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

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

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Bibliographic Details
Author / Creator:	Meinhardt, Holger Ingmar, 1965- author.
Imprint:	Heidelberg : Springer, 2014.
Description:	1 online resource (xxxiii, 242 pages) : illustrations (some color).
Language:	English
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.
Subject:	Game theory. Kernel functions. Game theory. Kernel functions.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11081840

Hidden Bibliographic Details
ISBN:	9783642395499 364239549X 3642395481 9783642395482 9783642395482
Notes:	Includes bibliographical references and indexes. Online resource; title from PDF title page (SpringerLink, viewed October 28, 2013).
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.
Standard no.:	10.1007/978-3-642-39549-9

Table of 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.