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A minimum dimensional class of simple games

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Abstract

This paper provides several extensions of the notion of dimension of a simple game and proves the existence of a minimum subclass of weighted games with the property that every simple game can be expressed as their intersection. Some further generalizations lead to the new concept of codimension which is obtained by considering the union instead of the intersection as the basic operation.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics III and High Engineering School of Manresa, Technical University of Catalonia, Av. Bases de Manresa, 61-73, 08242, Manresa, Spain

    Josep Freixas

  2. Institute of Mathematics of the Polish Academy of Sciences, ul. Śniadeckich 8, 00-956, Warsaw, Poland

    Dorota Marciniak

  3. National Institute of Telecommunications, Szachowa Str., 104-894, Warsaw, Poland

    Dorota Marciniak

Authors
  1. Josep Freixas
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  2. Dorota Marciniak
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Corresponding author

Correspondence to Josep Freixas.

Additional information

Research of the first author partially supported by Grant MTM 2009–08037 from the Spanish Science and Innovation Ministry, and SGR 2009–1029 of “Generalitat de Catalunya.”

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Freixas, J., Marciniak, D. A minimum dimensional class of simple games. TOP 17, 407–414 (2009). https://doi.org/10.1007/s11750-009-0115-2

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  • DOI: https://doi.org/10.1007/s11750-009-0115-2

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