© 2014

The Pre-Kernel as a Tractable Solution for Cooperative Games

An Exercise in Algorithmic Game Theory


Part of the Theory and Decision Library C book series (TDLC, volume 45)

Table of contents

  1. Front Matter
    Pages i-xxxiii
  2. Holger Ingmar Meinhardt
    Pages 1-6
  3. Holger Ingmar Meinhardt
    Pages 7-15
  4. Holger Ingmar Meinhardt
    Pages 17-25
  5. Holger Ingmar Meinhardt
    Pages 27-46
  6. Holger Ingmar Meinhardt
    Pages 47-61
  7. Holger Ingmar Meinhardt
    Pages 63-119
  8. Holger Ingmar Meinhardt
    Pages 121-168
  9. Holger Ingmar Meinhardt
    Pages 169-215
  10. Holger Ingmar Meinhardt
    Pages 217-222
  11. Holger Ingmar Meinhardt
    Pages 223-224
  12. Back Matter
    Pages 225-242

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.


Convex Analysis Cooperative Game Theory Fair Division Fairness Fenchel-Moreau Conjugation Pre-Kernel Solutions

Authors and affiliations

  1. 1.Karlsruhe Institute of Technology (KIT) Institute of Operations ResearchKarlsruheGermany

About the authors

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

Bibliographic information

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