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ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The counting vector of a simple game


Author: Eitan Lapidot
Journal: Proc. Amer. Math. Soc. 31 (1972), 228-231
DOI: https://doi.org/10.1090/S0002-9939-1972-0287916-7
MathSciNet review: 0287916
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Abstract | References | Additional Information

Abstract: The counting vector of a simple game is the vector $ f = (f(1),f(2), \cdots ,f(n))$ where $ f(i)$ is the number of winning coalitions containing the player $ i$. In this paper, we show that the counting vector of a weighted majority game determines the game uniquely. With the aid of the counting vector we find an upper bound on the number of weighted majority games.


References [Enhancements On Off] (What's this?)

  • [1] J. R. Isbell, On the enumeration of majority games, Math. Tables Aids Comput. 13 (1959), 21-28. MR 21 #1912. MR 0103129 (21:1912)
  • [2] E. Lapidot, On symmetry-groups of games, development in operations research, Proc. Third Annual Israel Conf. on Operations Research (1969), Gordon and Breach, London, 1970, pp. 571-583.
  • [3] M. Maschler and B. Peleg, A characterization, existence proof and dimension bounds for the kernel of a game, Pacific J. Math. 18 (1966), 289-328. MR 34 #5525. MR 0205699 (34:5525)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0287916-7
Keywords: Simple games, weighted majority game, counting vector, desirability relation, symmetric players
Article copyright: © Copyright 1972 American Mathematical Society

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