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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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