Abstract
This chapter reviews and sometimes modifies a number of concepts and results from utility theory needed elsewhere in this book. The reader already familiar with or not interested in these basics, which underly most of the other material in this book, may skip this chapter or the larger part of it. Only an understanding is required of the definition of a von NeumannMorgenstern utility function, which is presented in section 11.2. Everything else in this chapter may be read upon references in other chapters.
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Reference
These are axioms 2 and 3 in Herstein and Milnor (1953).
In accordance with what has by now become common practice, the word “axiom” is used for a mathematical assumption (that is, no further proof is required) which is believed to have something to do with reality. For instance, an axiom may capture possible human behavior. This usage is a result from a long period of inflation. Necessity (as for instance claimed by Immanuel Kant with respect to the Euclidean world view) has since long ceased to be a necessary ingredient of an axiom.
For compact sets, this definition was given in Peters and Tijs (1981), and for general sets in Wakker et d. (1985).
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© 1992 Springer Science+Business Media Dordrecht
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Peters, H.J.M. (1992). Elements from utility theory. In: Axiomatic Bargaining Game Theory. Theory and Decision Library, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8022-9_11
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DOI: https://doi.org/10.1007/978-94-015-8022-9_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4178-4
Online ISBN: 978-94-015-8022-9
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