Overview
- Characterizes a fair division rule of game theory by convex analysis
- Proposes tractable formula to solve fair division problems in real life situations
- Provides algorithms to implement vectorized and parallel computer programs designed to solve fair division problems?
- Includes supplementary material: sn.pub/extras
Part of the book series: Theory and Decision Library C (TDLC, volume 45)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: The Pre-Kernel as a Tractable Solution for Cooperative Games
Book Subtitle: An Exercise in Algorithmic Game Theory
Authors: Holger Ingmar Meinhardt
Series Title: Theory and Decision Library C
DOI: https://doi.org/10.1007/978-3-642-39549-9
Publisher: Springer Berlin, Heidelberg
eBook Packages: Business and Economics, Economics and Finance (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2014
Hardcover ISBN: 978-3-642-39548-2Published: 07 November 2013
Softcover ISBN: 978-3-662-51314-9Published: 27 August 2016
eBook ISBN: 978-3-642-39549-9Published: 23 October 2013
Series ISSN: 0924-6126
Series E-ISSN: 2194-3044
Edition Number: 1
Number of Pages: XXXIII, 242
Number of Illustrations: 5 b/w illustrations, 3 illustrations in colour
Topics: Game Theory, Game Theory, Economics, Social and Behav. Sciences, Economic Theory/Quantitative Economics/Mathematical Methods, Math Applications in Computer Science