Neural Networks for Non-independent Lotteries
Author(s)
Rotundo, Giulia
Date Issued
2010
Type
Book chapter
Abstract
The von Neuman-Morgenstern utility functions play a relevant role in
the set of utility functions. This paper shows the density of the set von Neuman-
Morgenstern utility functions on the set of utility utility function that can represent
arbitrarily well a given continuous but not independent preference relation over
monetary lotteries. The main result is that without independence it is possible to
approximate utility functions over monetary lotteries by von Neuman-Morgenstern
ones with arbitrary precision. The approach used is a constructive one. Neural networks
are used for their approximation properties in order to get the result, and their
functional form provides both the von Neumann-Morgenstern representation and
the necessary change of variables over the set of lotteries.
Citation
11. G. Rotundo, “Neural Networks for Non-independent Lotteries”. In: Springer series “Studies in Fuzziness and Soft Computing” (R.R. Kacprzyk, J. Ed.), “Preferences and Decisions” Greco, S., Marques Pereira, R.A., Squillante, M., Yager, R.R., Kacprzyk, J. (Eds.), , Vol. 257, pp. 369-375 (2010).
Subjects
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