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Rank-Dependent Utility Under Multiple Priors

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  • 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
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    References listed on IDEAS

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    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. Tomasz Strzalecki, 2011. "Axiomatic Foundations of Multiplier Preferences," Econometrica, Econometric Society, vol. 79(1), pages 47-73, January.
    3. 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.
    4. Adam Dominiak & Jean-Philippe Lefort, 2021. "Ambiguity and Probabilistic information," Post-Print hal-04002664, HAL.
    5. Charles M. Harvey, 1986. "Value Functions for Infinite-Period Planning," Management Science, INFORMS, vol. 32(9), pages 1123-1139, September.
    6. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    7. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Dean, Mark & Ortoleva, Pietro, 2017. "Allais, Ellsberg, and preferences for hedging," Theoretical Economics, Econometric Society, vol. 12(1), January.
    13. Werner, Jan, 2005. "A simple axiomatization of risk-averse expected utility," Economics Letters, Elsevier, vol. 88(1), pages 73-77, July.
    14. 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.
    15. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    16. Mohammed Abdellaoui & Peter Wakker, 2005. "The Likelihood Method for Decision under Uncertainty," Theory and Decision, Springer, vol. 58(1), pages 3-76, February.
    17. 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.
    18. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    19. 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.
    20. Alon, Shiri & Schmeidler, David, 2014. "Purely subjective Maxmin Expected Utility," Journal of Economic Theory, Elsevier, vol. 152(C), pages 382-412.
    21. Mark J. Machina, 2014. "Ambiguity Aversion with Three or More Outcomes," American Economic Review, American Economic Association, vol. 104(12), pages 3814-3840, December.
    22. 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..
    23. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    24. 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.
    25. 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.
    26. 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.
    27. 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.
    28. Mark J. Machina, 2009. "Risk, Ambiguity, and the Rank-Dependence Axioms," American Economic Review, American Economic Association, vol. 99(1), pages 385-392, March.
    29. 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..
    30. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    31. Adam Dominiak & Jean-Philippe Lefort, 2021. "Ambiguity and Probabilistic information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-04002664, HAL.
    32. 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.
    33. 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.
    34. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-1280, November.
    35. 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.
    36. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
    37. Peter Fishburn & Ward Edwards, 1997. "Discount-neutral utility models for denumerable time streams," Theory and Decision, Springer, vol. 43(2), pages 139-166, September.
    38. 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.
    39. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
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