Additive Representation of Non-Additive Measures and the Choquet Integral
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 large 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 inegrand; the Choquet integral with respect to any capacity is the differences 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 large space. We also discuss the interpretation o these results and the new light they shed on the theory of expected utility maximization with respect to non-additive measures.
Year of publication: |
1992
|
---|---|
Authors: | Gilboa, Itzhak ; Schmeidler, David |
Publisher: |
Evanston, IL : Northwestern University, Kellogg School of Management, Center for Mathematical Studies in Economics and Management Science |
Saved in:
freely available
Series: | Discussion Paper ; 985 |
---|---|
Type of publication: | Book / Working Paper |
Type of publication (narrower categories): | Working Paper |
Language: | English |
Other identifiers: | hdl:10419/221343 [Handle] RePEc:nwu:cmsems:985 [RePEc] |
Source: |
Persistent link: https://www.econbiz.de/10012235799
Saved in favorites
Similar items by person
-
Infinite Histories and Steady Orbits in Repeated Games
Gilboa, Itzhak, (1989)
-
Gilboa, Itzhak, (1991)
-
Canonical Representation of Set Functions
Gilboa, Itzhak, (1992)
- More ...