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Markovian Dependence in Utility Theory with Whole Product Sets

Author

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  • Peter C. Fishburn

    (Research Analysis Corporation, McLean, Virginia)

Abstract

This paper takes the notion of Markovian dependence, so well-known in the study of stochastic processes, and uses it in a study of utility theory for sequential processes. Markovian dependence in the utility sense is defined on the basis of indifference between special types of gambles for several sequential processes. Theorems that state how the basic utility function may be broken up into an additive form under Markovian dependence are presented. In addition, the notion of stationary transition value mechanisms is explored in the context of completely homogeneous sequential decision processes.

Suggested Citation

  • Peter C. Fishburn, 1965. "Markovian Dependence in Utility Theory with Whole Product Sets," Operations Research, INFORMS, vol. 13(2), pages 238-257, April.
    • Handle: RePEc:inm:oropre:v:13:y:1965:i:2:p:238-257
    DOI: 10.1287/opre.13.2.238
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    Cited by:

    1. E. S. Levine, 2012. "Estimating Conditional Probabilities of Terrorist Attacks: Modeling Adversaries with Uncertain Value Tradeoffs," Risk Analysis, John Wiley & Sons, vol. 32(2), pages 294-303, February.
    2. Ralph L. Keeney, 2007. "Modeling Values for Anti‐Terrorism Analysis," Risk Analysis, John Wiley & Sons, vol. 27(3), pages 585-596, June.
    3. Pauline Vorjohann, 2023. "Reference-dependent choice bracketing," Discussion Papers 2309, University of Exeter, Department of Economics.
    4. Miley W. Merkhofer & Ralph L. Keeney, 1987. "A Multiattribute Utility Analysis of Alternative Sites for the Disposal of Nuclear Waste," Risk Analysis, John Wiley & Sons, vol. 7(2), pages 173-194, June.
    5. Vicki Bier, 2020. "The Role of Decision Analysis in Risk Analysis: A Retrospective," Risk Analysis, John Wiley & Sons, vol. 40(S1), pages 2207-2217, November.
    6. Gordon B. Hazen, 2007. "Adding Extrinsic Goals to the Quality-Adjusted Life Year Model," Decision Analysis, INFORMS, vol. 4(1), pages 3-16, March.

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