IDEAS home Printed from https://ideas.repec.org/p/rza/wpaper/058.html
   My bibliography  Save this paper

Half empty, half full and why we can agree to disagree forever

Author

Listed:
  • Alexander Zimper

Abstract

Aumann (1976) derives his famous we cannot agree to disagree result under the assumption of rational Bayesian learning. Motivated by psychological evidence against this assumption, we develop formal models of optimistically, resp. pessimistically, biased Bayesian learning within the framework of Choquet expected utility theory. As a key feature of our approach the posterior subjective beliefs […]

Suggested Citation

  • Alexander Zimper, 2007. "Half empty, half full and why we can agree to disagree forever," Working Papers 058, Economic Research Southern Africa.
    • Handle: RePEc:rza:wpaper:058
    as

    Download full text from publisher

    File URL: https://econrsa.org/wp-content/uploads/2022/06/wp58.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Siniscalchi, Marciano, 2006. "A behavioral characterization of plausible priors," Journal of Economic Theory, Elsevier, vol. 128(1), pages 91-135, May.
    2. R. A. Pollak, 1968. "Consistent Planning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 201-208.
    3. Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-1059, July.
    4. 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.
    5. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    6. Kajii, Atsushi & Ui, Takashi, 2006. "Agreeable bets with multiple priors," Journal of Economic Theory, Elsevier, vol. 128(1), pages 299-305, May.
    7. Tonks, Ian, 1983. "Bayesian Learning and the Optimal Investment Decision of the Firm," Economic Journal, Royal Economic Society, vol. 93(369a), pages 87-98, Supplemen.
    8. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    9. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000. "Sharing Beliefs: Between Agreeing and Disagreeing," Econometrica, Econometric Society, vol. 68(3), pages 685-694, May.
    10. Eichberger, Jurgen & Grant, Simon & Kelsey, David, 2007. "Updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 888-899, September.
    11. Samet, Dov, 1990. "Ignoring ignorance and agreeing to disagree," Journal of Economic Theory, Elsevier, vol. 52(1), pages 190-207, October.
    12. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    13. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    14. Sarin, Rakesh & Wakker, Peter P, 1998. "Revealed Likelihood and Knightian Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 16(3), pages 223-250, July-Aug..
    15. Luca Rigotti & Chris Shannon, 2005. "Uncertainty and Risk in Financial Markets," Econometrica, Econometric Society, vol. 73(1), pages 203-243, January.
    16. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    17. Chateauneuf, Alain & Dana, Rose-Anne & Tallon, Jean-Marc, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 191-214, October.
    18. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallou, 2002. "Sharing beliefs and the absence of betting in the Choquet expected utility model," Statistical Papers, Springer, vol. 43(1), pages 127-136, January.
    19. Milgrom, Paul, 1981. "An Axiomatic Characterization of Common Knowledge," Econometrica, Econometric Society, vol. 49(1), pages 219-222, January.
    20. Ludwig, Alexander & Zimper, Alexander, 2006. "Investment behavior under ambiguity: The case of pessimistic decision makers," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 111-130, September.
    21. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
    22. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1275-1303.
    23. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    24. Dow, James & Werlang, Sérgio Ribeiro da Costa & Madrigal, Vicente, 1990. "Preferences, common knowledge and speculative trade," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 149, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    25. Kajii, Atsushi & Ui, Takashi, 2009. "Interim efficient allocations under uncertainty," Journal of Economic Theory, Elsevier, vol. 144(1), pages 337-353, January.
    26. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-1272, November.
    27. Chenghu Ma, 2001. "A No-Trade Theorem under Knightian Uncertainty with General Preferences," Theory and Decision, Springer, vol. 51(2), pages 173-181, December.
    28. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    29. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
    30. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
    31. Rubinstein, Ariel & Wolinsky, Asher, 1990. "On the logic of "agreeing to disagree" type results," Journal of Economic Theory, Elsevier, vol. 51(1), pages 184-193, June.
    32. Alexander Zimper & Alexander Ludwig, 2006. "Rational expectations and ambiguity: A comment on Abel (2002)," Economics Bulletin, AccessEcon, vol. 4(2), pages 1-15.
    33. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    34. ,, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    35. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    36. Atsushi Kajii & Takashi Ui, 2005. "Incomplete Information Games With Multiple Priors," The Japanese Economic Review, Japanese Economic Association, vol. 56(3), pages 332-351, September.
    37. Ghirardato, Paolo & Klibanoff, Peter & Marinacci, Massimo, 1998. "Additivity with multiple priors," Journal of Mathematical Economics, Elsevier, vol. 30(4), pages 405-420, November.
    38. Neeman, Zvika, 1996. "Approximating Agreeing to Disagree Results with Commonp-Beliefs," Games and Economic Behavior, Elsevier, vol. 12(1), pages 162-164, January.
    39. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    40. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    41. Marinacci, Massimo, 1999. "Limit Laws for Non-additive Probabilities and Their Frequentist Interpretation," Journal of Economic Theory, Elsevier, vol. 84(2), pages 145-195, February.
    42. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 579-608.
    43. 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.
    44. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    45. Halevy, Yoram, 2004. "The possibility of speculative trade between dynamically consistent agents," Games and Economic Behavior, Elsevier, vol. 46(1), pages 189-198, January.
    46. Bacharach, Michael, 1985. "Some extensions of a claim of Aumann in an axiomatic model of knowledge," Journal of Economic Theory, Elsevier, vol. 37(1), pages 167-190, October.
    47. Chateauneuf, Alain & Dana, Rose-Anne & Tallon, Jean-Marc, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 191-214, October.
    48. Viscusi, W. Kip, 1985. "A Bayesian perspective on biases in risk perception," Economics Letters, Elsevier, vol. 17(1-2), pages 59-62.
    49. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    50. Epstein Larry G. & Le Breton Michel, 1993. "Dynamically Consistent Beliefs Must Be Bayesian," Journal of Economic Theory, Elsevier, vol. 61(1), pages 1-22, October.
    51. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    52. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-1347, November.
    53. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    54. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    55. Viscusi, W Kip & O'Connor, Charles J, 1984. "Adaptive Responses to Chemical Labeling: Are Workers Bayesian Decision Makers?," American Economic Review, American Economic Association, vol. 74(5), pages 942-956, December.
    56. Marciano Siniscalchi, 2001. "Bayesian Updating for General Maxmin Expected Utility Preferences," Discussion Papers 1366, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    57. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-1280, November.
    58. Jürgen Eichberger & David Kelsey, 1999. "E-Capacities and the Ellsberg Paradox," Theory and Decision, Springer, vol. 46(2), pages 107-138, April.
    59. repec:dau:papers:123456789/5461 is not listed on IDEAS
    60. Massimo Marinacci, 2002. "Learning from ambiguous urns," Statistical Papers, Springer, vol. 43(1), pages 143-151, January.
    61. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    62. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
    63. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
    64. Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-175, October.
    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. 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.
    2. 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.
    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. A. Ludwig & A. Zimper, 2013. "A parsimonious model of subjective life expectancy," Theory and Decision, Springer, vol. 75(4), pages 519-541, October.
    5. Alexander Zimper & Alexander Ludwig, 2009. "On attitude polarization under Bayesian learning with non-additive beliefs," Journal of Risk and Uncertainty, Springer, vol. 39(2), pages 181-212, October.
    6. 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.
    7. Alexander Zimper & Wei Ma, 2017. "Bayesian learning with multiple priors and nonvanishing ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 409-447, October.
    8. 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.
    9. Gilboa, Itzhak & Samuelson, Larry & Schmeidler, David, 2022. "Learning (to disagree?) in large worlds," Journal of Economic Theory, Elsevier, vol. 199(C).
    10. Linardi, Sera, 2017. "Accounting for noise in the microfoundations of information aggregation," Games and Economic Behavior, Elsevier, vol. 101(C), pages 334-353.

    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. Alexander Zimper, 2011. "Do Bayesians Learn Their Way Out of Ambiguity?," Decision Analysis, INFORMS, vol. 8(4), pages 269-285, December.
    2. Ludwig, Alexander & Zimper, Alexander, 2006. "Investment behavior under ambiguity: The case of pessimistic decision makers," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 111-130, September.
    3. Alexander Zimper & Alexander Ludwig, 2009. "On attitude polarization under Bayesian learning with non-additive beliefs," Journal of Risk and Uncertainty, Springer, vol. 39(2), pages 181-212, October.
    4. 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.
    5. 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.
    6. 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.
    7. A. Ludwig & A. Zimper, 2013. "A parsimonious model of subjective life expectancy," Theory and Decision, Springer, vol. 75(4), pages 519-541, October.
    8. Dominiak, Adam & Lefort, Jean-Philippe, 2015. "“Agreeing to disagree” type results under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 119-129.
    9. Ludwig, Alexander & Zimper, Alexander, 2007. "Attitude polarization," Papers 07-66, Sonderforschungsbreich 504.
    10. Alexander Zimper, 2008. "Asset pricing in a Lucas ‘fruit-tree’ economy with non-additive beliefs," Working Papers 092, Economic Research Southern Africa.
    11. repec:awi:wpaper:0448 is not listed on IDEAS
    12. 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.
    13. Chambers, Robert G. & Melkonyan, Tigran, 2009. "Smoothing preference kinks with information," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 173-189, September.
    14. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    15. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.
    16. repec:ebl:ecbull:v:4:y:2006:i:2:p:1-15 is not listed on IDEAS
    17. Eichberger, Jürgen & Kelsey, David, 2007. "Ambiguity," Sonderforschungsbereich 504 Publications 07-50, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
      • Eichberger, Jürgen & Kelsey, David, 2007. "Ambiguity," Papers 07-50, Sonderforschungsbreich 504.
    18. Alexander Zimper, 2011. "Re-examining the law of iterated expectations for Choquet decision makers," Theory and Decision, Springer, vol. 71(4), pages 669-677, October.
    19. Aurélien Baillon & Han Bleichrodt & Umut Keskin & Olivier l’Haridon & Chen Li, 2018. "The Effect of Learning on Ambiguity Attitudes," Management Science, INFORMS, vol. 64(5), pages 2181-2198, May.
    20. 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.
    21. Georgalos, Konstantinos, 2021. "Dynamic decision making under ambiguity: An experimental investigation," Games and Economic Behavior, Elsevier, vol. 127(C), pages 28-46.
    22. Eisei Ohtaki, 2023. "Optimality in an OLG model with nonsmooth preferences," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(3), pages 611-659, September.

    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G20 - Financial Economics - - Financial Institutions and Services - - - General

    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:rza:wpaper:058. 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: Maggi Sigg (email available below). General contact details of provider: https://edirc.repec.org/data/ersacza.html .

    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.