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International Journal of Game Theory

, Volume 18, Issue 2, pp 195–207 | Cite as

Regular simple games

  • E. Einy
  • E. Lehrer
Article

Abstract

Using Kelley's intersection number (and a variant of it) we define two classes of simple games, the regular and the strongly regular games. We show that the strongly regular games are those in which the set of winning coalitions and the set of losing coalitions can be strictly separated by a finitely additive probability measure. This, in particular, provides a combinatorial characterization for the class of finite weighted majority games within the finite simple games. We also prove that regular games have some nice properties and show that the finite regular games are exactly those simple games which are uniquely determined by their counting vector. This, in particular, generalizes a result of Chow and Lapidot.

Keywords

Probability Measure Economic Theory Game Theory Additive Probability Intersection Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Physica-Verlag 1989

Authors and Affiliations

  • E. Einy
    • 1
  • E. Lehrer
    • 2
  1. 1.COREBelgium
  2. 2.Graduate School of ManagementNorthwestern UniversityEvanstonUSA

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