Independence, Additivity, Uncertainty
(Sprache: Englisch)
With contributions by B. Grodal
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Produktinformationen zu „Independence, Additivity, Uncertainty “
With contributions by B. Grodal
Klappentext zu „Independence, Additivity, Uncertainty “
The work on this book started many years ago as an attempt to simplify and unify some results usually taught in courses in mathematical economics. The economic interpretation of the re sults were representations of preferences as sums or integrals and the decomposition of preferences into utilities and probabilities. It later turned out that t.he approach taken in the earlier versions were also the proper approach in generalizing from preferences which were total preorders to preferences which were not total or tran sitive. The same mathematics would even in that situation give representations which were additive. It would also give decomposi tions where concepts of uncertainty appeared. Early versions of some of the results appeared as Working Pa pers No. 135, 140, 150, and 176 from The Center for Research in Management Science, Berkeley. A first version of chapters 2, 4, 6, 7, and 8 appeared 1969 with the title" Mean Groupoids" [177]. They are essentially unchanged -except for some notes especially in chapter 6. Another version appeared 1990 as [178]. Chapter 10 contains results from the same versions and from [181]. Chapter 11 by Birgit Grodal is based on [91] by Grodal and Jp,an-Francois Mertens. Chapters 11 and 12 - also by Birgit Gro dal -contains the results from the earlier versions, but have been extended (by Karl Vind) to take into account the new corollaries of the results in the other chapters.
Inhaltsverzeichnis zu „Independence, Additivity, Uncertainty “
- Introduction- Basic Mathematics: Totally preordered sets
- Preferences and preference functions
- Totally preordered product sets
- A subset of a product set
- Mean groupoids
- Products of two sets as a mean groupoid
- Relations on Functon Spaces: Totally preordered function spaces
- Relations on function spaces
- Relations on Measures: Relations on sets of probability measures
- Integral Representations: A general integral representation by Birgit Grodal
- Special integral representations by Birgit Grodal
- Decompositions and Uncertainty: Decompositions. Uncertainty
- Uncertainty on products
- Conditional uncertainty
- Applications: Production, utility, preference
- Preferences over time
- A foundation for statistics.
Bibliographische Angaben
- Autor: Karl Vind
- 2003, XIII, 277 Seiten, Maße: 23,5 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3540416838
- ISBN-13: 9783540416838
Sprache:
Englisch
Pressezitat
From the reviews of the first edition: "The most important contribution of this book is to formalize, simplify and unify concepts of uncertainity that occur in mathematical economics. ... This well-written book provides an elegant and serious introduction to the basic concepts and results of representations of preferences as sums and integrals. It discusses in detail the decomposition of preferences into utilities and probabilities. This lively presentation ... is impressive. The book will serve as an inspiration for further research and can be recommended ... ." (P.R. Parthasarathy, Zentralblatt MATH, Vol. 1080, 2006)
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