Entering of Newcomer in the Perturbed Voting Game
Abstract
The new class of voting games, in which the number of players and their power indexes are changing coherently, is considered. As a power index Shapley–Shubik value is taken. The following problem is considered: how to find a minimal investment, which guarantees the given value of the Shapley–Shubik power index for the newcomer. This value depends on the distribution of weights of players before entering of newcomer and on the capital that can be used to purchase shares of weights from different players.
Keywords:
voting game, Shapley–Shubic value, profitable investment, perspective coalitions, veto-player, Monte–Carlo
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References
Hu, X. (2006). An asymmetric Shapley-Shubik power index. International Journal of Game Theory, 34(1), 229–240.
Shapley, L. S., Shubik, M. (1969). On market games. Journal of Economic Theory, 1(1), 9–25.
Petrosian, L. A., Zenkevich, N. A., Shevkopyas, E. V. (2012). Game Theory. Saint-Peterburg: BHV-Petersburg (in russian).
Petrosian, O. L. (2013). Formation of new structure of coalitions in voting games. Mathematical Game Theory and its Applications, 5(1), 61–73 (in russian).
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Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
