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The Pre-Kernel as a Tractable Solution for Cooperative Games on Hardback by Holger Ingmar Meinhardt
The Pre-Kernel as a Tractable Solution for Cooperative Games on Hardback by Holger Ingmar Meinhardt
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The Pre-Kernel as a Tractable Solution for Cooperative Games

An Exercise in Algorithmic Game Theory
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Description

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.

Author Biography:

Dr. Holger Meinhardt is a Senior Research Affiliate at Karlsruhe Institute of Technology (KIT).
Release date NZ
November 7th, 2013
Audience
  • Professional & Vocational
Illustrations
3 Illustrations, color; 5 Illustrations, black and white; XXXIII, 242 p. 8 illus., 3 illus. in color.
Pages
242
Dimensions
155x235x21
ISBN-13
9783642395482
Product ID
21503585

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The Pre-Kernel as a Tractable Solution for Cooperative Games by Holger Ingmar Meinhardt
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