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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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    Cited by:

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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. 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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