When is there state independence?
AbstractIt 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by HEC Paris in its series Les Cahiers de Recherche with number 883.
Length: 883 pages
Date of creation: 22 Nov 2007
Date of revision:
Subjective expected utility; State-dependent utility; Monotonicity axiom;
Other versions of this item:
- C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-03-08 (All new papers)
- NEP-CDM-2008-03-08 (Collective Decision-Making)
- NEP-HPE-2008-03-08 (History & Philosophy of Economics)
- NEP-UPT-2008-03-08 (Utility Models & Prospect Theory)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Karni Edi, 1993. "Subjective Expected Utility Theory with State-Dependent Preferences," Journal of Economic Theory, Elsevier, vol. 60(2), pages 428-438, August.
- Karni, E. & Mongin, P., 1997.
"On the Determination of Subjective Probability by Choices,"
9737, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
- Edi Karni & Philippe Mongin, 2000. "On the Determination of Subjective Probability by Choices," Management Science, INFORMS, vol. 46(2), pages 233-248, February.
- E. Karni & Ph. Mongin, 1997. "On the determination of subjective probability by choices," THEMA Working Papers 97-37, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-98, January.
- Karni, Edi & Schmeidler, David, 1993.
"On the Uniqueness of Subjective Probabilities,"
Springer, vol. 3(2), pages 267-77, April.
- Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-31, July.
- Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
- F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
- Hill, Brian, 2010.
"An additively separable representation in the Savage framework,"
Journal of Economic Theory,
Elsevier, vol. 145(5), pages 2044-2054, September.
- Brian, HILL, 2007. "An additively separable representation in the Savage framework," Les Cahiers de Recherche 882, HEC Paris.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sandra Dupouy).
If references are entirely missing, you can add them using this form.