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Agreeing to agree

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Author Info

  • Ehud Lehrer
  • Dov Samet

Abstract

Aumann(1976) has shown that agents who have a common prior cannot have common knowledge of their posteriors for event E if these posteriors do not coincide. But given an event E, can the agents have posteriors with a common prior such that it is common knowledge that the posteriors for E *do* coincide? A necessary and sufficient condition for this is the existence of a nonempty *finite* event F with the following two properties. First, it is common knowledge at $F$ that the agents cannot tell whether or not $E$. Second, this still holds true at F, when F becomes common knowledge.

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File URL: http://128.118.178.162/eps/game/papers/0310/0310005.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 0310005.

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Length: 20 pages
Date of creation: 09 Oct 2003
Date of revision:
Handle: RePEc:wpa:wuwpga:0310005

Note: Type of Document - ; pages: 20
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Web page: http://128.118.178.162

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Keywords: agreement theorems; common knowledge;

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References

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  1. Dov Samet, 1997. "Common Priors and Separation of Convex Sets," Game Theory and Information 9701002, EconWPA.
  2. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer, vol. 28(3), pages 263-300.
  3. Dov Samet & Iddo Samet & David Schmeidler, 2003. "One Observation behind Two-Envelope Puzzles," Game Theory and Information 0310004, EconWPA.
  4. Geanakoplos, John, 1994. "Common knowledge," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 40, pages 1437-1496 Elsevier.
  5. Samet, Dov, 1999. "Bayesianism without learning," Research in Economics, Elsevier, vol. 53(2), pages 227-242, June.
  6. Samet, Dov, 2000. "Quantified Beliefs and Believed Quantities," Journal of Economic Theory, Elsevier, vol. 95(2), pages 169-185, December.
  7. Paul Milgrom & Nancy L.Stokey, 1979. "Information, Trade, and Common Knowledge," Discussion Papers 377R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Giacomo Bonanno & Klaus Nehring, . "Fundamental Agreement: A New Foundation For The Harsanyi Doctrine," Department of Economics 96-02, California Davis - Department of Economics.
  9. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
  10. Sergiu Hart & Aviad Heifetz & Dov Samet, 1994. "'Knowing Whether', 'Knowing That' and the Cardinality of State Spaces," Game Theory and Information 9404002, EconWPA.
  11. Heifetz, Aviad, 1996. "Comment on Consensus without Common Knowledge," Journal of Economic Theory, Elsevier, vol. 70(1), pages 273-277, July.
  12. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-47, November.
  13. Nielsen, Lars Tyge, et al, 1990. "Common Knowledge of an Aggregate of Expectations," Econometrica, Econometric Society, vol. 58(5), pages 1235-39, September.
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Citations

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Cited by:
  1. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
  2. Xiong, Siyang, 2012. "Agreeing to agree with uncountable information structures," Games and Economic Behavior, Elsevier, vol. 74(1), pages 442-446.
  3. Ghossoub, Mario, 2010. "Belief heterogeneity in the Arrow-Borch-Raviv insurance model," MPRA Paper 37630, University Library of Munich, Germany, revised 22 Mar 2012.
  4. Ziv Hellman, 2012. "Countable Spaces and Common Priors," Discussion Paper Series dp604, The Center for the Study of Rationality, Hebrew University, Jerusalem.

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