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Increasing Uncertainty: A Definition

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  • Grant, Simon

    (Rice U)

  • Quiggan, John

    (U of Queensland)

Abstract

We present a definition of increasing uncertainty, in which an elementary increase in the uncertainty of any act corresponds to the addition of an `elementary bet' that increases consumption by a fixed amount in (relatively) `good' states and decreases consumption by a fixed (and possibly different) amount in (relatively) `bad' states. This definition naturally gives rise to a dual definition of comparative aversion to uncertainty. We characterize this definition for a popular class of generalized models of choice under uncertainty.

Suggested Citation

  • Grant, Simon & Quiggan, John, 2004. "Increasing Uncertainty: A Definition," Working Papers 2002-11, Rice University, Department of Economics.
    • Handle: RePEc:ecl:riceco:2002-11
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    1. Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004. "Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547-571, August.
    2. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. Alain Chateauneuf & Michéle Cohen & Isaac Meilijson, 2005. "More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 649-667, April.
    5. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-1092, July.
    6. Paolo Ghirardato & Massimo Marinacci, 2001. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 864-890, November.
    7. Diamond, Peter A. & Stiglitz, Joseph E., 1974. "Increases in risk and in risk aversion," Journal of Economic Theory, Elsevier, vol. 8(3), pages 337-360, July.
    8. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
    9. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    10. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
    11. Chateauneuf, A. & Cohen, M. & Meilijson, I., 1997. "New Tools to Better Model Behavior Under Risk and UNcertainty: An Oevrview," Papiers d'Economie Mathématique et Applications 97.55, Université Panthéon-Sorbonne (Paris 1).
    12. Grant, Simon & Kajii, Atsushi & Polak, Ben, 1992. "Many good risks: An interpretation of multivariate risk and risk aversion without the Independence axiom," Journal of Economic Theory, Elsevier, vol. 56(2), pages 338-351, April.
    13. Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 197-213, September.
    14. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October.
    15. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    16. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    17. 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.
    18. 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.
    19. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
    20. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    21. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    22. Matthew J. Ryan, 2002. "What do uncertainty-averse decision-makers believe?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 47-65.
    23. Machina, Mark J & Pratt, John W, 1997. "Increasing Risk: Some Direct Constructions," Journal of Risk and Uncertainty, Springer, vol. 14(2), pages 103-127, March.
    24. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
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    Cited by:

    1. Gil-Lacruz, Ana I. & Gil-Lacruz, Marta, 2011. "Internal Inconsistency and Risk Aversion: Implications on Smoking Decisions/Consistencia interna y aversión al riesgo: implicaciones en la decisión de fumar," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 29, pages 387(18á.)-3, Abril.
    2. Johanna Etner & Meglena Jeleva & Jean‐Marc Tallon, 2012. "Decision Theory Under Ambiguity," Journal of Economic Surveys, Wiley Blackwell, vol. 26(2), pages 234-270, April.
    3. Bommier, Antoine & Chassagnon, Arnold & Le Grand, François, 2012. "Comparative risk aversion: A formal approach with applications to saving behavior," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1614-1641.
    4. Chambers, Robert G. & Melkonyan, Tigran, 2009. "Smoothing preference kinks with information," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 173-189, September.
    5. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    6. repec:awi:wpaper:0448 is not listed on IDEAS
    7. Heufer, Jan, 2014. "Nonparametric comparative revealed risk aversion," Journal of Economic Theory, Elsevier, vol. 153(C), pages 569-616.
    8. Zuber, Stéphane & Asheim, Geir B., 2012. "Justifying social discounting: The rank-discounted utilitarian approach," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1572-1601.
    9. Antoine Bommier & Francois Le Grand, "undated". "A Robust Approach to Risk Aversion," Working Papers ETH-RC-13-002, ETH Zurich, Chair of Systems Design.
    10. Antoine Bommier & Stéphane Zuber, 2012. "The Pareto Principle Of Optimal Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(2), pages 593-608, May.
    11. Michèle Cohen & Isaac Meilijson, 2014. "Preference for safety under the Choquet model: in search of a characterization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 619-642, April.
    12. Jean Baccelli & Georg Schollmeyer & Christoph Jansen, 2022. "Risk aversion over finite domains," Theory and Decision, Springer, vol. 93(2), pages 371-397, September.
    13. Pavlo Blavatskyy, 2021. "A measure of ambiguity (Knightian uncertainty)," Theory and Decision, Springer, vol. 91(2), pages 153-171, September.
    14. Eichberger, Jürgen & Kelsey, David, 2007. "Ambiguity," Papers 07-50, Sonderforschungsbreich 504.
    15. Marie-Charlotte Guetlein, 2016. "Comparative Risk Aversion in the Presence of Ambiguity," American Economic Journal: Microeconomics, American Economic Association, vol. 8(3), pages 51-63, August.

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    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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