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An additively separable representation in the Savage framework

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  • Hill, Brian

Abstract

This paper proposes necessary and sufficient conditions for an additively separable representation of preferences in the Savage framework (where the objects of choice are acts: measurable functions from an infinite set of states to a potentially finite set of consequences). A preference relation over acts is represented by the integral over the subset of the product of the state space and the consequence space which corresponds to the act, where this integral is calculated with respect to an evaluation measure on this space. The result requires neither Savage's P3 (monotonicity) nor his P4 (weak comparative probability). Nevertheless, the representation it provides is as useful as Savage's for many economic applications.

Suggested Citation

  • Hill, Brian, 2010. "An additively separable representation in the Savage framework," Journal of Economic Theory, Elsevier, vol. 145(5), pages 2044-2054, September.
  • Handle: RePEc:eee:jetheo:v:145:y:2010:i:5:p:2044-2054
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    References listed on IDEAS

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    1. Hill, Brian, 2009. "When is there state independence?," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1119-1134, May.
    2. Castagnoli, Erio & LiCalzi, Marco, 2006. "Benchmarking real-valued acts," Games and Economic Behavior, Elsevier, vol. 57(2), pages 236-253, November.
    3. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," Review of Economic Studies, Oxford University Press, vol. 23(3), pages 165-180.
    4. Karni, Edi, 1996. "Probabilities and Beliefs," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 249-262, November.
    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. Mohammed Abdellaoui & Peter Wakker, 2005. "The Likelihood Method for Decision under Uncertainty," Theory and Decision, Springer, vol. 58(1), pages 3-76, February.
    7. Gilboa, Itzhak, 1985. "Expected Utility with Purely Subjective Non-Additive Probabilities," Foerder Institute for Economic Research Working Papers 275389, Tel-Aviv University > Foerder Institute for Economic Research.
    8. 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.
    9. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    10. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
    11. Karni Edi, 1993. "Subjective Expected Utility Theory with State-Dependent Preferences," Journal of Economic Theory, Elsevier, vol. 60(2), pages 428-438, August.
    12. Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-1031, July.
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    Cited by:

    1. Ganguli, Jayant & Heifetz, Aviad & Lee, Byung Soo, 2016. "Universal interactive preferences," Journal of Economic Theory, Elsevier, vol. 162(C), pages 237-260.
    2. Edi Karni, 2009. "A Theory of Bayesian Decision Making," EIEF Working Papers Series 0904, Einaudi Institute for Economics and Finance (EIEF), revised May 2009.

    More about this item

    Keywords

    Expected utility Additive representation State-dependent utility Monotonicity;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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