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 $\alpha=(\alpha_1,\dots,\alpha_n)$: $\sum_{i=1}^n\alpha_{i}\leq M$, $\alpha_i\geq0$, $\forall i=1,\dots,n$. 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.