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Random Sets Lotteries and Decision Theory

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  • Marc-Arthur Diaye

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

  • Gleb Koshevoy

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

Abstract

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.

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File URL: http://epee.univ-evry.fr/RePEc/2011/11-09.pdf
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Bibliographic Info

Paper provided by Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne in its series Documents de recherche with number 11-09.

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Length: 27 pages
Date of creation: Oct 2011
Date of revision:
Handle: RePEc:eve:wpaper:11-09

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Related research

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

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  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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