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Random Sets Lotteries and Decision Theory


  • Marc-Arthur Diaye

    () (EPEE, Université d’Evry-Val-d’Essonne)

  • Gleb Koshevoy

    () (Central Institute of Economics and Mathematics, Russian Academy of Sciences)


Even if its roots are much older, random sets theory has been considered as an academic area, part of stochastic geometry, since Matheron [7]. Random sets theory was first applied in some fields related to engineering sciences like geology, image analysis and expert systems (see Goutsias et al. [4]), and recently in non-parametric statistics (Koshevoy et al. [5]) or also (see Molchanov [9]) in economic theory (for instance in finance and game the- ory) and in econometrics (for instance in linear models with interval-valued dependent or independent variables). We apply in this paper random sets theory to decision making. Our main result states that under a kind of vNM condition decision making for an arbitrary random set lottery reduces to de- cision making for a single-valued random set lottery, and the latter set is the set-valued expectation of the former random set. Through experiments in a laboratory, we observe consistency of decision making for ordering random sets with fixed act and varied random sets.

Suggested Citation

  • Marc-Arthur Diaye & Gleb Koshevoy, 2011. "Random Sets Lotteries and Decision Theory," Documents de recherche 11-09, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
  • Handle: RePEc:eve:wpaper:11-09

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    References listed on IDEAS

    1. Bewley, Truman F., 2011. "Knightian decision theory and econometric inferences," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1134-1147, May.
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    More about this item


    Knightian decision maker; Choquet-type decision maker; Random sets; Set-valued expectation;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General


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