Additive Representations of Non-Additive Measures and the Choquet Integral

Itzhak Gilboa and David Schmeidler

Post-Print from HAL

Abstract: This paper studies some new properties of set functions (and, in particular, "non-additive probabilities" or "capacities") and the Choquet integral with respect to such functions, in the case of a finite domain. We use an isomorphism between non-additive measures on the original space (of states of the world) and additive ones on a larger space (of events), and embed the space of real-valued functions on the former in the corresponding space on the latter. This embedding gives rise to the following results: -the Choquet integral with respect to any totally monotone capacity is an average over minima of the integrand; -the Choquet integral with respect to any capacity is the difference between minima of regular integrals over sets of additive measures; -under fairly general conditions one may define a "Radon-Nikodym derivative" of one capacity with respect to another; -the "optimistic" pseudo-Bayesian update of a non-additive measure follows from the Bayesian update of the corresponding additive measure on the larger space. We also discuss the interpretation of these results and the new light they shed on the theory of expected utility maximization with respect to non-additive measures.

Keywords: Non-additive probabilities; Choquet integral; capacities (search for similar items in EconPapers)
Date: 1994
References: Add references at CitEc
Citations: View citations in EconPapers (67)

Published in Annals of Operations Research, 1994, vol. 52, issue 1, pp. 43-65. ⟨10.1007/BF02032160⟩

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
Working Paper: Additive Representation of Non-Additive Measures and the Choquet Integral (1992)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00753149

DOI: 10.1007/BF02032160

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().