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.
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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)
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- Hill, Brian, 2010. "An additively separable representation in the Savage framework," Journal of Economic Theory, Elsevier, vol. 145(5), pages 2044-2054, September.
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