The pre-kernel as a tractable solution for cooperative games [electronic resource] : an exercise in algorithmic game theory / Holger Ingmar Meinhardt.
Meinhardt, Holger Ingmar, author.
2014
QA272.4
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Title The pre-kernel as a tractable solution for cooperative games [electronic resource] : an exercise in algorithmic game theory / Holger Ingmar Meinhardt.
Author Meinhardt, Holger Ingmar, author.
ISBN 9783642395499 electronic book
364239549X electronic book
9783642395482
DOI https://doi.org/10.1007/978-3-642-39549-9
Published Heidelberg : Springer, 2014.
Language English
Description 1 online resource (xxxiii, 242 pages) : illustrations (some color).
Other Standard Identifiers 10.1007/978-3-642-39549-9 doi
Call Number QA272.4
Dewey Decimal Classification 519.3
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, etc. Note Includes bibliographical references and indexes.
Access Note Access limited to authorized users.
Source of Description Description based on online resource; title from PDF title page (SpringerLink, viewed October 28, 2013).
Series Theory and decision library. Series C, Game theory, mathematical programming, and operations research ; v.45. 0924-6126
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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.

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