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When is there state independence?

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  • Brian Hill

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

Abstract

It has been noticed that whether a preference relation can be represented by state-independent utilities as opposed to state-dependent utilities may depend on which acts count as constant acts [Schervish et al., 1990]. Indeed, this remark underlies an extension of Savage's expected utility theory to the state-dependent case that was proposed by Edi Karni [Karni, 1993]. This paper contains a characterisation of the preference relations that permit a choice of acts which can play the role of constant acts, and relative to which there is a representation involving a state-independent utility function. This result applies both in the Savage and in the Anscombe & Aumann frameworks. It has as an immediate corollary an extension of Karni's representation theorem. Finally, it is of methodological interest, insofar that it harnesses techniques from mathematical logic to prove a theorem of interest to decision theorists and economists.

Suggested Citation

  • Brian Hill, 2007. "When is there state independence?," Working Papers hal-00582662, HAL.
    • Handle: RePEc:hal:wpaper:hal-00582662
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    References listed on IDEAS

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    1. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    2. Edi Karni & Philippe Mongin, 2000. "On the Determination of Subjective Probability by Choices," Management Science, INFORMS, vol. 46(2), pages 233-248, February.
    3. Karni, Edi & Schmeidler, David, 1993. "On the Uniqueness of Subjective Probabilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 267-277, April.
    4. Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-1031, July.
    5. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
    6. Karni Edi, 1993. "Subjective Expected Utility Theory with State-Dependent Preferences," Journal of Economic Theory, Elsevier, vol. 60(2), pages 428-438, August.
    7. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-198, January.
    8. Peter P. Wakker & Horst Zank, 1999. "State Dependent Expected Utility for Savage's State Space," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 8-34, February.
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    Cited by:

    1. Jean Baccelli, 2015. "Do Bets Reveal Beliefs?," Post-Print hal-01462293, HAL.
    2. Hill, Brian, 2010. "An additively separable representation in the Savage framework," Journal of Economic Theory, Elsevier, vol. 145(5), pages 2044-2054, September.
    3. Jean Baccelli, 2019. "The Problem of State-Dependent Utility: A Reappraisal," Post-Print hal-02172207, HAL.

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    More about this item

    Keywords

    Subjective expected utility; State-dependent utility; Monotonicity axiom;
    All these keywords.

    JEL classification:

    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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