The Pre-Kernel as a Tractable Solution for Cooperative Games

An Exercise in Algorithmic Game Theory

Nonfiction, Science & Nature, Mathematics, Game Theory, Business & Finance, Economics, Theory of Economics
Cover of the book The Pre-Kernel as a Tractable Solution for Cooperative Games by Holger Ingmar Meinhardt, Springer Berlin Heidelberg
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Author: Holger Ingmar Meinhardt ISBN: 9783642395499
Publisher: Springer Berlin Heidelberg Publication: October 23, 2013
Imprint: Springer Language: English
Author: Holger Ingmar Meinhardt
ISBN: 9783642395499
Publisher: Springer Berlin Heidelberg
Publication: October 23, 2013
Imprint: Springer
Language: English

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.

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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.

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