IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v52y2013i1p1-13.html
   My bibliography  Save this article

Agreement theorem for neo-additive beliefs

Author

Listed:
  • Adam Dominiak
  • Jean-Philippe Lefort

Abstract

In this paper, we extend Aumann’s (Ann Stat 4:1236–1239, 1976 ) probabilistic agreement theorem to situations in which agents’ prior beliefs are represented by a common neo-additive capacity. In particular, we characterize the family of updating rules for neo-additive capacities, which are necessary and sufficient for the impossibility of “agreeing to disagree” on the values of posterior capacities as well as on the values of posterior Choquet expectations for binary acts. Furthermore, we show that generalizations of this result to more general acts are impossible. Copyright Springer-Verlag 2013

Suggested Citation

  • Adam Dominiak & Jean-Philippe Lefort, 2013. "Agreement theorem for neo-additive beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 1-13, January.
    • Handle: RePEc:spr:joecth:v:52:y:2013:i:1:p:1-13
    DOI: 10.1007/s00199-011-0678-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00199-011-0678-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00199-011-0678-7?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. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    2. Jürgen Eichberger & David Kelsey & Burkhard C. Schipper, 2009. "Ambiguity and social interaction," Oxford Economic Papers, Oxford University Press, vol. 61(2), pages 355-379, April.
    3. Eichberger, Jurgen & Grant, Simon & Kelsey, David, 2005. "CEU preferences and dynamic consistency," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 143-151, March.
    4. Jürgen Eichberger & David Kelsey, 2011. "Are the treasures of game theory ambiguous?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 313-339, October.
    5. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
    6. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 83-92.
    7. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    8. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    9. Jürgen Eichberger & Simon Grant & David Kelsey, 2008. "Differentiating ambiguity: an expository note," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 327-336, August.
    10. Zimper, Alexander, 2009. "Half empty, half full and why we can agree to disagree forever," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 283-299, August.
    11. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    12. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    13. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    14. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
    15. Jurgen Eichberger & Simon Grant & David Kelsey & Gleb A. Koshevoy, 2009. "The a-MEU Model: A Comment," Discussion Papers 0903, University of Exeter, Department of Economics.
    16. Eichberger, Jurgen & Grant, Simon & Kelsey, David, 2007. "Updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 888-899, September.
    17. Klaus Nehring, 2001. "Common priors under incomplete information: a unification," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(3), pages 535-553.
    18. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    19. Eichberger, Jürgen & Grant, Simon & Kelsey, David, 2010. "Comparing three ways to update Choquet beliefs," Economics Letters, Elsevier, vol. 107(2), pages 91-94, May.
    20. John Dickhaut & Radhika Lunawat & Kira Pronin & Jack Stecher, 2011. "Decision making and trade without probabilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 275-288, October.
    21. Kim Border & Paolo Ghirardato & Uzi Segal, 2008. "Unanimous subjective probabilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(2), pages 383-387, February.
    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. Tarbush, Bassel, 2016. "Counterfactuals in “agreeing to disagree” type results," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 125-133.
    2. Craig Webb, 2015. "Piecewise additivity for non-expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 371-392, October.
    3. Zimper, Alexander, 2014. "On the impossibility of insider trade in rational expectations equilibria," The North American Journal of Economics and Finance, Elsevier, vol. 28(C), pages 109-118.
    4. Nicolas Lampach & Kene Boun My & Sandrine Spaeter, 2016. "Risk, Ambiguity and Efficient Liability Rules: An experiment," Working Papers of BETA 2016-30, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    5. Emy Lécuyer & Jean-Philippe Lefort, 2021. "Put–call parity and generalized neo-additive pricing rules," Theory and Decision, Springer, vol. 90(3), pages 521-542, May.
    6. Nicolas Lampach & Sandrine Spaeter, 2016. "The Efficiency of (strict) Liability Rules revised in Risk and Ambiguity," Working Papers of BETA 2016-29, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    7. Dominiak, Adam & Lefort, Jean-Philippe, 2015. "“Agreeing to disagree” type results under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 119-129.
    8. Craig S. Webb, 2017. "Piecewise linear rank-dependent utility," Theory and Decision, Springer, vol. 82(3), pages 403-414, March.

    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. Jürgen Eichberger & Simon Grant & David Kelsey, 2012. "When is ambiguity–attitude constant?," Journal of Risk and Uncertainty, Springer, vol. 45(3), pages 239-263, December.
    2. Heyen, Daniel, 2018. "Ambiguity aversion under maximum-likelihood updating," LSE Research Online Documents on Economics 80342, London School of Economics and Political Science, LSE Library.
    3. Georgalos, Konstantinos, 2021. "Dynamic decision making under ambiguity: An experimental investigation," Games and Economic Behavior, Elsevier, vol. 127(C), pages 28-46.
    4. Daniel Heyen, 2018. "Ambiguity aversion under maximum-likelihood updating," Theory and Decision, Springer, vol. 84(3), pages 373-386, May.
    5. Konstantinos Georgalos, 2019. "An experimental test of the predictive power of dynamic ambiguity models," Journal of Risk and Uncertainty, Springer, vol. 59(1), pages 51-83, August.
    6. Eichberger, Jürgen & Grant, Simon & Lefort, Jean-Philippe, 2009. "Neo-additive capacities and updating," Working Papers 0490, University of Heidelberg, Department of Economics.
    7. Gérard Mondello, 2022. "Information Source's Reliability," GREDEG Working Papers 2022-21, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France, revised Oct 2022.
    8. Dominiak, Adam & Duersch, Peter & Lefort, Jean-Philippe, 2012. "A dynamic Ellsberg urn experiment," Games and Economic Behavior, Elsevier, vol. 75(2), pages 625-638.
    9. Gérard Mondello, 2021. "Uncertainty And Information Sources' Reliability," Working Papers halshs-03502603, HAL.
    10. Spyros Galanis, 2021. "Dynamic consistency, valuable information and subjective beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1467-1497, June.
    11. Adam Dominiak & Ani Guerdjikova, 2021. "Special Issue on Ambiguity and Strategic Interactions in Honor of Jürgen Eichberger," Theory and Decision, Springer, vol. 90(3), pages 301-307, May.
    12. Dominiak, Adam & Eichberger, Jürgen & Lefort, Jean-Philippe, 2012. "Agreeable trade with optimism and pessimism," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 119-126.
    13. Christopher Boortz, 2016. "Irrational Exuberance and Herding in Financial Markets," SFB 649 Discussion Papers SFB649DP2016-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. Dominiak, Adam & Lefort, Jean-Philippe, 2015. "“Agreeing to disagree” type results under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 119-129.
    15. Aliyev, Nihad & He, Xue-Zhong, 2023. "Ambiguous price formation," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    16. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    17. Zimper, Alexander, 2012. "Asset pricing in a Lucas fruit-tree economy with the best and worst in mind," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 610-628.
    18. Alexander Ludwig & Alexander Zimper, 2013. "A decision-theoretic model of asset-price underreaction and overreaction to dividend news," Annals of Finance, Springer, vol. 9(4), pages 625-665, November.
    19. Ludwig, Alexander & Zimper, Alexander, 2014. "Biased Bayesian learning with an application to the risk-free rate puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 79-97.
    20. A. Ludwig & A. Zimper, 2013. "A parsimonious model of subjective life expectancy," Theory and Decision, Springer, vol. 75(4), pages 519-541, October.

    More about this item

    Keywords

    Ambiguity; Neo-additive capacities; Choquet expected utility; Asymmetric information; Common knowledge; Agreement theorem; D70; D81; D82;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • 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:spr:joecth:v:52:y:2013:i:1:p:1-13. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.