IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v93y2015icp108-116.html
   My bibliography  Save this article

Agreeing to agree and Dutch books

Author

Listed:
  • Chen, Yi-Chun
  • Lehrer, Ehud
  • Li, Jiangtao
  • Samet, Dov
  • Shmaya, Eran

Abstract

We say that agreeing to agree is possible for an event E if there exist posterior beliefs of the agents with a common prior such that it is common knowledge that the agents' posteriors for E coincide. We propose a notion called Dutch book which is a profile of interim contracts between an outsider and the agents based on the occurrence of E, such that the outsider makes positive profit in all states. We show that in a finite state space, when the agents cannot tell whether E occurred or not, agreeing to agree is possible for E if and only if there is no Dutch book on E. This characterization also holds in countable state spaces with two agents. We weaken the notion of Dutch book to characterize agreeing to agree in a countable state space with multiple agents, when each set in each agent's information partition is finite.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:gamebe:v:93:y:2015:i:c:p:108-116
    DOI: 10.1016/j.geb.2015.08.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825615001141
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2015.08.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. Ng, Man-Chung, 2003. "On the duality between prior beliefs and trading demands," Journal of Economic Theory, Elsevier, vol. 109(1), pages 39-51, March.
    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. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    5. Giacomo Bonanno & Klaus Nehring, 1999. "How to make sense of the common prior assumption under incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 409-434.
    6. , & ,, 2011. "Agreeing to agree," Theoretical Economics, Econometric Society, vol. 6(2), May.
    7. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-1347, November.
    8. Lehrer, Ehud & Samet, Dov, 2014. "Belief consistency and trade consistency," Games and Economic Behavior, Elsevier, vol. 83(C), pages 165-177.
    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.
    as


    Cited by:

    1. Christian W. Bach & Jérémie Cabessa, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Post-Print hal-04271274, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ziv Hellman, 2014. "Countable spaces and common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 193-213, February.
    2. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
    3. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    5. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    6. Hellman, Ziv, 2011. "Iterated expectations, compact spaces, and common priors," Games and Economic Behavior, Elsevier, vol. 72(1), pages 163-171, May.
    7. Ziv Hellman & Miklós Pintér, 2022. "Charges and bets: a general characterisation of common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(3), pages 567-587, November.
    8. Barelli, Paulo, 2009. "Consistency of beliefs and epistemic conditions for Nash and correlated equilibria," Games and Economic Behavior, Elsevier, vol. 67(2), pages 363-375, November.
    9. Galanis, Spyros, 2018. "Speculation under unawareness," Games and Economic Behavior, Elsevier, vol. 109(C), pages 598-615.
    10. Guarino, Pierfrancesco & Tsakas, Elias, 2021. "Common priors under endogenous uncertainty," Journal of Economic Theory, Elsevier, vol. 194(C).
    11. Lipman, Barton L., 2010. "Finite order implications of common priors in infinite models," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 56-70, January.
    12. Atsushi Kajii & Takashi Ui, 2004. "Trade with Heterogeneous Multiple Priors," KIER Working Papers 582, Kyoto University, Institute of Economic Research.
    13. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
    14. Halpern, Joseph Y., 2002. "Characterizing the Common Prior Assumption," Journal of Economic Theory, Elsevier, vol. 106(2), pages 316-355, October.
    15. Rodrigues-Neto, José Alvaro, 2009. "From posteriors to priors via cycles," Journal of Economic Theory, Elsevier, vol. 144(2), pages 876-883, March.
    16. Kajii, Atsushi & Ui, Takashi, 2009. "Interim efficient allocations under uncertainty," Journal of Economic Theory, Elsevier, vol. 144(1), pages 337-353, January.
    17. Lehrer, Ehud & Samet, Dov, 2014. "Belief consistency and trade consistency," Games and Economic Behavior, Elsevier, vol. 83(C), pages 165-177.
    18. Hellwig, Martin, 2022. "Incomplete-information games in large populations with anonymity," Theoretical Economics, Econometric Society, vol. 17(1), January.
    19. Fiorini, Luciana C. & Rodrigues-Neto, José A., 2017. "Self-consistency, consistency and cycles in non-partitional knowledge models," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 11-21.
    20. Gizatulina, Alia & Hellman, Ziv, 2019. "No trade and yes trade theorems for heterogeneous priors," Journal of Economic Theory, Elsevier, vol. 182(C), pages 161-184.

    More about this item

    Keywords

    Agreement theorem; Common knowledge; Common prior; Dutch book; No trade theorem;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:93:y:2015:i:c:p:108-116. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.