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State-dependent utility and decision theory

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  • DREZE , Jacques H.
  • RUSTICHINI, Aldo

Abstract

This survey paper prepared for the Handbook of Utility Theory covers the axiomatic foundations of decision making under uncertainty when conditional preferences are allowed to be state dependent, leading to an expected state-dependent utility representation. In the context of games against nature, subjective probabilities are not identified from observable choices among games, suggesting recourse to hypothetical preferences. In the context of one-person games with moral hazard, a generalised representation theorem (proved in the Appendix) asserts the existence of a closed convex set O of probabilities in the state space. Choices among games, with associated unobservable strategies, correspond to expected state-dependent utility maximisation, with probabilities chosen in the set O. When that set is full-dimensional, it is uniquely identified. Otherwise, identification is partial, suggesting again recourse to hypothetical preferences, as per a revised version of "conditional expected utility theory". The extent to which the state-dependent utility is identified is the same as that prevailing for the probabilities. The paper includes a discussion of risk aversion with state-dependent preferences; it concludes with a brief survey of applications to the demand for life insurance (a context of games against nature) and for safety (a context of one-person games with moral hazard).

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2000007.

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Date of creation: 01 Feb 2000
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Handle: RePEc:cor:louvco:2000007

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  1. Edi Karni & Philippe Mongin, 2000. "On the Determination of Subjective Probability by Choices," Management Science, INFORMS, vol. 46(2), pages 233-248, February.
  2. RUSTICHINI, Aldo & DREZE, Jacques H., 1994. "State Dependent Utility," CORE Discussion Papers 1994043, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Lanoie, Paul & Pedro, Carmen & Latour, Robert, 1995. "The Value of a Statistical Life: A Comparison of Two Approaches," Journal of Risk and Uncertainty, Springer, vol. 10(3), pages 235-57, May.
  4. Jones-Lee, M W & Hammerton, M & Philips, P R, 1985. "The Value of Safety: Results of a National Sample Survey," Economic Journal, Royal Economic Society, vol. 95(377), pages 49-72, March.
  5. Cook, Philip J & Graham, Daniel A, 1977. "The Demand for Insurance and Protection: The Case of Irreplaceable Commodities," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 143-56, February.
  6. Viscusi, W Kip, 1993. "The Value of Risks to Life and Health," Journal of Economic Literature, American Economic Association, vol. 31(4), pages 1912-46, December.
  7. Biswas, Tapan, 1983. "A note on the generalised measures of risk aversion," Journal of Economic Theory, Elsevier, vol. 29(2), pages 347-352, April.
  8. Krupnick, Alan J & Cropper, Maureen L, 1992. " The Effect of Information on Health Risk Valuations," Journal of Risk and Uncertainty, Springer, vol. 5(1), pages 29-48, February.
  9. Hanoch, Giora, 1977. "Risk Aversion and Consumer Preferences," Econometrica, Econometric Society, vol. 45(2), pages 413-26, March.
  10. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-98, January.
  11. Kniesner, Thomas J & Leeth, John D, 1991. " Compensating Wage Differentials for Fatal Injury Risk in Australia, Japan, and the United States," Journal of Risk and Uncertainty, Springer, vol. 4(1), pages 75-90, January.
  12. Mishan, E J, 1971. "Evaluation of Life and Limb: A Theoretical Approach," Journal of Political Economy, University of Chicago Press, vol. 79(4), pages 687-705, July-Aug..
  13. Deschamps, Robert, 1973. "Risk Aversion and Demand Functions," Econometrica, Econometric Society, vol. 41(3), pages 455-65, May.
  14. DREZE, Jacques H. & RUSTICHINI, Aldo, 1995. "Moral Hazard and Conditional Preferences," CORE Discussion Papers 1995010, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
  16. Milleron, Jean-Claude, 1972. "Theory of value with public goods: A survey article," Journal of Economic Theory, Elsevier, vol. 5(3), pages 419-477, December.
  17. Mirman, Leonard J, 1971. "Uncertainty and Optimal Consumption Decisions," Econometrica, Econometric Society, vol. 39(1), pages 179-85, January.
  18. Villeneuve, Bertrand, 2000. "Life Insurance," Economics Papers from University Paris Dauphine 123456789/5369, Paris Dauphine University.
  19. Grossman, Michael, 1972. "On the Concept of Health Capital and the Demand for Health," Journal of Political Economy, University of Chicago Press, vol. 80(2), pages 223-55, March-Apr.
  20. Johannesson, Magnus & Johansson, Per-Olov, 1996. "To Be, or Not to Be, That Is the Question: An Empirical Study of the WTP for an Increased Life Expectancy at an Advanced Age," Journal of Risk and Uncertainty, Springer, vol. 13(2), pages 163-74, September.
  21. Karni, Edi, 1979. "On Multivariate Risk Aversion," Econometrica, Econometric Society, vol. 47(6), pages 1391-1401, November.
  22. Karni, Edi, 1983. "On the correspondence between multivariate risk aversion and risk aversion with state-dependent preferences," Journal of Economic Theory, Elsevier, vol. 30(2), pages 230-242, August.
  23. Stiglitz, Joseph E, 1969. "Behavior Towards Risk with Many Commodities," Econometrica, Econometric Society, vol. 37(4), pages 660-67, October.
  24. Broder, Ivy E, 1990. " The Cost of Accidental Death: A Capital Market Approach," Journal of Risk and Uncertainty, Springer, vol. 3(1), pages 51-63, March.
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