Formation of new structure of coalitions in voting games
The new (n+1)st player enters the voting game and buys the stock from another players, investing the vector $\alpha=(\alpha_{1},\ldots,\alpha_{n}): \sum\limits_{i=1}^{n}\alpha_{i}\leq M, \alpha_{i}\geq 0, \forall i=1,\ldots,n$. The optimal investment is defined as $\alpha^{\ast}$, 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.