Random Sets Lotteries and Decision Theory
AbstractEven if its roots are much older, random sets theory has been considered as an academic area, part of stochastic geometry, since Matheron . Random sets theory was first applied in some fields related to engineering sciences like geology, image analysis and expert systems (see Goutsias et al. ), and recently in non-parametric statistics (Koshevoy et al. ) or also (see Molchanov ) 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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Bibliographic InfoPaper 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.
Length: 27 pages
Date of creation: Oct 2011
Date of revision:
Knightian decision maker; Choquet-type decision maker; Random sets; Set-valued expectation;
Find related papers by 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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- 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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