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An additively separable representation in the Savage framework

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  • Brian, HILL

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Abstract

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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Bibliographic Info

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

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Keywords: Expected utility; additive representation; state-dependent utility; monotonicity;

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References

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  1. Karni, E. & Schmeidler, D., 1991. "On the Uniqueness of Subjective Probabilities," Papers 1-92, Tel Aviv - the Sackler Institute of Economic Studies.
  2. Karni Edi, 1993. "Subjective Expected Utility Theory with State-Dependent Preferences," Journal of Economic Theory, Elsevier, vol. 60(2), pages 428-438, August.
  3. Hill, Brian, 2009. "When is there state independence?," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1119-1134, May.
  4. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  5. Mohammed Abdellaoui & Peter Wakker, 2005. "The Likelihood Method for Decision under Uncertainty," Theory and Decision, Springer, vol. 58(1), pages 3-76, 02.
  6. Karni, Edi, 1996. "Probabilities and Beliefs," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 249-62, November.
  7. Erio Castagnoli & Marco LiCalzi, 2005. "Benchmarking real-valued acts," Microeconomics 0502001, EconWPA.
  8. Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-31, July.
  9. 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..
  10. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
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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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