The Pre-Kernel as a Tractable Solution for Cooperative Games : An Exercise in Algorithmic Game Theory

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...

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Main Author: Meinhardt, Holger Ingmar
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2014, 2014
Edition:1st ed. 2014
Series:Theory and Decision Library C, Game Theory, Social Choice, Decision Theory, and Optimization
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Summary: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
Physical Description:XXXIII, 242 p. 8 illus., 3 illus. in color online resource
ISBN:9783642395499