The Pre-Kernel as a Tractable Solution for Cooperative Games / Theory and Decision Library C Bd.45 (PDF)
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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.
- Autor: Holger Ingmar Meinhardt
- 2013, 2014, 242 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 364239549X
- ISBN-13: 9783642395499
- Erscheinungsdatum: 23.10.2013
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