The counting vector of a simple game
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- by Eitan Lapidot PDF
- Proc. Amer. Math. Soc. 31 (1972), 228-231 Request permission
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
- John R. Isbell, On the enumeration of majority games, Math. Tables Aids Comput. 13 (1959), 21–28. MR 103129, DOI 10.1090/S0025-5718-1959-0103129-5 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.
- 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 205699
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 228-231
- DOI: https://doi.org/10.1090/S0002-9939-1972-0287916-7
- MathSciNet review: 0287916