Random Sets Lotteries and Decision Theory

Marc-Arthur Diaye () and Gleb Koshevoy ()
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Gleb Koshevoy: Central Institute of Economics and Mathematics, Russian Academy of Sciences

No 11-09, Documents de recherche from Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne

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.

Keywords: Knightian decision maker; Choquet-type decision maker; Random sets; Set-valued expectation (search for similar items in EconPapers)
JEL-codes: C10 C91 D01 D81 (search for similar items in EconPapers)
Pages: 27 pages
Date: 2011-10
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