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A Theory of Bayesian Decision Making

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  • Edi Karni

    (Johns Hopkins University)

Abstract

This paper presents a complete, choice-based, axiomatic Bayesian decision theory. It introduces a new choice set consisting of information-contingent plans for choosing actions and bets and subjective expected utility model with effect-dependent utility functions and action-dependent subjective probabilities which, in conjunction with the updating of the probabilities using Bayes’ rule, gives rise to a unique prior and a set of action-dependent posterior probabilities representing the decision maker’s prior and posterior beliefs.

Suggested Citation

  • Edi Karni, 2009. "A Theory of Bayesian Decision Making," EIEF Working Papers Series 0904, Einaudi Institute for Economics and Finance (EIEF), revised May 2009.
  • Handle: RePEc:eie:wpaper:0904
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    References listed on IDEAS

    as
    1. Machina Mark J. & Schmeidler David, 1995. "Bayes without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice," Journal of Economic Theory, Elsevier, vol. 67(1), pages 106-128, October.
    2. Karni, Edi, 1996. "Probabilities and Beliefs," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 249-262, November.
    3. Hill, Brian, 2010. "An additively separable representation in the Savage framework," Journal of Economic Theory, Elsevier, vol. 145(5), pages 2044-2054, September.
    4. Karni, Edi, 2006. "Subjective expected utility theory without states of the world," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 325-342, June.
    5. Karni, Edi & Schmeidler, David, 1993. "On the Uniqueness of Subjective Probabilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 267-277, April.
    6. Edi Karni, 2008. "On Optimal Insurance in the Presence of Moral Hazard*," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 33(1), pages 1-18, June.
    7. Nau, Robert F, 1995. "Coherent Decision Analysis with Inseparable Probabilities and Utilities," Journal of Risk and Uncertainty, Springer, vol. 10(1), pages 71-91, January.
    8. Wakker, Peter, 1987. "Subjective probabilities for state dependent continuous utility," Mathematical Social Sciences, Elsevier, vol. 14(3), pages 289-298, December.
    9. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
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