IDEAS home Printed from https://ideas.repec.org/p/wap/wpaper/1902.html
   My bibliography  Save this paper

Expected Utility Theory with Probability Grids and Preference Formation

Author

Listed:
  • Mamoru Kaneko

    (Waseda University)

Abstract

We reformulate expected utility theory, from the viewpoint of bounded rationality, by introducing probability grids and a cognitive bound; we restrict permissible probabilities only to decimal (`-ary in general) fractions of Önite depths up to a given cognitive bound. We distinguish between measurements of utilities from pure alternatives and their extensions to lotteries involving more risks. Our theory is constructive, from the viewpoint of the decision maker. When a cognitive bound is small, the preference relation involves many incomparabilities, but these diminish as the cognitive bound is is relaxed. Similarly, the EU hypothesis would hold more for a weaker cognitive bound. The main part of the paper is a study of preferences including incomparabilities in cases with Önite cogntive bounds; we give representation theorems in terms of a 2-dimensional vector-valued utility functions. We exemplify the theory with one experimental result reported by Kahneman-Tversky.

Suggested Citation

  • Mamoru Kaneko, 2019. "Expected Utility Theory with Probability Grids and Preference Formation," Working Papers 1902, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:1902
    as

    Download full text from publisher

    File URL: https://www.waseda.jp/fpse/winpec/assets/uploads/2019/04/WP_E1902.pdf
    File Function: First version,
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Tai-Wei Hu, 2013. "Expected utility theory from the frequentist perspective," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(1), pages 9-25, May.
    2. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    4. Mamoru Kaneko & Akihiko Matsui, 1999. "Inductive Game Theory: Discrimination and Prejudices," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 1(1), pages 101-137, January.
    5. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345.
    6. Kaneko, Mamoru, 1992. "The Ordered Field Property and a Finite Algorithm for the Nash Bargaining Solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 227-236.
    7. 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..
    8. Juan Dubra & Fabio Maccheroni & Efe A. Ok, 2004. "Expected Utility Without the Completeness Axiom," Yale School of Management Working Papers ysm404, Yale School of Management.
    9. Juan Dubra & Efe A. Ok, 2002. "A Model of Procedural Decision Making in the Presence of Risk," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1053-1080, November.
    10. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    11. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    12. Gijs Kuilen & Peter Wakker, 2006. "Learning in the Allais paradox," Journal of Risk and Uncertainty, Springer, vol. 33(3), pages 155-164, December.
    13. Kaneko, Mamoru & Nakamura, Kenjiro, 1979. "The Nash Social Welfare Function," Econometrica, Econometric Society, vol. 47(2), pages 423-435, March.
    14. Mamoru Kaneko & J. Jude Kline, 2015. "Understanding the Other Through Social Roles," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 1-31.
    15. Rubinstein, Ariel, 1988. "Similarity and decision-making under risk (is there a utility theory resolution to the Allais paradox?)," Journal of Economic Theory, Elsevier, vol. 46(1), pages 145-153, October.
    Full references (including those not matched with items on IDEAS)

    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. Mamoru Kaneko, 2020. "Expected utility theory with probability grids and preference formation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 723-764, October.
    2. Cettolin, E. & Riedl, A.M., 2015. "Revealed incomplete preferences under uncertainty," Research Memorandum 016, Maastricht University, Graduate School of Business and Economics (GSBE).
    3. Simone Cerreia-Vioglio & Efe A. Ok, 2018. "The Rational Core of Preference Relations," Working Papers 632, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    4. Ilke Aydogan & Yu Gao, 2020. "Experience and rationality under risk: re-examining the impact of sampling experience," Experimental Economics, Springer;Economic Science Association, vol. 23(4), pages 1100-1128, December.
    5. Cettolin, Elena & Riedl, Arno, 2019. "Revealed preferences under uncertainty: Incomplete preferences and preferences for randomization," Journal of Economic Theory, Elsevier, vol. 181(C), pages 547-585.
    6. Kraus, Alan & Sagi, Jacob S., 2006. "Inter-temporal preference for flexibility and risky choice," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 698-709, September.
    7. Andersen, Steffen & Harrison, Glenn W. & Lau, Morten Igel & Rutström, Elisabet E., 2010. "Behavioral econometrics for psychologists," Journal of Economic Psychology, Elsevier, vol. 31(4), pages 553-576, August.
    8. M. Ali Khan & Metin Uyanık, 2021. "Topological connectedness and behavioral assumptions on preferences: a two-way relationship," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 411-460, March.
    9. repec:cup:judgdm:v:16:y:2021:i:6:p:1324-1369 is not listed on IDEAS
    10. Arts, Sara & Ong, Qiyan & Qiu, Jianying, 2020. "Measuring subjective decision confidence," MPRA Paper 106811, University Library of Munich, Germany.
    11. Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2015. "Harsanyi's Aggregation Theorem with Incomplete Preferences," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 61-69, February.
    12. Königsheim, C. & Lukas, M. & Nöth, M., 2019. "Salience theory: Calibration and heterogeneity in probability distortion," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 477-495.
    13. Walter Bossert & Kotaro Suzumura, 2015. "Expected utility without full transitivity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 707-722, December.
    14. 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.
    15. Eric Danan, 2010. "Randomization vs. Selection: How to Choose in the Absence of Preference?," Management Science, INFORMS, vol. 56(3), pages 503-518, March.
    16. Heller, Yuval, 2012. "Justifiable choice," Games and Economic Behavior, Elsevier, vol. 76(2), pages 375-390.
    17. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    18. Eddie Dekel & Barton L. Lipman, 2010. "How (Not) to Do Decision Theory," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 257-282, September.
    19. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2017. "Stochastic Dominance Analysis Without the Independence Axiom," Management Science, INFORMS, vol. 63(4), pages 1097-1109, April.
    20. Nobuo Koida, 2021. "Intransitive indifference with direction-dependent sensitivity," KIER Working Papers 1061, Kyoto University, Institute of Economic Research.
    21. Belianin, A., 2017. "Face to Face to Human Being: Achievements and Challenges of Behavioral Economics," Journal of the New Economic Association, New Economic Association, vol. 34(2), pages 166-175.

    More about this item

    Keywords

    Expected Utility; Measurement of Utility; Bounded Rationality; Probability;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:wap:wpaper:1902. 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: Haruko Noguchi (email available below). General contact details of provider: https://edirc.repec.org/data/spwasjp.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.