DGOR pp 517-527

Substitution Decomposition of Multilinear Functions with Applications to Utility and Game Theory

  • Bernhard von Stengel
Conference paper

DOI: 10.1007/978-3-642-72557-9_95

Part of the Operations Research Proceedings 1986 book series (ORP, volume 1986)
Cite this paper as:
von Stengel B. (1987) Substitution Decomposition of Multilinear Functions with Applications to Utility and Game Theory. In: Isermann H., Merle G., Rieder U., Schmidt R., Streitferdt L. (eds) DGOR. Operations Research Proceedings 1986, vol 1986. Springer, Berlin, Heidelberg

Abstract

A theory of decomposition “by substitution” for multi-linear (i.e. multi-affine) functions is presented. A representation theorem for such functions is shown to be given by a Moebius inversion formula. The concept of autonomous sets of variables (a “linear separability” of some kind, also known as “generalized utility independence”) captures the decomposition possibilities of a multi-linear function. Their entirety can be hierarchically represented by a so-called composition tree. Distinguished, strong forms of decompositions are shown to be given by multiplicative or additive functions. Important applications to the theories of multi-attribute expected-utilitv functions, switching circuits and cooperative n-person games are outlined.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Bernhard von Stengel
    • 1
  1. 1.Universität PassauDeutschland

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