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The Banzhaf Index in Complete and Incomplete Shareholding Structures: A New Algorithm

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  • Marc Levy

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.

Suggested Citation

  • Marc Levy, 2010. "The Banzhaf Index in Complete and Incomplete Shareholding Structures: A New Algorithm," Working Papers CEB 10-046, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:sol:wpaper:2013/63872
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    References listed on IDEAS

    as
    1. Marc Levy, 2006. "Control in Pyramidal Structures," Working Papers CEB 06-023.RS, ULB -- Universite Libre de Bruxelles.
    2. T. Biebuyck & Ariane Chapelle & Ariane Szafarz, 2002. "Les leviers de contrôle des actionnaires majoritaires," Working Papers CEB 03-001.RS, ULB -- Universite Libre de Bruxelles.
    3. Ariane Chapelle, 2001. "Corporate governance en Belgique: l'effet des pyramides," ULB Institutional Repository 2013/9933, ULB -- Universite Libre de Bruxelles.
    4. Dan Felsenthal & Moshé Machover & William Zwicker, 1998. "The Bicameral Postulates and Indices of a Priori Voting Power," Theory and Decision, Springer, vol. 44(1), pages 83-116, January.
    5. Rafael La Porta & Florencio Lopez-De-Silanes & Andrei Shleifer, 1999. "Corporate Ownership Around the World," Journal of Finance, American Finance Association, vol. 54(2), pages 471-517, April.
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    7. Ariane Chapelle & Ariane Szafarz, 2006. "Control consolidation with a threshold: an algorithm," Working Papers CEB 06-007.RS, ULB -- Universite Libre de Bruxelles.
    8. Bilbao, J. M. & Fernandez, J. R. & Jimenez, N. & Lopez, J. J., 2002. "Voting power in the European Union enlargement," European Journal of Operational Research, Elsevier, vol. 143(1), pages 181-196, November.
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    Cited by:

    1. Armando Rungi & Gregory Morrison & Fabio Pammolli, 2017. "Global ownership and corporate control networks," Working Papers 07/2017, IMT Institute for Advanced Studies Lucca, revised Sep 2017.
    2. Duarte Brito & António Osório & Ricardo Ribeiro & Hélder Vasconcelos, 2015. "Unilateral Effects Screens for Partial Horizontal Acquisitions: The Generalized HHI and GUPPI," Working Papers de Economia (Economics Working Papers) 02, Católica Porto Business School, Universidade Católica Portuguesa.
    3. Brito, Duarte & Ribeiro, Ricardo & Vasconcelos, Helder, 2013. "Quantifying the Coordinated Effects of Partial Horizontal Acquisitions," CEPR Discussion Papers 9536, C.E.P.R. Discussion Papers.
    4. Chen, Jiguang & Hu, Qiying & Song, Jing-Sheng, 2017. "Effect of partial cross ownership on supply chain performance," European Journal of Operational Research, Elsevier, vol. 258(2), pages 525-536.
    5. Marc Levy & Ariane Szafarz, 2017. "Cross-Ownership: A Device for Management Entrenchment?," Review of Finance, European Finance Association, vol. 21(4), pages 1675-1699.
    6. Marc Levy & Ariane Szafarz, 2011. "Corporate Control with Cross-Ownership," Working Papers CEB 11-053, ULB -- Universite Libre de Bruxelles.
    7. Tejada, Juan & Molina, Elisenda & Flores Díaz, Ramón Jesús, 2013. "The Shapley group value," DES - Working Papers. Statistics and Econometrics. WS ws133430, Universidad Carlos III de Madrid. Departamento de Estadística.

    More about this item

    Keywords

    Ownership structure; Control; Banzhaf index;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • L22 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Organization and Market Structure

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