Formation of new structure of coalitions in voting games

Ovanes L. Petrosian

Saint-Petersburg State University

Abstract: The new $(n+1)$st player enters the voting game and buys the stock from another players, investing the vector $\alpha=(\alpha_1,\dots,\alpha_n)$: $\sum_{i=1}^n\alpha_{i}\leq M$, $\alpha_i\geq0$, $\forall i=1,\dots,n$. The optimal investment is defined as $\alpha^*$, which maximizes the component of Shapley–Shubik value of entering player. The mathematical statement of the problem is given, some properties of the optimal investment are considered and Monte-Karlo method for the calculation of optimal investment is proposed.

Keywords: voting game, Shapley–Shubic value, profitable investment, perspective coalitions, veto-player, Monte-Karlo method.

UDC: 519.83
BBK: 22.18

 English version: Automation and Remote Control, 2015, 76:11, 2070–2077

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