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The Pre-Kernel as a Tractable Solution for Cooperative Games

An Exercise in Algorithmic Game Theory

Holger Ingmar Meinhardt (Autor)

Buch | Hardcover

XXXIII, 242 Seiten

2013
Springer Berlin (Verlag)
978-3-642-39548-2 (ISBN)

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This present book provides an alternative approach to study the pre-kernel solution of transferable utility games based on a generalized conjugation theory from convex analysis. Although the pre-kernel solution possesses an appealing axiomatic foundation that lets one consider this solution concept as a standard of fairness, the pre-kernel and its related solutions are regarded as obscure and too technically complex to be treated as a real alternative to the Shapley value. Comprehensible and efficient computability is widely regarded as a desirable feature to qualify a solution concept apart from its axiomatic foundation as a standard of fairness. We review and then improve an approach to compute the pre-kernel of a cooperative game by the indirect function. The indirect function is known as the Fenchel-Moreau conjugation of the characteristic function. Extending the approach with the indirect function, we are able to characterize the pre-kernel of the grand coalition simply by the solution sets of a family of quadratic objective functions.

Dr. Holger Meinhardt is a Senior Research Affiliate at Karlsruhe Institute of Technology (KIT).

Introduction.- Some Solution Schemes and Game Properties.- The Shapley Value and (Pre-Kernel) as a Fairness Concept.- Fair Division in Cournot Markets.- Some Preliminary Results.- A Pre-Kernel Characterization and Orthogonal Projection.- Characterization of the Pre-Kernel by Solution Sets.- Algorithms for Computing the Pre-Kernel.- An Upper Dimension Bound of the Pre-Kernel.- Concluding Remarks.

Erscheint lt. Verlag	7.11.2013
Reihe/Serie	Theory and Decision Library C
Zusatzinfo	XXXIII, 242 p. 8 illus., 3 illus. in color.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	539 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
	Wirtschaft ► Allgemeines / Lexika
	Wirtschaft ► Volkswirtschaftslehre
Schlagworte	Convex Analysis • cooperative game theory • fair division • Fairness • Fenchel-Moreau Conjugation • Pre-Kernel Solutions
ISBN-10	3-642-39548-1 / 3642395481
ISBN-13	978-3-642-39548-2 / 9783642395482
Zustand	Neuware