Logo - springer
Slogan - springer

Economics - Game Theory / Mathematical Methods | The Pre-Kernel as a Tractable Solution for Cooperative Games

The Pre-Kernel as a Tractable Solution for Cooperative Games

An Exercise in Algorithmic Game Theory

Meinhardt, Holger Ingmar

2014, XXXIII, 242 p. 8 illus., 3 illus. in color.

Available Formats:

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.


(net) price for USA

ISBN 978-3-642-39549-9

digitally watermarked, no DRM

Included Format: PDF and EPUB

download immediately after purchase

learn more about Springer eBooks

add to marked items


Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.


(net) price for USA

ISBN 978-3-642-39548-2

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days

add to marked items

  • 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​

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.

Content Level » Research

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

Related subjects » Applications - Economic Theory - Game Theory / Mathematical Methods - Theoretical Computer Science

Table of contents / Preface / Sample pages 

Popular Content within this publication 



Read this Book on Springerlink

New Book Alert

Get alerted on new Springer publications in the subject area of Game Theory / Mathematical Methods.