The Pre-Kernel as a Tractable Solution for Cooperative Games : An Exercise in Algorithmic Game Theory

Holger Ingmar Meinhardt

ISBN 10: 3642395481 / ISBN 13: 9783642395482

Published by Springer Berlin Heidelberg, 2013

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783642395482

Bibliographic Details

• Title: The Pre-Kernel as a Tractable Solution for Cooperative Games : An Exercise in Algorithmic Game Theory
• Publisher: Springer Berlin Heidelberg
• Publication Date: 2013
• Language: English
• ISBN 10: 3642395481
• ISBN 13: 9783642395482
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 21D millimeters 241 millimeters width by 160 millimeters height by 21 millimeters depth
• Weight: 582 grams

About this title

Synopsis

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.

About the Author

Dr. Holger Meinhardt is a Senior Research Affiliate at Karlsruhe Institute of Technology (KIT).