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Bounds for Owen's Multilinear Extension

Part of: Operations research and management science Game theory Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Josep Freixas
Josep Freixas*
Affiliation:
Engineering School of Manresa and Technical University of Catalonia
*
∗Postal address: Department of Applied Mathematics 3, Engineering School of Manresa, Av. Bases de Manresa 61-73, E-08242 Manresa, Spain. Email address: [email protected]
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Abstract

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Owen's multilinear extension (MLE) of a game is a very important tool in game theory and particularly in the field of simple games. Among other applications it serves to efficiently compute several solution concepts. In this paper we provide bounds for the MLE. Apart from its self-contained theoretical interest, the bounds offer the means in voting system studies of approximating the probability that a proposal is approved in a particular simple game having a complex component arrangement. The practical interest of the bounds is that they can be useful for simple games having a tedious MLE to evaluate exactly, but whose minimal winning coalitions and minimal blocking coalitions can be determined by inspection. Such simple games are quite numerous.

Keywords

Simple gamesOwen's multilinear extensionboundsapproximations

MSC classification

Secondary: 91A12: Cooperative games 90B50: Management decision making, including multiple objectives 90C59: Approximation methods and heuristics 91B12: Voting theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 44 , Issue 4 , December 2007 , pp. 852 - 864
Copyright
Copyright © Applied Probability Trust 2007 

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