On Some Applications of the Shapley-Shubik Index for Finance and Politics

Some properties of the Shapley-Shubik index are presented in this chapter, along with indications as to how such characteristics may be especially useful in predicting the outcome of bargaining in simple games. With regard to this, certain applications of this index regarding politics and finance that were undertaken at universities in Bergamo, Krakow, Manresa, and Monterey are provided.
In the first section, we present a very short presentation of the theory of simple games and power indices. In the following section, we supply a historical overview of the main power indices that have been identified up until now; then, several indices are presented and compared. At this point, we provide some applications of the Shapley and Shubik index regarding finance (e.g., the direct and indirect control of firms, take-over operations, stability, and portfolio theory) and politics (e.g., democratic electoral systems, simulations, and forecasts). Some related algorithms are then shown. Lastly, we provide some information regarding open problems in the theoretical and applicative fields.