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Moral Hazard, the Savage Framework, and State-Dependent Utility

  • Jean BaccelliEmail author
Original Research


In this paper, I investigate the betting behavior of a decision-maker who can influence the likelihood of the events upon which she is betting. In decision theory, this is best known as a situation of moral hazard. Focusing on a particularly simple case, I sketch the first systematic analysis of moral hazard in the canonical Savage framework. From the results of this analysis, I draw two philosophical conclusions. First, from an observational and a descriptive point of view, there need to be no incompatibility between moral hazard and the Savage framework. This qualifies the incompatibility view, that is ubiquitous in decision theory. Second, in general, moral hazard is not sufficient to overcome the challenges posed by state-dependent utility to the behavioral identification of beliefs. This qualifies the sufficiency view, that is influential in decision theory. These two philosophical conclusions are the main contributions of my paper.



Funding was provided by the Wagemann Foundation and the Ludwig-Maximilians-Universität München.


  1. Alon, S. (2015). Worst-case expected utility. Journal of Mathematical Economics, 60, 43–48.Google Scholar
  2. Alon, S., & Schmeidler, D. (2014). Purely subjective maxmin expected utility. Journal of Economic Theory, 152, 382–412.Google Scholar
  3. Anscombe, F., & Aumann, R. (1963). A definition of subjective probability. The Annals of Mathematical Statistics, 34(1), 199–205.Google Scholar
  4. Baccelli, J. (2017). Do bets reveal beliefs? Synthese, 194(9), 3393–3419.Google Scholar
  5. Cerreia-Vioglio, S., Maccheroni, F., Marinacci, M., & Montrucchio, L. (2011). Uncertainty averse preferences. Journal of Economic Theory, 146(4), 1275–1330.Google Scholar
  6. Dillenberger, D., Postlewaite, A., & Rozen, K. (2017). Optimism and pessimism with expected utility. Journal of the European Economic Association, 15(5), 1158–1175.Google Scholar
  7. Drèze, J. (1961). “Les fondements logiques de la probabilité subjective et de l’utilité”, La décision. In Colloques Internationaux du Centre National de la Recherche Scientifique (pp. 73–87).Google Scholar
  8. Drèze, J. (1987a). Decision theory with moral hazard and state-dependent preferences. In J. Drèze (Ed.), Essays on economic decisions under uncertainty (pp. 23–89). Cambridge: Cambridge University Press.Google Scholar
  9. Drèze, J. (1987b). Logical foundations of cardinal utility and subjective probability. In J. Drèze (Ed.), Essays on economic decisions under uncertainty (pp. 90–104). Cambridge: Cambridge University Press.Google Scholar
  10. Drèze, J., & Rustichini, A. (1999). Moral hazard and conditional preferences. Journal of Mathematical Economics, 31(2), 159–181.Google Scholar
  11. Drèze, J., & Rustichini, A. (2004). State-dependent utility theory. In S. Barbera, P. Hammond, & C. Seidl (Eds.), Handbook of utility theory, volume II: Extensions (pp. 839–892). Boston: Kluwer Academic Press.Google Scholar
  12. Ellsberg, D. (1961). Risk, ambiguity, and the Savage axioms. The Quarterly Journal of Economics, 75(4), 643–669.Google Scholar
  13. Epstein, L., & Le Breton, M. (1993). Dynamically consistent beliefs must be Bayesian. Journal of Economic Theory, 61(1), 1–22.Google Scholar
  14. Finkelstein, A., Luttmer, E., & Notowidigdo, M. (2013). What good is wealth without health? The effect of health on the marginal utility of consumption. Journal of the European Economic Association, 11(1), 221–258.Google Scholar
  15. Fishburn, P. (1970). Utility theory for decision making. New York: Wiley.Google Scholar
  16. Gaifman, H. (1999). Self-reference and the acyclicity of rational choice. Annals of Pure and Applied Logic, 96(1–3), 117–140.Google Scholar
  17. Ghirardato, P., & Marinacci, M. (2001). Risk, ambiguity, and the separation of utility and beliefs. Mathematics of Operations Research, 26(4), 864–890.Google Scholar
  18. Gilboa, I., & Schmeidler, D. (1989). Maxmin expected utility with non-unique prior. Journal of Mathematical Economics, 18(2), 141–153.Google Scholar
  19. Hart, O., & Hölmstrom, B. (1987). The theory of contracts. In T. Bewley (Ed.), Advances in economic theory (pp. 71–155). Cambridge: Cambridge University Press.Google Scholar
  20. Hart, S., Modica, S., & Schmeidler, D. (1994). A \(\text{ Neo }^{2}\) Bayesian foundation of the maxmin value for two-person zero-sum games. International Journal of Game Theory, 23(4), 347–358.Google Scholar
  21. Hill, B. (2009). When is there state independence? Journal of Economic Theory, 144(3), 1119–1134.Google Scholar
  22. Jeffrey, R. (1965). The logic of decision (1st ed.). New York: McGraw-Hill Book Company.Google Scholar
  23. Jeffrey, R. (1983). The logic of decision (2nd ed.). Chicago: Chicago University Press.Google Scholar
  24. Joyce, J. (1999). The foundations of causal decision theory. New York: Cambridge University Press.Google Scholar
  25. Karni, E. (1992). Subjective probabilities and utility with event-dependent preferences. Journal of Risk and Uncertainty, 5(2), 107–125.Google Scholar
  26. Karni, E. (1993). Subjective expected utility theory with state-dependent preferences. Journal of Economic Theory, 60(2), 428–438.Google Scholar
  27. Karni, E. (1996). Probabilities and beliefs. Journal of Risk and Uncertainty, 13(3), 249–262.Google Scholar
  28. Karni, E. (2006). Subjective expected utility theory without states of the world. Journal of Mathematical Economics, 42(3), 325–342.Google Scholar
  29. Karni, E. (2008). State-dependent utility. In P. Anand, P. Pattanaik, & C. Puppe (Eds.), The handbook of rational and social choice (pp. 223–238). Oxford: Oxford University Press.Google Scholar
  30. Karni, E. (2011a). Subjective probabilities on a state space. American Economic Journal: Microeconomics, 3(4), 172–185.Google Scholar
  31. Karni, E. (2011b). A theory of Bayesian decision making with action-dependent subjective probabilities. Economic Theory, 48(1), 125–146.Google Scholar
  32. Karni, E. (2013). Bayesian decision theory with action-dependent probabilities and risk attitudes. Economic Theory, 53(2), 335–356.Google Scholar
  33. Köbberling, V., & Wakker, P. (2003). Preference foundations for nonexpected utility: A generalized and simplified technique. Mathematics of Operations Research, 28(3), 395–423.Google Scholar
  34. Levi, I. (1993). Rationality, prediction, and autonomous choice. Canadian Journal of Philosophy, 23(suppl.), 339–363.Google Scholar
  35. Lu, J. (2016). A Bayesian theory of state-dependent utilities. Working paper. Accessed 7 Feb 2019.
  36. Nau, R. (2001). de Finetti was right: Probability does not exist. Theory and Decision, 51(2–4), 89–124.Google Scholar
  37. Savage, L. (1954). The foundations of statistics (1st ed.). New York: Wiley.Google Scholar
  38. Savage, L. (1972). The foundations of statistics (2nd ed.). New York: Dover.Google Scholar
  39. Schervish, M., Seidenfeld, T., & Kadane, J. (1990). State-dependent utilities. Journal of the American Statistical Association, 85(411), 840–847.Google Scholar
  40. Spohn, W. (1977). Where Luce and Krantz do really generalize Savage’s decision model. Erkenntnis, 11(1), 113–134.Google Scholar
  41. Wakker, P. (2010). Prospect theory-for risk and ambiguity. Cambridge: Cambridge University Press.Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Munich Center for Mathematical PhilosophyMunichGermany

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