# Agreeing to agree

## Author

Listed:
• Lehrer, Ehud

() (School of Mathematical Sciences, Tel Aviv University)

• Samet, Dov

() (Faculty of Management, Tel Aviv University)

## Abstract

Aumann 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 $E$ \emph{do} coincide? We show that a necessary and sufficient condition for this is the existence of a nonempty \emph{finite} event $F$ with the following two properties. First, it is common knowledge at $F$ that the agents cannot tell whether or not $E$ occurred. Second, this still holds true at $F$, when $F$ itself becomes common knowledge.

## Suggested Citation

• Lehrer, Ehud & Samet, Dov, 2011. "Agreeing to agree," Theoretical Economics, Econometric Society, vol. 6(2), May.
• Handle: RePEc:the:publsh:578
as

File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20110269/5201/186

## References listed on IDEAS

as
1. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
2. Samet, Dov, 2000. "Quantified Beliefs and Believed Quantities," Journal of Economic Theory, Elsevier, vol. 95(2), pages 169-185, December.
3. 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.
4. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
5. Dov Samet & Iddo Samet & David Schmeidler, 2003. "One Observation behind Two-Envelope Puzzles," Game Theory and Information 0310004, University Library of Munich, Germany.
6. Samet, Dov, 1999. "Bayesianism without learning," Research in Economics, Elsevier, vol. 53(2), pages 227-242, June.
7. Nielsen, Lars Tyge, et al, 1990. "Common Knowledge of an Aggregate of Expectations," Econometrica, Econometric Society, vol. 58(5), pages 1235-1239, September.
8. Giacomo Bonanno & Klaus Nehring, "undated". "Fundamental Agreement: A New Foundation For The Harsanyi Doctrine," Department of Economics 96-02, California Davis - Department of Economics.
9. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
10. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-1347, November.
11. Heifetz, Aviad, 1996. "Comment on Consensus without Common Knowledge," Journal of Economic Theory, Elsevier, vol. 70(1), pages 273-277, July.
12. 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.
13. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
Full references (including those not matched with items on IDEAS)

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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Cited by:

1. Chen, Yi-Chun & Lehrer, Ehud & Li, Jiangtao & Samet, Dov & Shmaya, Eran, 2015. "Agreeing to agree and Dutch books," Games and Economic Behavior, Elsevier, vol. 93(C), pages 108-116.
2. Xiong, Siyang, 2012. "Agreeing to agree with uncountable information structures," Games and Economic Behavior, Elsevier, vol. 74(1), pages 442-446.
3. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
4. Ghossoub, Mario, 2010. "Belief heterogeneity in the Arrow-Borch-Raviv insurance model," MPRA Paper 37630, University Library of Munich, Germany, revised 22 Mar 2012.
5. Ziv Hellman, 2014. "Countable spaces and common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 193-213, February.
6. Dominiak, Adam & Lefort, Jean-Philippe, 2015. "“Agreeing to disagree” type results under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 119-129.
7. Hellman, Ziv & Levy, Yehuda, 2017. "Bayesian games with a continuum of states," Theoretical Economics, Econometric Society, vol. 12(3), September.

### Keywords

Agreeing theorem; common knowledge; common prior; no trade theorem;

### JEL classification:

• C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
• D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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