Ghossoub, Mario (2011): Monotone equimeasurable rearrangements with nonadditive probabilities.

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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 nonadditive 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.
Item Type:  MPRA Paper 

Original Title:  Monotone equimeasurable rearrangements with nonadditive probabilities 
Language:  English 
Keywords:  Ambiguity, Capacity, NonAdditive Probability, Choquet Integral, Monotone Equimeasurable Rearrangement, Production under Uncertainty 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C65  Miscellaneous Mathematical Tools C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D89  Other D  Microeconomics > D2  Production and Organizations > D24  Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity 
Item ID:  37629 
Depositing User:  Mario Ghossoub 
Date Deposited:  27. Mar 2012 22:04 
Last Modified:  14. Feb 2013 21:43 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/37629 