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Indirect control and power in mutual control structures

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  • Karos, D.

    (Externe publicaties SBE)

  • Peters, H.J.M.

    (Quantitative Economics)

Abstract

In a mutual control structure 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. In this paper we formulate a general model for such situations. There is a fixed set of agents, and a mutual control structure assigns to each subset (coalition) the subset of agents controlled by that coalition. Such a mutual control structure captures direct control. We propose a procedure in order to incorporate indirect control as well: if S controls T, and S and T jointly control R, then S controls R indirectly. This way, invariant mutual control structures result. Alternatively, mutual control can be described by vectors of simple games, called simple game structures, each simple game describing who controls a certain player, and also those simple games can be updated in order to capture indirect control. We show that both approaches lead to equivalent invariant structures. In the second part of the paper, we axiomatically develop a class of power indices for invariant mutual control structures. 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. By adding an extra condition a unique power index is singled out. In this index, each player accumulates his Shapley-Shubik power index assignments from controlling other players, diminished by the sum of the Shapley-Shubik power index assignments to other players controlling him.

Suggested Citation

  • Karos, D. & Peters, H.J.M., 2013. "Indirect control and power in mutual control structures," Research Memorandum 048, Maastricht University, Graduate School of Business and Economics (GSBE).
  • Handle: RePEc:unm:umagsb:2013048
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    References listed on IDEAS

    as
    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.
    2. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
    3. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 277-293.
    4. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
    5. Einy, Ezra & Haimanko, Ori, 2011. "Characterization of the Shapley–Shubik power index without the efficiency axiom," Games and Economic Behavior, Elsevier, vol. 73(2), pages 615-621.
    6. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: controls," Games and Economic Behavior, Elsevier, vol. 45(1), pages 153-170, October.
    7. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    8. Enrico Denti & Nando Prati, 2004. "Relevance of winning coalitions in indirect control of corporations," Theory and Decision, Springer, vol. 56(1), pages 183-192, April.
    9. 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.
    10. Gambarelli, Gianfranco & Owen, Guillermo, 1994. "Indirect Control of Corporations," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(4), pages 287-302.
    11. Enrico Denti & Nando Prati, 2004. "Relevance of winning coalitions in indirect control of corporations," Theory and Decision, Springer, vol. 56(2_2), pages 183-192, February.
    12. 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.
    13. Hao Sun & Theo Driessen, 2006. "Semi-marginalistic Values for Set Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(2), pages 241-258, August.
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    Cited by:

    1. Karos, Dominik & Peters, Hans, 2016. "Effectivity and Power," Research Memorandum 034, Maastricht University, Graduate School of Business and Economics (GSBE).
    2. Dominik Karos, 2016. "Coordinated Adoption of Social Innovations," Economics Series Working Papers 797, University of Oxford, Department of Economics.
    3. Marc Levy & Ariane Szafarz, 2017. "Cross-Ownership: A Device for Management Entrenchment?," Review of Finance, European Finance Association, vol. 21(4), pages 1675-1699.
    4. Rene van den Brink & Judith Timmer & Hans Peters, 2016. "Power on digraphs," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 2, pages 107-125.
      • Peters, Hans & Timmer, Judith & van den Brink, Rene, "undated". "Power on digraphs," Research Memorandum 019, Maastricht University, Graduate School of Business and Economics (GSBE).
    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. repec:eee:gamebe:v:108:y:2018:i:c:p:363-378 is not listed on IDEAS

    More about this item

    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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