The Pre-Kernel as a Tractable Solution for Cooperative Games
An Exercise in Algorithmic Game Theory
(Sprache: Englisch)
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...
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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.Inhaltsverzeichnis zu „The Pre-Kernel as a Tractable Solution for Cooperative Games “
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.
Autoren-Porträt von Holger Ingmar Meinhardt
Dr. Holger Meinhardt is a Senior Research Affiliate at Karlsruhe Institute of Technology (KIT).
Bibliographische Angaben
- Autor: Holger Ingmar Meinhardt
- 2013, 2014, XXXIII, 242 Seiten, 3 farbige Abbildungen, Masse: 16,2 x 23,8 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3642395481
- ISBN-13: 9783642395482
Sprache:
Englisch
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