Today, the shareholding structure of companies is sometimes so complex that it can be difficult to find back their actual owners and controllers. In particular, in continental Europe and in Asia, control tunnelling appears frequently through pyramidal structure. After describing the ownership structure through a graph association, this paper analyses the voting game at stake in the race for control. It compares existing methods and algorithms to identify the owners and controllers of a firm in a pyramidal structure without cross-ownership. As a real life example, the case of the Belgian retail company, Colruyt, is used to apply these different methods and compare their results. Furthermore, it shows how the ownership structure allows to the Colruyt family to keep the control of Colruyt even if there are discordances inside the family. JEL Classification: G32, L22

By artificially inflating capital and creating own shares, cross-ownership can be a key device for managerial entrenchment. This paper proposes a game-theoretical method to measure the extent of shareholder expropriation through crossownership. By properly accounting for cross-ownership linkages, we show how managers can seize indirect voting rights, and so insulate their firms from outside control. Significant examples of cross-ownership are found not only in civil law countries, but also in the U.S. mutual fund industry. We apply our method to Germany's Allianz Group. This paper paves the way to better regulatory appraisal of management entrenchment through cross-ownership.

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 often is a difficult task. To measure this influence, game theory allows modeling voting game and computing the Banzhaf index. This paper first offers a new algorithm to compute this index in all structures and 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. Abstract: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 often is a difficult task. To measure this influence, game theory allows modeling voting game and computing the Banzhaf index. This paper first offers a new algorithm to compute this index in all structures and 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. JEL Classifications: C63, G32, L22

Cross-ownership breaks the traditional rule of one-sided corporate control. Using a novel approach based on stochastic voting processes, this paper proposes a general method to determine control stakes in the presence of cross-ownership. It offers a generalization of the Banzhaf index, which allows coping with crossownership-inclusive ownership graphs. The original feature of this approach is its absolute sequentiality. We also operationalize this new approach by building an algorithm, which determines the shareholders' respective control powers in any corporate structure. From a governance viewpoint, we emphasize that crossownership may act as a powerful device for shareholder expropriation. To make this point, we revisit the leading example of the German Allianz Group. AbstractCross-ownership breaks the traditional rule of one-sided corporate control. Using a novel approach based on stochastic voting processes, this paper suggests a general method to determine control stakes in the presence of cross-ownership. It offers a generalization of the Banzhaf index, which applies to cross-ownership-inclusive graphs. The original feature of this approach is its absolute sequentiality. Accordingly, we build a new algorithm that evaluates the shareholders' control powers in any corporate structure. From a governance viewpoint, we emphasize that cross-ownership may act as a powerful device for shareholder expropriation.To illustrate this point, we revisit the leading example of the German Allianz Group.3