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An Expected Utility Theory for State-Dependent Preferences

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  • Karni, Edi
  • Schmeidler, David

Abstract

This note is a generalization and improved interpretation of the main result of Karni and Schmeidler (An Expected utility theory for state-dependent preferences. Working paper no. 48-80 of the Foerder Institute for Economic Research, Faculty of Social Sciences, Tel Aviv University, 1980). A decision-maker is supposed to possess a preference relation on acts and another preference relation on state-prize lotteries, both of which are assumed to satisfy the von Neumann–Morgenstern axioms. In addition, the two preference relations restricted to a state of nature are assumed to agree. We show that these axioms are necessary and sufficient for the existence of subjective expected utility over acts with state-dependent utility functions and a subjective probability measure. This subjective probability measure is unique when conditioned on the set of states of nature in which not all the prizes are equally desirable.
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Suggested Citation

  • Karni, Edi & Schmeidler, David, 1980. "An Expected Utility Theory for State-Dependent Preferences," Foerder Institute for Economic Research Working Papers 275328, Tel-Aviv University > Foerder Institute for Economic Research.
    • Handle: RePEc:ags:isfiwp:275328
    DOI: 10.22004/ag.econ.275328
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    References listed on IDEAS

    as
    1. Edi Karni & David Schmeidler, 2016. "An expected utility theory for state-dependent preferences," Theory and Decision, Springer, vol. 81(4), pages 467-478, November.
    2. Fishburn, Peter C, 1973. "A Mixture-Set Axiomatization of Conditional Subjective Expected Utility," Econometrica, Econometric Society, vol. 41(1), pages 1-25, January.
    3. Robert Nau, 2001. "De Finetti was Right: Probability Does Not Exist," Theory and Decision, Springer, vol. 51(2), pages 89-124, December.
    4. Hirshleifer, J & Riley, John G, 1979. "The Analytics of Uncertainty and Information-An Expository Survey," Journal of Economic Literature, American Economic Association, vol. 17(4), pages 1375-1421, December.
    5. Edi Karni & Philippe Mongin, 2000. "On the Determination of Subjective Probability by Choices," Management Science, INFORMS, vol. 46(2), pages 233-248, February.
    6. Karni, Edi, 1983. "Risk Aversion for State-Dependent Utility Functions: Measurement and Applications," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 637-647, October.
    7. Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-1031, July.
    8. Karni, Edi & Safra, Zvi, 2016. "A theory of stochastic choice under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 164-173.
    9. Philip J. Cook & Daniel A. Graham, 1977. "The Demand for Insurance and Protection: The Case of Irreplaceable Commodities," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(1), pages 143-156.
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    Cited by:

    1. Chew, Soo Hong & Wang, Wenqian, 2020. "On the robustness of indeterminacy in subjective probability," Economics Letters, Elsevier, vol. 188(C).
    2. Assa, Hirbod & Zimper, Alexander, 2018. "Preferences over all random variables: Incompatibility of convexity and continuity," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 71-83.
    3. Grant, Simon & Karni, Edi, 2004. "A theory of quantifiable beliefs," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 515-546, August.
    4. Elias Tsakas, 2022. "Belief identification with state-dependent utilities," Papers 2203.10505, arXiv.org, revised Nov 2022.
    5. Edi Karni & David Schmeidler, 2016. "An expected utility theory for state-dependent preferences," Theory and Decision, Springer, vol. 81(4), pages 467-478, November.
    6. Jean Baccelli, 2019. "The Problem of State-Dependent Utility: A Reappraisal," Post-Print hal-02172207, HAL.
    7. Karni, Edi, 2020. "On the indeterminacy of the representation of beliefs by probabilities," Economics Letters, Elsevier, vol. 196(C).
    8. Karni, Edi & Safra, Zvi, 2016. "A theory of stochastic choice under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 164-173.
    9. Elias Tsakas, 2023. "Belief identification by proxy," Papers 2311.13394, arXiv.org.
    10. Urmee Khan, 2016. "State-dependent Preferences in Prediction Markets and Prices as Aggregate Statistic," Studies in Microeconomics, , vol. 4(1), pages 70-77, June.
    11. Vilkkumaa, Eeva & Liesiö, Juuso & Salo, Ahti & Ilmola-Sheppard, Leena, 2018. "Scenario-based portfolio model for building robust and proactive strategies," European Journal of Operational Research, Elsevier, vol. 266(1), pages 205-220.

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