Theory and Decision

, Volume 81, Issue 4, pp 467–478 | Cite as

An expected utility theory for state-dependent preferences



This note is a generalization and improved interpretation of the main result of Karni and Schmeidler (An Expected utility theory for state-dependent preferences. Working paper no. 48-80 of the Foerder Institute for Economic Research, Faculty of Social Sciences, Tel Aviv University, 1980). A decision-maker is supposed to possess a preference relation on acts and another preference relation on state-prize lotteries, both of which are assumed to satisfy the von Neumann–Morgenstern axioms. In addition, the two preference relations restricted to a state of nature are assumed to agree. We show that these axioms are necessary and sufficient for the existence of subjective expected utility over acts with state-dependent utility functions and a subjective probability measure. This subjective probability measure is unique when conditioned on the set of states of nature in which not all the prizes are equally desirable.


Subjective expected utility State-dependent preferences  State-dependent utility Subjective probabilities 


  1. Anscombe, F. J., & Aumann, R. J. (1963). A definition of subjective probability. Annals of Mathematical Statistics, 43, 199–205.CrossRefGoogle Scholar
  2. Baccelli, J. (2016). Do bets reveal beliefs? A unified perspective on state-dependent utility issues. Synthese.Google Scholar
  3. Cook, P. J., & Graham, D. A. (1977). The demand of insurance and protection: the case of irreplaceable commodities. Quarterly Journal of Economics, 91, 143–156.CrossRefGoogle Scholar
  4. Drèze, J. H. (1987). Decision theory wit moral hazard and state-dependent preferences. In Essays on economic decisions under uncertainty. Cambridge: Cambridge University Press.Google Scholar
  5. Dreze, J. H., & Rustichini, A. (2004). State dependent utility and decision theory. In S. Barbera, P. Hammond, & C. Seidl (Eds.), Handbook of utility theory: volume 2 extensions (pp. 839–892). New York: Springer.CrossRefGoogle Scholar
  6. Fishburn, P. C. (1970). Utility theory for decision making. New York: Wiley.Google Scholar
  7. Fishburn, P. C. (1973). A mixture-set axiomatization of conditional subjective expected utility. Econometrica, 41, 1–25.CrossRefGoogle Scholar
  8. Fishburn, P. C. (1974). On the foundations of decision making under uncertainty. In M. S. Balch, D. L. McFadden, & S. Y. Wu (Eds.), Essays on economic behavior under uncertainty. Amsterdam: North-Holland.Google Scholar
  9. Hirshleifer, J., & Riley, J. G. (1979). The analytics of uncertainty and information—an expository survey. Journal of Economic Literature, 17, 1375–1421.Google Scholar
  10. Karni, E. (1985). Decision making under uncertainty: the case of state-dependent preferences. Cambridge: Harvard University Press.CrossRefGoogle Scholar
  11. Karni, E. (2009). State-dependent utility. In P. Anand, P. K. Pattanaik, & C. Puppe (Eds.), Handbook of rational and social choice. Oxford: Oxford University Press.Google Scholar
  12. Karni, E., & Mongin, P. (2000). On the Determination of subjective probability by choice. Management Science, 46, 233–248.CrossRefGoogle Scholar
  13. Karni, E., & Safra, Z. (2016). A theory of stochastic choice under uncertianty. Journal of Mathematical Economics (forthcoming).Google Scholar
  14. Karni, E., & Schmeidler, D. (1980). An Expected utility theory for state-dependent preferences. Working paper no. 48–80 of the Foerder Institute for Economic Research, Faculty of Social Sciences, Tel Aviv University.Google Scholar
  15. Karni, E., Schmeidler, D., & Vind, K. (1983). On state dependent preferences and subjective probabilities. Econometrica, 51, 1021–1032.CrossRefGoogle Scholar
  16. Lu, J. (2015). A Bayesian theory of state-dependent utilities. (unpublished).Google Scholar
  17. Nau, R. (2001). De Finetti was right: probability does not exist. Theory and Decision, pp. 89–124.Google Scholar
  18. Riedener, S. (2015). Maximising expected value under axiological uncertainty an axiomatic approach. PhD dissertation.Google Scholar
  19. Savage, L. J. (1954). The foundations of statistics. New York: Wiley.Google Scholar
  20. von Neumann, J., & Morgenstern, O. (1947). Theory of games and economic behavior. Princeton: Princeton University Press.Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Johns Hopkins UniversityBaltimoreUSA
  2. 2.University of WarwickCoventryUK
  3. 3.Tel Aviv UniversityTel AvivIsrael

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