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Some Remarks on Simple Games and Matroids

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Operations Research ’92
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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. K. G. Ramamurthy and T. Partasaraty, Matroidal Games, International Journal of Game Theory, Vol. 15, 1986.

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  2. Sagonti, E., On the Strong Monotonicy of Power Indices, Internatinal Journal of Game Theory, Vo1. 21, 1991.

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  3. Edmonds, J., Submodular Functions, Matroids and Certain Polyhedra, in Guy (Ed.), Combinatorical Structures and there Applications, 1971.

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  4. Aigner, M., Kombinatorik 2, Berlin-Heidelberg-New York, 1976.

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  5. Lawler, E.L., Combinatorical Optimization. Networks and Matroids, New York 1976.

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  6. Jeworrek, T. Zur Lösung von Optimierungsproblemen über den Durchschnitt von drei Matroiden, Dissertation A, TU Magdeburg 1988.

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© 1993 Springer-Verlag Berlin Heidelberg

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Stumpe, D. (1993). Some Remarks on Simple Games and Matroids. In: Karmann, A., Mosler, K., Schader, M., Uebe, G. (eds) Operations Research ’92. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-12629-5_121

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  • DOI: https://doi.org/10.1007/978-3-662-12629-5_121

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-0679-3

  • Online ISBN: 978-3-662-12629-5

  • eBook Packages: Springer Book Archive

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