IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v271y2018i2d10.1007_s10479-018-2914-z.html
   My bibliography  Save this article

Random expected utility theory with a continuum of prizes

Author

Listed:
  • Wei Ma

    (Xi’an Jiaotong-Liverpool University
    University of Pretoria)

Abstract

This note generalizes Gul and Pesendorfer’s random expected utility theory, a stochastic reformulation of von Neumann–Morgenstern expected utility theory for lotteries over a finite set of prizes, to the circumstances with a continuum of prizes. Let [0, M] denote this continuum of prizes; assume that each utility function is continuous, let $$C_0[0,M]$$ C 0 [ 0 , M ] be the set of all utility functions which vanish at the origin, and define a random utility function to be a finitely additive probability measure on $$C_0[0,M]$$ C 0 [ 0 , M ] (associated with an appropriate algebra). It is shown here that a random choice rule is mixture continuous, monotone, linear, and extreme if, and only if, the random choice rule maximizes some regular random utility function. To obtain countable additivity of the random utility function, we further restrict our consideration to those utility functions that are continuously differentiable on [0, M] and vanish at zero. With this restriction, it is shown that a random choice rule is continuous, monotone, linear, and extreme if, and only if, it maximizes some regular, countably additive random utility function. This generalization enables us to make a discussion of risk aversion in the framework of random expected utility theory.

Suggested Citation

  • Wei Ma, 2018. "Random expected utility theory with a continuum of prizes," Annals of Operations Research, Springer, vol. 271(2), pages 787-809, December.
  • Handle: RePEc:spr:annopr:v:271:y:2018:i:2:d:10.1007_s10479-018-2914-z
    DOI: 10.1007/s10479-018-2914-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-018-2914-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10479-018-2914-z?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. McFadden, Daniel, 1980. "Econometric Models for Probabilistic Choice among Products," The Journal of Business, University of Chicago Press, vol. 53(3), pages 13-29, July.
    2. 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.
    3. Fishburn, Peter C, 1991. "Nontransitive Preferences in Decision Theory," Journal of Risk and Uncertainty, Springer, vol. 4(2), pages 113-134, April.
    4. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 245-264, August.
    5. Clark, Stephen A, 1996. "The Random Utility Model with an Infinite Choice Space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 179-189, January.
    6. 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.
    7. Faruk Gul & Wolfgang Pesendorfer, 2006. "Random Expected Utility," Econometrica, Econometric Society, vol. 74(1), pages 121-146, January.
    8. Nakamura, Yutaka, 2015. "Differentiability of von Neumann–Morgenstern utility functions," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 74-80.
    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. Wei Ma, 2023. "Random dual expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(2), pages 293-315, February.
    2. Mira Frick & Ryota Iijima & Tomasz Strzalecki, 2019. "Dynamic Random Utility," Econometrica, Econometric Society, vol. 87(6), pages 1941-2002, November.

    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. Wei Ma, 2018. "Random Expected Utility Theory with a Continuum of Prizes," Working Papers 201854, University of Pretoria, Department of Economics.
    2. Wei Ma, 2018. "Random Expected Utility Theory with a Continuum of Prizes," Working Papers 760, Economic Research Southern Africa.
    3. Minardi, Stefania & Savochkin, Andrei, 2015. "Preferences with grades of indecisiveness," Journal of Economic Theory, Elsevier, vol. 155(C), pages 300-331.
    4. McClellon, Morgan, 2016. "Confidence models of incomplete preferences," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 30-34.
    5. Hill, Brian, 2016. "Incomplete preferences and confidence," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 83-103.
    6. 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.
    7. Heller, Yuval, 2012. "Justifiable choice," Games and Economic Behavior, Elsevier, vol. 76(2), pages 375-390.
    8. Ellis, Andrew, 2018. "Foundations for optimal inattention," Journal of Economic Theory, Elsevier, vol. 173(C), pages 56-94.
    9. Koida, Nobuo, 2022. "Indecisiveness, preference for flexibility, and a unique subjective state space," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    10. Chew, Soo Hong & Miao, Bin & Shen, Qiang & Zhong, Songfa, 2022. "Multiple-switching behavior in choice-list elicitation of risk preference," Journal of Economic Theory, Elsevier, vol. 204(C).
    11. Karni, Edi & Safra, Zvi, 2016. "A theory of stochastic choice under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 164-173.
    12. Guo, Liang, 2021. "Contextual deliberation and the choice-valuation preference reversal," Journal of Economic Theory, Elsevier, vol. 195(C).
    13. 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.
    14. Dino Borie, 2016. "Expected Multi-Utility Representations by "Simplex" with Applications," GREDEG Working Papers 2016-10, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    15. Andrew J. Keith & Darryl K. Ahner, 2021. "A survey of decision making and optimization under uncertainty," Annals of Operations Research, Springer, vol. 300(2), pages 319-353, May.
    16. Tigran Melkonyan & Zvi Safra, 2016. "Intrinsic Variability in Group and Individual Decision Making," Management Science, INFORMS, vol. 62(9), pages 2651-2667, September.
    17. Stoye, Jörg, 2015. "Choice theory when agents can randomize," Journal of Economic Theory, Elsevier, vol. 155(C), pages 131-151.
    18. Jacques Dreze, 2012. "Nested identification of subjective probabilities," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 259-271, March.
    19. Cosimo Munari, 2020. "Multi-utility representations of incomplete preferences induced by set-valued risk measures," Papers 2009.04151, arXiv.org.
    20. Sujoy Mukerji & Peter Klibanoff and Kyoungwon Seo, 2011. "Relevance and Symmetry," Economics Series Working Papers 539, University of Oxford, Department of Economics.

    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:annopr:v:271:y:2018:i:2:d:10.1007_s10479-018-2914-z. 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.