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Some Remarks on Simple Games and Matroids

  • Dieter Stumpe
Conference paper

Abstract

Between simple games and matroids there are certain connections. Edmonds showed that the core of a supermodular game (it is a simple game) is a polymatroid. The combinatorial structure of a simple game is not known in general. However for a matroidal simple game we can use cetain combinatorial results.

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References

  1. [1]
    K. G. Ramamurthy and T. Partasaraty, Matroidal Games, International Journal of Game Theory, Vol. 15, 1986.Google Scholar
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    Sagonti, E., On the Strong Monotonicy of Power Indices, Internatinal Journal of Game Theory, Vo1. 21, 1991.Google Scholar
  3. [3]
    Edmonds, J., Submodular Functions, Matroids and Certain Polyhedra, in Guy (Ed.), Combinatorical Structures and there Applications, 1971.Google Scholar
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    Aigner, M., Kombinatorik 2, Berlin-Heidelberg-New York, 1976.Google Scholar
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    Lawler, E.L., Combinatorical Optimization. Networks and Matroids, New York 1976.Google Scholar
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    Jeworrek, T. Zur Lösung von Optimierungsproblemen über den Durchschnitt von drei Matroiden, Dissertation A, TU Magdeburg 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Dieter Stumpe
    • 1
  1. 1.Faculty of MathematicsTechnical University of MagdeburgMagdeburgGermany

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