Entering of Newcomer in the Perturbed Voting Game

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.