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The Banzhaf index in complete and incomplete shareholding structures: A new algorithm

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  • Levy, Marc

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 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.

Suggested Citation

  • Levy, Marc, 2011. "The Banzhaf index in complete and incomplete shareholding structures: A new algorithm," European Journal of Operational Research, Elsevier, vol. 215(2), pages 411-421, December.
    • Handle: RePEc:eee:ejores:v:215:y:2011:i:2:p:411-421
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    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. Chapelle, Ariane & Szafarz, Ariane, 2005. "Controlling firms through the majority voting rule," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(2), pages 509-529.
    6. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    7. Lucian A. Bebchuk & Reinier Kraakman & George Triantis, 2000. "Stock Pyramids, Cross-Ownership, and Dual Class Equity: The Mechanisms and Agency Costs of Separating Control from Cash-Flow Rights," NBER Chapters, in: Concentrated Corporate Ownership, pages 295-318, National Bureau of Economic Research, Inc.
    8. 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.
    9. Morck, Randall K. (ed.), 2000. "Concentrated Corporate Ownership," National Bureau of Economic Research Books, University of Chicago Press, edition 1, number 9780226536781, December.
    10. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    11. Ariane Chapelle & Ariane Szafarz, 2006. "Control consolidation with a threshold: an algorithm," Working Papers CEB 06-007.RS, ULB -- Universite Libre de Bruxelles.
    12. 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.
    13. Cheung, Yan-Leung & Stouraitis, Aris & Wong, Anita W.S., 2005. "Ownership concentration and executive compensation in closely held firms: Evidence from Hong Kong," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 511-532, September.
    14. Brioschi, Francesco & Buzzacchi, Luigi & Colombo, Massimo G., 1989. "Risk capital financing and the separation of ownership and control in business groups," Journal of Banking & Finance, Elsevier, vol. 13(4-5), pages 747-772, September.
    15. Leech, Dennis, 2002. "Shareholder Voting Power and Ownership Control of Companies," Economic Research Papers 269335, University of Warwick - Department of Economics.
    16. Crama, Y. & Leruth, L. & Renneboog, L.D.R., 2003. "Corporate control concentration measurement and firm performance," Discussion Paper 17, Tilburg University, Tilburg Law and Economic Center.
    17. Julan Du & Yi Dai, 2005. "Ultimate Corporate Ownership Structures and Capital Structures: evidence from East Asian economies," Corporate Governance: An International Review, Wiley Blackwell, vol. 13(1), pages 60-71, January.
    18. Faccio, Mara & Lang, Larry H. P., 2002. "The ultimate ownership of Western European corporations," Journal of Financial Economics, Elsevier, vol. 65(3), pages 365-395, September.
    19. Dubey, Pradeep & Einy, Ezra & Haimanko, Ori, 2005. "Compound voting and the Banzhaf index," Games and Economic Behavior, Elsevier, vol. 51(1), pages 20-30, April.
    20. Gambarelli, Gianfranco & Owen, Guillermo, 1994. "Indirect Control of Corporations," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(4), pages 287-302.
    21. Claessens, Stijn & Djankov, Simeon & Lang, Larry H. P., 2000. "The separation of ownership and control in East Asian Corporations," Journal of Financial Economics, Elsevier, vol. 58(1-2), pages 81-112.
    22. Alessandro Zattoni, 1999. "The Structure of Corporate Groups: the Italian case," Corporate Governance: An International Review, Wiley Blackwell, vol. 7(1), pages 38-48, January.
    23. Dennis Leech, 2002. "Shareholder Voting Power and Ownership Control of Companies," Homo Oeconomicus, Institute of SocioEconomics, vol. 19, pages 345-371.
    24. Flath, David, 1992. "Indirect shareholding within Japan's business groups," Economics Letters, Elsevier, vol. 38(2), pages 223-227, February.
    25. Crama, Yves & Leruth, Luc, 2007. "Control and voting power in corporate networks: Concepts and computational aspects," European Journal of Operational Research, Elsevier, vol. 178(3), pages 879-893, May.
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    2. Brito, Duarte & Ribeiro, Ricardo & Vasconcelos, Helder, 2018. "Quantifying the coordinated effects of partial horizontal acquisitions," European Economic Review, Elsevier, vol. 110(C), pages 108-149.
    3. Brito, Duarte & Osório, António & Ribeiro, Ricardo & Vasconcelos, Helder, 2018. "Unilateral effects screens for partial horizontal acquisitions: The generalized HHI and GUPPI," International Journal of Industrial Organization, Elsevier, vol. 59(C), pages 127-189.
    4. Marc Levy & Ariane Szafarz, 2017. "Cross-Ownership: A Device for Management Entrenchment?," Review of Finance, European Finance Association, vol. 21(4), pages 1675-1699.
    5. Flores Díaz, Ramón Jesús & Molina, Elisenda & Tejada, Juan, 2013. "The Shapley group value," DES - Working Papers. Statistics and Econometrics. WS ws133430, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. 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.
    7. Marc Levy & Ariane Szafarz, 2011. "Corporate Control with Cross-Ownership," Working Papers CEB 11-053, ULB -- Universite Libre de Bruxelles.
    8. Jung, Jihye & Choi, In-Chan, 2022. "A multi-objective optimization model for dissolving circular shareholdings in Korean conglomerates," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).

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    More about this item

    Keywords

    Control Game theory Graph theory Ownership structure 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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