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Indirect control and power in mutual control structures

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  • Karos, Dominik
  • Peters, Hans

Abstract

In a mutual control structure (mcs) agents exercise control over each other. Typical examples occur in the area of corporate governance: firms and investment companies exercise mutual control, in particular by owning each others' stocks. We represent such situations in two equivalent ways: by a function assigning to each coalition the set of controlled players, and by a simple game structure in which for each player a simple game describes who controls that player. These concepts are similar to authority distributions and command games in Hu and Shapley (2003a, 2003b). An mcs is invariant if it incorporates all indirect control relations. We axiomatically develop a class of power indices for invariant mcs. We impose four axioms with a plausible interpretation in this framework, which together characterize a broad class of power indices based on dividends resulting both from exercising and from undergoing control. Extra conditions can further refine this broad class.

Suggested Citation

  • Karos, Dominik & Peters, Hans, 2015. "Indirect control and power in mutual control structures," Games and Economic Behavior, Elsevier, vol. 92(C), pages 150-165.
    • Handle: RePEc:eee:gamebe:v:92:y:2015:i:c:p:150-165
    DOI: 10.1016/j.geb.2015.06.003
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    1. Karos, Dominik & Peters, Hans, 2015. "Indirect control and power in mutual control structures," Games and Economic Behavior, Elsevier, vol. 92(C), pages 150-165.
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    Cited by:

    1. André Casajus & Frank Huettner, 2019. "The Coleman–Shapley index: being decisive within the coalition of the interested," Public Choice, Springer, vol. 181(3), pages 275-289, December.
    2. Marc Levy & Ariane Szafarz, 2017. "Cross-Ownership: A Device for Management Entrenchment?," Review of Finance, European Finance Association, vol. 21(4), pages 1675-1699.
    3. Hans Peters & Judith Timmer & Rene van den Brink, 2016. "Power on digraphs," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 26(2), pages 107-125.
    4. Karos, Dominik & Peters, Hans, 2018. "Effectivity and power," Games and Economic Behavior, Elsevier, vol. 108(C), pages 363-378.
    5. Karos, Dominik & Peters, Hans, 2015. "Indirect control and power in mutual control structures," Games and Economic Behavior, Elsevier, vol. 92(C), pages 150-165.
    6. Kong, Qianqian & Peters, Hans, 2023. "Power indices for networks, with applications to matching markets," European Journal of Operational Research, Elsevier, vol. 306(1), pages 448-456.
    7. Stylianos Artsidakis & Yiannis Thalassinos & Theofanis Petropoulos & Konstantinos Liapis, 2022. "Optimum Structure of Corporate Groups," JRFM, MDPI, vol. 15(2), pages 1-16, February.
    8. Qianqian Kong & Hans Peters, 2021. "An issue based power index," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 23-38, March.
    9. Dominik Karos, 2016. "Coordinated Adoption of Social Innovations," Economics Series Working Papers 797, University of Oxford, Department of Economics.

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    More about this item

    Keywords

    Mutual control structure; Simple games; Power index;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • G34 - Financial Economics - - Corporate Finance and Governance - - - Mergers; Acquisitions; Restructuring; Corporate Governance

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