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Choquet Integrals and Belief Functions

Author

Listed:
  • Takao Asano

    (Okayama University)

  • Hiroyuki Kojima

    (Teikyo University)

Abstract

This paper investigates characterizations of a class of belief functions. Our main contributions are threefold. First, using the notion of invariant weights, we characterize the Choquet integral with respect to belief functions along the lines of Schmeidler (1986). Second, we directly derive a class of belief functions on a state space and a collection of events that determines whether Möbius inversions are strictly positive or zero. Third, we show that the derived collection is simple-complete.

Suggested Citation

  • Takao Asano & Hiroyuki Kojima, 2022. "Choquet Integrals and Belief Functions," KIER Working Papers 1077, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:1077
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    References listed on IDEAS

    as
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    5. Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 263-283, June.
    6. Michel Grabisch, 2016. "Set Functions, Games and Capacities in Decision Making," Theory and Decision Library C, Springer, number 978-3-319-30690-2, March.
    7. Gilboa, Itzhak, 1989. "Expectation and Variation in Multi-period Decisions," Econometrica, Econometric Society, vol. 57(5), pages 1153-1169, September.
    8. Sarin, Rakesh & Wakker, Peter P, 1998. "Revealed Likelihood and Knightian Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 16(3), pages 223-250, July-Aug..
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    Cited by:

    1. Takao Asano & Hiroyuki Kojima & Kaname Miyagishima, 2022. "A Simple Axiomatization of Neo-Additive Choquet Expected Utility Theory on a Finite State Space," KIER Working Papers 1080, Kyoto University, Institute of Economic Research.

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    More about this item

    Keywords

    Mobius inversions; Invariant weights; Simple-completeness;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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