Universität zu Köln

Faigle, Ulrich and Grabisch, Michel (2016). Bases and linear transforms of TU-games and cooperation systems. Int. J. Game Theory, 45 (4). S. 875 - 893. HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1432-1270

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Abstract

We study linear properties of TU-games, revisiting well-known issues like interaction transforms, the inverse Shapley value problem and potentials. We embed TU-games into the model of cooperation systems and influence patterns, which allows us to introduce linear operators on games in a natural way. We focus on transforms, which are linear invertible maps, relate them to bases and investigate many examples (Mobius transform, interaction transform, Walsh transform and Fourier analysis etc.). In particular, we present a simple solution to the inverse problem in its general form: Given a linear value and a game v, find all games such that . Generalizing Hart and Mas-Colell's concept of a potential, we introduce general potentials and show that every linear value is induced by an appropriate potential.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Faigle, Ulrich UNSPECIFIED UNSPECIFIED UNSPECIFIED Grabisch, Michel UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-256616
DOI:	10.1007/s00182-015-0490-x
Journal or Publication Title:	Int. J. Game Theory
Volume:	45
Number:	4
Page Range:	S. 875 - 893
Date:	2016
Publisher:	SPRINGER HEIDELBERG
Place of Publication:	HEIDELBERG
ISSN:	1432-1270
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language SET-FUNCTIONS; SHAPLEY VALUE; MODEL Multiple languages Economics; Mathematics, Interdisciplinary Applications; Social Sciences, Mathematical Methods; Statistics & Probability Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/25661