IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v68y2022i11p8166-8183.html
   My bibliography  Save this article

Rank-Dependent Utility Under Multiple Priors

Author

Listed:
  • Fan Wang

    (ESSEC Business School, Singapore, Singapore 139408)

Abstract

Nonlinear perception of risk is integrated into models of decision under ambiguity, thereby providing a theoretical basis for behavioral analyses that involve both risk and ambiguity. The main model replaces the risk front of maxmin expected utility by rank-dependent utility, and it is derived from simple, observable axioms that are not restricted to expected utility under risk. The model highlights the interaction between risk attitude and ambiguity attitude, and it is compatible with the paradoxical choices hypothesized by Machina. Following the same idea, nonlinear perception of risk can also be integrated into variational and multiplier preferences. When applied to comparative ambiguity attitudes, the idea enables more comparisons by allowing for both heterogeneous taste and perception of risk.

Suggested Citation

  • Fan Wang, 2022. "Rank-Dependent Utility Under Multiple Priors," Management Science, INFORMS, vol. 68(11), pages 8166-8183, November.
    • Handle: RePEc:inm:ormnsc:v:68:y:2022:i:11:p:8166-8183
    DOI: 10.1287/mnsc.2021.4254
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.2021.4254
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.2021.4254?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
    ---><---

    References listed on IDEAS

    as
    1. Olivier L’Haridon & Lætitia Placido, 2010. "Betting on Machina’s reflection example: an experiment on ambiguity," Theory and Decision, Springer, vol. 69(3), pages 375-393, September.
    2. 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.
    3. Tomasz Strzalecki, 2011. "Axiomatic Foundations of Multiplier Preferences," Econometrica, Econometric Society, vol. 79(1), pages 47-73, January.
    4. Aurelien Baillon & Olivier L'Haridon & Laetitia Placido, 2011. "Ambiguity Models and the Machina Paradoxes," American Economic Review, American Economic Association, vol. 101(4), pages 1547-1560, June.
    5. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    6. Adam Dominiak & Jean-Philippe Lefort, 2021. "Ambiguity and Probabilistic information," Post-Print hal-04002664, HAL.
    7. Charles M. Harvey, 1986. "Value Functions for Infinite-Period Planning," Management Science, INFORMS, vol. 32(9), pages 1123-1139, September.
    8. Mark J. Machina, 2009. "Risk, Ambiguity, and the Rank-Dependence Axioms," American Economic Review, American Economic Association, vol. 99(1), pages 385-392, March.
    9. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    10. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    11. Segal, Uzi, 1987. "The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 175-202, February.
    12. 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..
    13. Mohammed Abdellaoui, 2002. "A Genuine Rank-Dependent Generalization of the Von Neumann-Morgenstern Expected Utility Theorem," Econometrica, Econometric Society, vol. 70(2), pages 717-736, March.
    14. Mohammed Abdellaoui & Han Bleichrodt & Olivier L’Haridon, 2008. "A tractable method to measure utility and loss aversion under prospect theory," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 245-266, June.
    15. 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.
    16. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    17. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    18. Adam Dominiak & Jean-Philippe Lefort, 2021. "Ambiguity and Probabilistic information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-04002664, HAL.
    19. Dean, Mark & Ortoleva, Pietro, 2017. "Allais, Ellsberg, and preferences for hedging," Theoretical Economics, Econometric Society, vol. 12(1), January.
    20. David Dillenberger & Uzi Segal, 2015. "Recursive Ambiguity And Machina'S Examples," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 55-61, February.
    21. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2003. "A Subjective Spin on Roulette Wheels," Econometrica, Econometric Society, vol. 71(6), pages 1897-1908, November.
    22. Veronika Köbberling & Peter P. Wakker, 2003. "Preference Foundations for Nonexpected Utility: A Generalized and Simplified Technique," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 395-423, August.
    23. Werner, Jan, 2005. "A simple axiomatization of risk-averse expected utility," Economics Letters, Elsevier, vol. 88(1), pages 73-77, July.
    24. David Dillenberger & Uzi Segal, 2015. "Recursive Ambiguity And Machina'S Examples," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(1), pages 55-61, February.
    25. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-1280, November.
    26. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    27. Itzhak Gilboa & Stefania Minardi & Larry Samuelson & David Schmeidler, 2020. "States and Contingencies: How to Understand Savage without Anyone Being Hanged," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 365-385.
    28. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    29. Mohammed Abdellaoui & Peter Wakker, 2005. "The Likelihood Method for Decision under Uncertainty," Theory and Decision, Springer, vol. 58(1), pages 3-76, February.
    30. Stephen G. Dimmock & Roy Kouwenberg & Peter P. Wakker, 2016. "Ambiguity Attitudes in a Large Representative Sample," Management Science, INFORMS, vol. 62(5), pages 1363-1380, May.
    31. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
    32. Peter Fishburn & Ward Edwards, 1997. "Discount-neutral utility models for denumerable time streams," Theory and Decision, Springer, vol. 43(2), pages 139-166, September.
    33. Alon, Shiri & Schmeidler, David, 2014. "Purely subjective Maxmin Expected Utility," Journal of Economic Theory, Elsevier, vol. 152(C), pages 382-412.
    34. Mark J. Machina, 2014. "Ambiguity Aversion with Three or More Outcomes," American Economic Review, American Economic Association, vol. 104(12), pages 3814-3840, December.
    35. Ying He, 2021. "Revisiting Ellsberg’s and Machina’s Paradoxes: A Two-Stage Evaluation Model Under Ambiguity," Management Science, INFORMS, vol. 67(11), pages 6897-6914, November.
    36. 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.
    37. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
    38. Adam Dominiak & Jean-Philippe Lefort, 2021. "Ambiguity and Probabilistic Information," Management Science, INFORMS, vol. 67(7), pages 4310-4326, July.
    39. 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.
    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. Mohammed Abdellaoui & Horst Zank, 2023. "Source and rank-dependent utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 949-981, May.
    2. Adam Dominiak & Jean-Philippe Lefort, 2021. "Ambiguity and Probabilistic Information," Management Science, INFORMS, vol. 67(7), pages 4310-4326, July.
    3. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.
    4. Evren, Özgür, 2019. "Recursive non-expected utility: Connecting ambiguity attitudes to risk preferences and the level of ambiguity," Games and Economic Behavior, Elsevier, vol. 114(C), pages 285-307.
    5. Wakker, Peter P. & Yang, Jingni, 2019. "A powerful tool for analyzing concave/convex utility and weighting functions," Journal of Economic Theory, Elsevier, vol. 181(C), pages 143-159.
    6. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    7. Laurent Denant-Boemont & Olivier L’Haridon, 2013. "La rationalité à l'épreuve de l'économie comportementale," Revue française d'économie, Presses de Sciences-Po, vol. 0(2), pages 35-89.
    8. Mohammed Abdellaoui & Horst Zank, 2022. "Source and Rank-dependent Utility," Post-Print hal-03924295, HAL.
    9. Dean, Mark & Ortoleva, Pietro, 2017. "Allais, Ellsberg, and preferences for hedging," Theoretical Economics, Econometric Society, vol. 12(1), January.
    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. Gijs van de Kuilen & Peter P. Wakker, 2011. "The Midweight Method to Measure Attitudes Toward Risk and Ambiguity," Management Science, INFORMS, vol. 57(3), pages 582-598, March.
    12. Stefan Trautmann & Peter P. Wakker, 2018. "Making the Anscombe-Aumann approach to ambiguity suitable for descriptive applications," Journal of Risk and Uncertainty, Springer, vol. 56(1), pages 83-116, February.
    13. Aurélien Baillon & Zhenxing Huang & Asli Selim & Peter P. Wakker, 2018. "Measuring Ambiguity Attitudes for All (Natural) Events," Econometrica, Econometric Society, vol. 86(5), pages 1839-1858, September.
    14. Blavatskyy, Pavlo R., 2013. "Two examples of ambiguity aversion," Economics Letters, Elsevier, vol. 118(1), pages 206-208.
    15. Dorian Jullien & Alexandre Truc, 2024. "Towards a History of Behavioral and Experimental Economics in France," GREDEG Working Papers 2024-23, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    16. König-Kersting, Christian & Kops, Christopher & Trautmann, Stefan T., 2023. "A test of (weak) certainty independence," Journal of Economic Theory, Elsevier, vol. 209(C).
    17. Aurélien Baillon & Han Bleichrodt & Zhenxing Huang & Rogier Potter van Loon, 2017. "Measuring ambiguity attitude: (Extended) multiplier preferences for the American and the Dutch population," Journal of Risk and Uncertainty, Springer, vol. 54(3), pages 269-281, June.
    18. Ying He, 2021. "Revisiting Ellsberg’s and Machina’s Paradoxes: A Two-Stage Evaluation Model Under Ambiguity," Management Science, INFORMS, vol. 67(11), pages 6897-6914, November.
    19. repec:hal:cesptp:halshs-04810987 is not listed on IDEAS
    20. Shaw, W. Douglass & Woodward, Richard T., 2008. "Why environmental and resource economists should care about non-expected utility models," Resource and Energy Economics, Elsevier, vol. 30(1), pages 66-89, January.
    21. Baillon, Aurélien & Driesen, Bram & Wakker, Peter P., 2012. "Relative concave utility for risk and ambiguity," Games and Economic Behavior, Elsevier, vol. 75(2), pages 481-489.

    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:inm:ormnsc:v:68:y:2022:i:11:p:8166-8183. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.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.