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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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 145 (2010)
Issue (Month): 5 (September)
Pages: 2044-2054

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Handle: RePEc:eee:jetheo:v:145:y:2010:i:5:p:2044-2054

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Expected utility Additive representation State-dependent utility Monotonicity;

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References

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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. Karni, Edi & Schmeidler, David, 1993. "On the Uniqueness of Subjective Probabilities," Economic Theory, Springer, vol. 3(2), pages 267-77, April.
  3. Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-31, July.
  4. Karni Edi, 1993. "Subjective Expected Utility Theory with State-Dependent Preferences," Journal of Economic Theory, Elsevier, vol. 60(2), pages 428-438, August.
  5. Karni, Edi, 1996. "Probabilities and Beliefs," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 249-62, November.
  6. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  7. Karni, E. & Mongin, P., 1997. "On the Determination of Subjective Probability by Choices," Papers 9737, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  8. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
  9. Erio Castagnoli & Marco LiCalzi, 2005. "Benchmarking real-valued acts," Microeconomics 0502001, EconWPA.
  10. Mohammed Abdellaoui & Peter Wakker, 2005. "The Likelihood Method for Decision under Uncertainty," Theory and Decision, Springer, vol. 58(1), pages 3-76, 02.
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Cited by:
  1. Edi Karni, 2009. "A Theory of Bayesian Decision Making," EIEF Working Papers Series 0904, Einaudi Institute for Economics and Finance (EIEF), revised May 2009.
  2. Edi Karni, 2009. "A Theory of Bayesian Decision Making," Economics Working Paper Archive 550, The Johns Hopkins University,Department of Economics.

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