An Upper Dimension Bound of the Pre-Kernel

  • Holger Ingmar Meinhardt
Chapter
Part of the Theory and Decision Library C book series (TDLC, volume 45)

Abstract

The dual representation of the pre-kernel enables us to provide a simple upper dimension bound formula on the pre-kernel set. This upper bound is equal to n − 3, from which we can finally determine a refined assignment on the maximum number of iteration steps required to successfully terminate a pre-kernel search process. At most \(\binom{n}{2} - 1\)-iteration steps are needed to single out a member of the pre-kernel under a regime of orthogonal projections.

Bibliography

  1. Maschler, M., & Peleg, B. (1966). A characterization, existence proof and dimension bounds for the Kernel of a game. Pacific Journal of Mathematics, 18(2), 289–328.CrossRefGoogle Scholar
  2. Meinhardt, H. I. (2012a). Tugames: A mathematica package for cooperative game theory. Version: 2.2, Karlsruhe Institute of Technology (KIT), Karlsruhe, Mimeo.Google Scholar
  3. Meinhardt, H. I. (2012b). MatTugames: A matlab toolbox for cooperative game theory. Version: 0.3, Karlsruhe Institute of Technology (KIT), Karlsruhe. http://www.mathworks.com/matlabcentral/fileexchange/35933.

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Holger Ingmar Meinhardt
    • 1
  1. 1.Institute of Operations ResearchKarlsruhe Institute of Technology (KIT)KarlsruheGermany

Personalised recommendations