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An additively separable representation in the Savage framework

  • Brian, HILL

    ()

This paper elicits 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 a “state-dependent utility” measure on this space. The result applies at the stage prior to the separation of probabilities and utilities, and requires neither Savage’s P3 (monotonicity) nor his P4 (likelihood ordering). It may thus prove useful for the development of state-dependent utility representation theorems in the Savage framework.

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File URL: http://www.hec.fr/var/fre/storage/original/application/6ca5daddd4fcf95986020ee53ae97635.pdf
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Paper provided by HEC Paris in its series Les Cahiers de Recherche with number 882.

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Length: 14 pages
Date of creation: 29 Oct 2007
Date of revision:
Handle: RePEc:ebg:heccah:0882
Contact details of provider: Postal: HEC Paris, 78351 Jouy-en-Josas cedex, France
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  1. 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..
  2. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  3. Karni, Edi, 1996. "Probabilities and Beliefs," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 249-62, November.
  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 & Schmeidler, David, 1993. "On the Uniqueness of Subjective Probabilities," Economic Theory, Springer, vol. 3(2), pages 267-77, April.
  6. Castagnoli, Erio & LiCalzi, Marco, 2006. "Benchmarking real-valued acts," Games and Economic Behavior, Elsevier, vol. 57(2), pages 236-253, November.
  7. Hill, Brian, 2009. "When is there state independence?," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1119-1134, May.
  8. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
  9. Mohammed Abdellaoui & Peter Wakker, 2005. "The Likelihood Method for Decision under Uncertainty," Theory and Decision, Springer, vol. 58(1), pages 3-76, 02.
  10. Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-31, July.
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