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The Pre-Kernel as a Tractable Solution for Cooperative Games: An Exercise in Algorithmic Game Theory by Holger Ingmar Meinhardt (Paperback, 2016)

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Binding: Paperback Language: english. Used-like N : The book pretty much look like a new book. There will be no stains or markings on the book, the cover is clean and crisp, the book will look unread, the only marks there may be are slight bumping marks to the edges of the book where it may have been on a shelf previously.

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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.