Theory and Decision Library C

The Pre-Kernel as a Tractable Solution for Cooperative Games

An Exercise in Algorithmic Game Theory

Authors: Meinhardt, Holger Ingmar

  • 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​
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  • ISBN 978-3-642-39549-9
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Hardcover $129.00
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  • ISBN 978-3-642-39548-2
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Softcover $129.00
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  • Due: October 14, 2016
  • ISBN 978-3-662-51314-9
  • Free shipping for individuals worldwide
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.

About the authors

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

Table of contents (10 chapters)

  • Introduction

    Meinhardt, Holger Ingmar

    Pages 1-6

  • Some Solution Schemes and Game Properties

    Meinhardt, Holger Ingmar

    Pages 7-15

  • The Shapley Value and (Pre-)Kernel as a Fairness Concept

    Meinhardt, Holger Ingmar

    Pages 17-25

  • Fair Division in Cournot Markets

    Meinhardt, Holger Ingmar

    Pages 27-46

  • Some Preliminary Results

    Meinhardt, Holger Ingmar

    Pages 47-61

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-642-39549-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-642-39548-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 14, 2016
  • ISBN 978-3-662-51314-9
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
The Pre-Kernel as a Tractable Solution for Cooperative Games
Book Subtitle
An Exercise in Algorithmic Game Theory
Authors
Series Title
Theory and Decision Library C
Series Volume
45
Copyright
2014
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-39549-9
DOI
10.1007/978-3-642-39549-9
Hardcover ISBN
978-3-642-39548-2
Softcover ISBN
978-3-662-51314-9
Series ISSN
0924-6126
Edition Number
1
Number of Pages
XXXIII, 242
Number of Illustrations and Tables
5 b/w illustrations, 3 illustrations in colour
Topics