. Davis 03:30, 11 September 2009 (UTC)
From Hanson's paper http://hanson.gmu.edu/prior.pdf and intuition it does seem clear that Aumann's result uses common knowledge of the same priors; but when people say it requires "priors are the same" they're probably just leaving common knowledge as an unstated background fact, just like they're leaving out the fact that it's common knowledge that the agents do Bayesian updating; and so I'm not sure "common priors" actually *means* "common knowledge of the same priors", rather than "the same priors" with the common knowledge part being taken for granted. (Is there any other foo where "common foo" means "common knowledge of the same foo"?) --steven0461