The Pre-Kernel as a Tractable Solution for Cooperative Games: An Exercise in Algorithmic Game Theory (Theory and Decision Library C, 45, Band 45) - Hardcover

Meinhardt, Holger Ingmar

Hardcover

ISBN 10: 3642395481 ISBN 13: 9783642395482

Verlag: Springer, 2013

Inhaltsangabe

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.

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Über die Autorin bzw. den Autor

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

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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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2013
• Sprache: Englisch
• ISBN 10: 3642395481
• ISBN 13: 9783642395482
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 275
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland