Random Sets Lotteries and Decision Theory
Even 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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- 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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