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Indirect control and power in mutual control structures

  • Peters H.J.M.
  • Karos D.

    (GSBE)

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 directcontrol. 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 gamestructures, 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.

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Paper provided by Maastricht University, Graduate School of Business and Economics (GSBE) in its series Research Memorandum with number 048.

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Date of creation: 2013
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Handle: RePEc:unm:umagsb:2013048
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  1. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
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  3. repec:hal:journl:halshs-00583867 is not listed on IDEAS
  4. 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.
  5. Peters H.J.M. & Karos D., 2013. "Indirect control and power in mutual control structures," Research Memorandum 048, Maastricht University, Graduate School of Business and Economics (GSBE).
  6. 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.
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  9. 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.
  10. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: controls," Games and Economic Behavior, Elsevier, vol. 45(1), pages 153-170, October.
  11. Yves Crama & Luc Leruth, 2013. "Power Indices And The Measurement Of Control In Corporate Structures," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1340017-1-1.
  12. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
  13. 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.
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