Agreeing to agree
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.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
- Paul Milgrom & Nancy L.Stokey, 1979.
"Information, Trade, and Common Knowledge,"
377R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Dov Samet, 1997.
"Common Priors and Separation of Convex Sets,"
Game Theory and Information
- Samet, Dov, 1999.
"Bayesianism without learning,"
Research in Economics,
Elsevier, vol. 53(2), pages 227-242, June.
- Samet, Dov, 2000.
"Quantified Beliefs and Believed Quantities,"
Journal of Economic Theory,
Elsevier, vol. 95(2), pages 169-185, December.
- Hart, Sergiu & Heifetz, Aviad & Samet, Dov, 1996.
""Knowing Whether," "Knowing That," and The Cardinality of State Spaces,"
Journal of Economic Theory,
Elsevier, vol. 70(1), pages 249-256, July.
- Sergiu Hart & Aviad Heifetz & Dov Samet, 1994. "'Knowing Whether', 'Knowing That' and the Cardinality of State Spaces," Game Theory and Information 9404002, EconWPA.
- Dov Samet & Iddo Samet & David Schmeidler, 2003. "One Observation behind Two-Envelope Puzzles," Game Theory and Information 0310004, EconWPA.
- Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-47, November.
- 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.
- Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
- Heifetz, Aviad, 1996. "Comment on Consensus without Common Knowledge," Journal of Economic Theory, Elsevier, vol. 70(1), pages 273-277, July.
- Klaus Nehring & Giacomo Bonanno & Massimiliano Marcellino, 2003.
"Fundamental Agreement: A new foundation for the Harsanyi Doctrine,"
962, University of California, Davis, Department of Economics.
- Giacomo Bonanno & Klaus Nehring, . "Fundamental Agreement: A New Foundation For The Harsanyi Doctrine," Department of Economics 96-02, California Davis - Department of Economics.
- Nielsen, Lars Tyge, et al, 1990. "Common Knowledge of an Aggregate of Expectations," Econometrica, Econometric Society, vol. 58(5), pages 1235-39, September.
When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpga:0310005. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA)
If references are entirely missing, you can add them using this form.