The Banzhaf index in complete and incomplete shareholding structures: A new algorithm
In this global world, many firms present a complex shareholding structure with indirect participation, such that it may become difficult to assess a firms controllers. Furthermore, if there are numerous dominant shareholders, the control can be shared between them. Determining who has the most influence is often a difficult task. To measure this influence, game theory allows the modeling of voting games and the computing of the Banzhaf index. This paper firstly offers a new algorithm to compute this index in all structures and then suggests some modelisations of the floating shareholder. Then, our model is applied to a real case study: the French group Lafarge. This exemplary case demonstrates how the floats structure and hidden coalition can impact the power relationship between dominant shareholders.
banzhaf index control game theory graph theory ownership structure