Erschienen: 07.11.2013 Abbildung von Meinhardt | The Pre-Kernel as a Tractable Solution for Cooperative Games | 2013 | An Exercise in Algorithmic Gam... | 45


The Pre-Kernel as a Tractable Solution for Cooperative Games

An Exercise in Algorithmic Game Theory

Buch. Hardcover


xxxiii, 242 S.

Springer. ISBN 978-3-642-39548-2

Format (B x L): 15,5 x 23,5 cm

Gewicht: 578 g

Das Werk ist Teil der Reihe: Theory and Decision Library C; 45


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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