G-continuity, impatience and G-cores of exact games

Alain Chateauneuf and Caroline Ventura ()
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Caroline Ventura: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: This paper is concerned with real valued set functions defined on the set of Borel sets of a locally compact σ-compact topological space Ω. The first part characterizes the strong and weak impatience in the context of discrete and continuous time flows of income (consumption) valued through a Choquet integral with respect to an (exact) capacity. We show that the impatience of the decision maker translates into continuity properties of the capacity. In the second part, we recall the generalization given by Rébillé [8] of the Yosida-Hewitt decomposition of an additive set function into a continuous part and a pathological part and use it to give a characterization of those convex capacities whose core contains at least one G-continuous measure. We then proceed to characterize the exact capacities whose core contains only G-continuous measures. As a dividend, a simple characterization of countably additive Borel probabilities on locally compact σ-compact metric spaces is obtained.

Keywords: Impatience; exact and convex capacities; G-cores; σcores; Yosida-Hewitt decomposition.; Yosida-Hewitt decomposition; capacités exactes et convexes; G-coeurs; σ-coeurs; décomposition de Yosida-Hewitt. (search for similar items in EconPapers)
Date: 2009-07
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00442855v1
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Published in 2009

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Related works:
Working Paper: G-continuity, impatience and G-cores of exact games (2009)
Working Paper: G-continuity, impatience and G-cores of exact games (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:halshs-00442855

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