Title The pre-kernel as a tractable solution for cooperative games : an exercise in algorithmic game theory / Holger Ingmar Meinhardt

Published Heidelberg : Springer, 2014

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Description 1 online resource (xxxiii, 242 pages) : illustrations (some color) Series Theory and decision library. Series C, Game theory, mathematical programming, and operations research, 0924-6126 ; volume 45 Theory and decision library. Series C, Game theory, mathematical programming, and operations research ; v. 45. 0924-6126 Contents 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 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 Bibliography Includes bibliographical references and indexes Notes Online resource; title from PDF title page (SpringerLink, viewed October 28, 2013) Subject Game theory. Kernel functions. Game Theory MATHEMATICS -- Applied. MATHEMATICS -- Probability & Statistics -- General. Science économique. Affaires. Game theory Kernel functions Form Electronic book ISBN 9783642395499 364239549X 3642395481 9783642395482

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