The Pre-Kernel as a Tractable Solution for Cooperative Games : An Exercise in Algorithmic Game Theory (Theory and Decision Library C)

Meinhardt, Holger Ingmar

Springer-Verlag Berlin and Heidelberg GmbH & Co. K（2013/11発売）

• 製本 Hardcover:ハードカバー版／ページ数 242 p.
• 言語 ENG
• 商品コード 9783642395482
• DDC分類 004.0151

Full 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.

Contents

Introduction.- 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.