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 firm’s 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 float’s structure and hidden coalition can impact the power relationship between dominant shareholders.

► We propose an algorithm to compute the Banzhaf index in ownership structures.
► The paper also suggests different models for the float (small shareholders).
► The model is applied to the ownership structure of Lafarge.
► The importance of main shareholders may depend on the float’s structure.
► The order of importance of main shareholders may depend on the float’s structure.