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When is there state independence?

  • Brian, HILL

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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.

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Paper provided by HEC Paris in its series Les Cahiers de Recherche with number 883.

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Length: 883 pages
Date of creation: 22 Nov 2007
Date of revision:
Handle: RePEc:ebg:heccah:0883
Contact details of provider: Postal: HEC Paris, 78351 Jouy-en-Josas cedex, France
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  1. Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-31, July.
  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. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  4. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-98, January.
  5. Karni, Edi & Schmeidler, David, 1993. "On the Uniqueness of Subjective Probabilities," Economic Theory, Springer, vol. 3(2), pages 267-77, April.
  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. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
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