Monotone equimeasurable rearrangements with non-additive probabilities

Mario Ghossoub

MPRA Paper from University Library of Munich, Germany

Abstract: In the classical theory of monotone equimeasurable rearrangements of functions, “equimeasurability” (i.e. the fact the two functions have the same distribution) is defined relative to a given additive probability measure. These rearrangement tools have been successfully used in many problems in economic theory dealing with uncertainty where the monotonicity of a solution is desired. However, in all of these problems, uncertainty refers to the classical Bayesian understanding of the term, where the idea of ambiguity is absent. Arguably, Knighitan uncertainty, or ambiguity is one of the cornerstones of modern decision theory. It is hence natural to seek an extension of these classical tools of equimeasurable rearrangements to situations of ambiguity. This paper introduces the idea of a monotone equimeasurable rearrangement in the context of non-additive probabilities, or capacities that satisfy a property that I call strong nonatomicity. The latter is a strengthening of the notion of nonatomicity, and these two properties coincide for additive measures and for submodular (i.e. concave) capacities. To illustrate the usefulness of these tools in economic theory, I consider an application to a problem arising in the theory of production under uncertainty.

Keywords: Ambiguity; Capacity; Non-Additive Probability; Choquet Integral; Monotone Equimeasurable Rearrangement; Production under Uncertainty (search for similar items in EconPapers)
JEL-codes: C02 C65 D24 D89 (search for similar items in EconPapers)
Date: 2011-10-07, Revised 2012-03-23
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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