Skip to main content
SpringerLink
Log in

Algorithms for Measuring Indirect Control in Corporate Networks and Effects of Divestment

  • Chapter
  • First Online:
Transactions on Computational Collective Intelligence XXXVII

Part of the book series: Lecture Notes in Computer Science ((TCCI,volume 13750))

Abstract

This paper discusses algorithms for measuring indirect control in complex corporate shareholding networks and investigates the importance of mutual connections in the network in the sense of shareholdings of one firm in another. Our algorithms rely on the concept of power indices from cooperative game theory. We focus on a variant of the implicit power index by Stach and Mercik based on the absolute Banzhaf index. We extend this algorithm by determining the number of regressions in an adaptive network-dependent manner taking into account the maximal length of a path to each controlled company in the network and by a model for the float, i.e., the set of unidentified small shareholders. We compare our method with existing algorithms and discuss the importance of linkages by investigating divestment of shares for a theoretical network with 21 players.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Algaba, E., Bilbao, J., Fernández, J., Jiménez, N., López, J.: Algorithms for computing the Myerson value by dividends. In: Moore, K.B. (ed.) Discrete Mathematics Research Progress, pp. 1–13. Nova Science Publishers (2007)

    Google Scholar 

  2. Algaba, E., Bilbao, J.M., Fernández Garcıa, J.R.: The distribution of power in the European constitution. Eur. J. Oper. Res. 176(3), 1752–1766 (2007). https://doi.org/10.1016/j.ejor.2005.12.002

    Article  MATH  Google Scholar 

  3. Algaba, E., Bilbao, J.M., Fernández Garcıa, J.R., López, J.: Computing power indices in weighted multiple majority games. Math. Soc. Sci. 46(1), 63–80 (2003). https://doi.org/10.1016/S0165-4896(02)00086-0

    Article  MATH  Google Scholar 

  4. Algaba, E., Fragnelli, V., Sánchez-Soriano, J.: Handbook of the Shapley value. CRC Press, Boca Raton (2020). https://doi.org/10.1201/9781351241410

    Book  Google Scholar 

  5. Alonso-Meijide, J.M., Bowles, C., Holler, M.J., Napel, S.: Monotonicity of power in games with a priori unions. Theor. Decis. 66(1), 17–37 (2009). https://doi.org/10.1007/s11238-008-9114-2

    Article  MATH  Google Scholar 

  6. Bang-Jensen, J., Gutin, G.Z.: Digraphs: theory, algorithms and applications. Springer Science & Business Media, Berlin (2008)

    MATH  Google Scholar 

  7. Banzhaf, J.F.: Weighted voting doesn’t work: a mathematical analysis. Rutgers L. Rev. 19, 317–343 (1965)

    Google Scholar 

  8. Berghammer, R., Bolus, S.: On the use of binary decision diagrams for solving problems on simple games. Eur. J. Oper. Res. 222(3), 529–541 (2012)

    Article  MATH  Google Scholar 

  9. Berghammer, R., Bolus, S., Rusinowska, A., De Swart, H.: A relation-algebraic approach to simple games. Eur. J. Oper. Res. 210(1), 68–80 (2011)

    Article  MATH  Google Scholar 

  10. Bertini, C., Freixas, J., Gambarelli, G., Stach, I.: Comparing power indices. Int. Game Theory Rev. 15(02), 1340004 (2013)

    Article  MATH  Google Scholar 

  11. Bertini, C., Mercik, J., Stach, I.: Indirect control and power. Oper. Res. Decisions 26(2), 7–30 (2016). https://doi.org/10.5277/ord160202

    Article  Google Scholar 

  12. Bertini, C., Stach, I.: Banzhaf voting power measure. In: Dowding, K. (ed.) Encyclopedia of Power, SAGE Publications, pp. 54–55. Sage Publications (2011)

    Google Scholar 

  13. Bolus, S.: Power indices of simple games and vector-weighted majority games by means of binary decision diagrams. Eur. J. Oper. Res. 210(2), 258–272 (2011)

    Article  MATH  Google Scholar 

  14. Bolus, S.: A QOBDD-based approach to simple games. Ph.D. thesis, Christian-Albrechts Universität Kiel (2012)

    Google Scholar 

  15. Borm, P., Owen, G., Tijs, S.: On the position value for communication situations. SIAM J. Discret. Math. 5(3), 305–320 (1992)

    Article  MATH  Google Scholar 

  16. Chakravarty, S.R., Mitra, M., Sarkar, P.: A Course on Cooperative Game Theory. Cambridge University Press, Cambridge (2015)

    MATH  Google Scholar 

  17. Crama, Y., Leruth, L.: Control and voting power in corporate networks: concepts and computational aspects. Eur. J. Oper. Res. 178(3), 879–893 (2007). https://doi.org/10.1016/j.ejor.2006.02.020

    Article  MATH  Google Scholar 

  18. Crama, Y., Leruth, L.: Power indices and the measurement of control in corporate structures. Int. Game Theory Rev. 15(03), 1340017 (2013). https://doi.org/10.1142/S0219198913400173

    Article  MATH  Google Scholar 

  19. Csardi, G., Nepusz, T., et al.: The igraph software package for complex network research. Int. J. complex syst. 1695(5), 1–9 (2006). https://igraph.org/

  20. Deegan, J., Packel, E.: A new index of power for simple n-person games. Int. J. Game Theory 7(2), 113–123 (1978)

    Article  MATH  Google Scholar 

  21. Derks, J., Haller, H.: Null players out? linear values for games with variable supports. Int. Game Theory Rev. 1(03n04), 301–314 (1999)

    Article  MATH  Google Scholar 

  22. Dubey, P., Shapley, L.S.: Mathematical properties of the Banzhaf power index. Math. Oper. Res. 4(2), 99–131 (1979)

    Article  MATH  Google Scholar 

  23. Eddelbuettel, D., et al.: RCPP: seamless R and C++ integration. J. Stat. Softw. 40(8), 1–18 (2011)

    Article  MATH  Google Scholar 

  24. Fernández, J.R., Algaba, E., Bilbao, J.M., Jiménez, A., Jiménez, N., López, J.J.: Generating functions for computing the Myerson value. Ann. Oper. Res. 109(1), 143–158 (2002). https://doi.org/10.1023/A:1016348001805

    Article  MATH  Google Scholar 

  25. Holler, M.J.: Forming coalitions and measuring voting power. Polit. Stud. 30(2), 262–271 (1982)

    Article  Google Scholar 

  26. Holler, M.J., Packel, E.: Power, luck and the right index. Z. f. Nationalökonomie 43(1), 21–29 (1983). https://doi.org/10.1007/BF01283881

    Article  Google Scholar 

  27. Johnston, R.: On the measurement of power: some reactions to Laver. Environ. Plan. A 10(8), 907–914 (1978). https://doi.org/10.1068/a100907

    Article  Google Scholar 

  28. Karos, D., Peters, H.: Indirect control and power in mutual control structures. Games Econom. Behav. 92, 150–165 (2015). https://doi.org/10.1016/j.geb.2015.06.003

    Article  MATH  Google Scholar 

  29. Kirsch, W., Langner, J.: Power indices and minimal winning coalitions. Soc. Choice Welf. 34(1), 33–46 (2010). https://doi.org/10.1007/s00355-009-0387-3

    Article  MATH  Google Scholar 

  30. Lange, F., Kóczy, L.Á.: Power indices expressed in terms of minimal winning coalitions. Soc. Choice Welf. 41(2), 281–292 (2013). https://doi.org/10.1007/s00355-012-0685-z

    Article  MATH  Google Scholar 

  31. Leech, D.: Voting power in the governance of the international monetary fund. Ann. Oper. Res. 109(1), 375–397 (2002). https://doi.org/10.1023/A:1016324824094

    Article  MATH  Google Scholar 

  32. Leech, D.: Computing power indices for large voting games. Manage. Sci. 49(6), 831–837 (2003)

    Article  MATH  Google Scholar 

  33. Leech, D.: Power indices in large voting bodies. Public Choice 155(1), 61–79 (2013)

    Article  Google Scholar 

  34. Levy, M.: Control in pyramidal structures. Corp. Gov. Int. Rev. 17(1), 77–89 (2009)

    Article  Google Scholar 

  35. Levy, M.: The Banzhaf index in complete and incomplete shareholding structures: a new algorithm. Eur. J. Oper. Res. 215(2), 411–421 (2011)

    Article  MATH  Google Scholar 

  36. Levy, M., Szafarz, A.: Cross-ownership: a device for management entrenchment? Rev. Finan. 21(4), 1675–1699 (2017). https://doi.org/10.1093/rof/rfw009

    Article  MATH  Google Scholar 

  37. Malawski, M.: Counting power indices for games with a priori unions. In: Gambarelli, G. (ed.) Essays in Cooperative Games. Theory and Decision Library, vol. 36, pp. 125–140. Springer, Boston (2004). https://doi.org/10.1007/978-1-4020-2936-3_10

    Chapter  MATH  Google Scholar 

  38. Matsui, Y., Matsui, T.: NP-completeness for calculating power indices of weighted majority games. Theoret. Comput. Sci. 263(1–2), 305–310 (2001)

    Article  MATH  Google Scholar 

  39. Mercik, J., Gładysz, B., Stach, I., Staudacher, J.: Shapley-based estimation of company value-concept, algorithms and parameters. Entropy 23(12), 1598 (2021). https://doi.org/10.3390/e23121598

    Article  Google Scholar 

  40. Mercik, J., Łobos, K.: Index of implicit power as a measure of reciprocal ownership. In: Nguyen, N.T., Kowalczyk, R., Mercik, J. (eds.) Transactions on Computational Collective Intelligence XXIII. LNCS, vol. 9760, pp. 128–140. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-52886-0_8

    Chapter  Google Scholar 

  41. Mercik, J., Ramsey, D.M.: The effect of Brexit on the balance of power in the European union council: an approach based on pre-coalitions. In: Mercik, J. (ed.) Transactions on Computational Collective Intelligence XXVII. LNCS, vol. 10480, pp. 87–107. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70647-4_7

    Chapter  MATH  Google Scholar 

  42. Mercik, J., Stach, I.: On measurement of control in corporate structures. In: Nguyen, N.T., Kowalczyk, R., Mercik, J., Motylska-Kuźma, A. (eds.) Transactions on Computational Collective Intelligence XXXI. LNCS, vol. 11290, pp. 64–79. Springer, Heidelberg (2018). https://doi.org/10.1007/978-3-662-58464-4_7

    Chapter  Google Scholar 

  43. Myerson, R.B.: Graphs and cooperation in games. Math. Oper. Res. 2(3), 225–229 (1977)

    Article  MATH  Google Scholar 

  44. Shapley, L.S.: A value for n-person games. In: Kuhn, H., Tucker, A. (eds.) Contributions to the Theory of Games II, pp. 307–317. Princeton University Press (1953). https://doi.org/10.1515/9781400881970-018

  45. Shapley, L.S., Shubik, M.: A method for evaluating the distribution of power in a committee system. Am. Polit. Sci. Rev. 48(3), 787–792 (1954). https://doi.org/10.2307/1951053

    Article  Google Scholar 

  46. Stach, I.: Shapley-Shubik index. In: Dowding, K. (eds.) Encyclopedia of Power, pp. 603–606. Sage Publications (2011)

    Google Scholar 

  47. Stach, I.: Indirect control of corporations: analysis and simulations. Decis. Mak. Manuf. Serv. 11(1–2), 31–51 (2017). https://doi.org/10.7494/dmms.2017.11.1-2.31

    Article  MATH  Google Scholar 

  48. Stach, I.: Sub-coalitional approach to values. In: Mercik, J. (ed.) Transactions on Computational Collective Intelligence XXVII. LNCS, vol. 10480, pp. 74–86. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70647-4_6

    Chapter  Google Scholar 

  49. Stach, I., Mercik, J.: Measurement of control power in corporate networks. Oper. Res. Decis. 31(1), 97–121 (2021). https://doi.org/10.37190/ord210106

    Article  MATH  Google Scholar 

  50. Stach, I., Mercik, J., Bertini, C.: Some propositions of approaches for measuring indirect control power of firms and mutual connections in corporate shareholding structures. In: Nguyen, N.T., Kowalczyk, R., Mercik, J., Motylska-Kuźma, A. (eds.) Transactions on Computational Collective Intelligence XXXV. LNCS, vol. 12330, pp. 116–132. Springer, Heidelberg (2020). https://doi.org/10.1007/978-3-662-62245-2_8

    Chapter  Google Scholar 

  51. Staudacher, J.: Computing the public good index for weighted voting games with precoalitions using dynamic programming. In: Power & Responsibility: Interdisciplinary Perspectives for the 21st Century in Honor of Manfred J. Holler, p. 17. Springer, Berlin (2022)

    Google Scholar 

  52. Staudacher, J., Anwander, J.: Using the R package CoopGame for the analysis, solution and visualization of cooperative games with transferable utility, R Vignette (2021). https://cran.r-project.org/package=CoopGame

  53. Staudacher, J., et al.: Computing power indices for weighted voting games via dynamic programming. Oper. Res. Decis. 31(2), 123–145 (2021). https://doi.org/10.37190/ord210206

    Article  MATH  Google Scholar 

  54. Staudacher, J., Olsson, L., Stach, I.: Implicit power indices for measuring indirect control in corporate structures. In: Nguyen, N.T., Kowalczyk, R., Motylska-Kuźma, A., Mercik, J. (eds.) Transactions on Computational Collective Intelligence XXXVI. LNCS, vol. 13010, pp. 73–93. Springer, Heidelberg (2021). https://doi.org/10.1007/978-3-662-64563-5_4

    Chapter  Google Scholar 

  55. Staudacher, J., Wagner, F., Filipp, J.: Dynamic programming for computing power indices for weighted voting games with Precoalitions. Games 13(1), 6 (2022). https://doi.org/10.3390/g13010006

    Article  MATH  Google Scholar 

  56. The R Core team and others: R: A language and environment for statistical computing. Vienna, Austria (2021). https://www.r-project.org/

  57. Wickham, H.: R packages: organize, test, document, and share your code. O’Reilly Media (2015). https://r-pkgs.org/

Download references

Acknowledgements

The first author thanks the funding of the Bavarian State Ministry of Science and Arts. The third author’s contribution to the article was funded under subvention funds for the AGH University of Science and Technology in Krakow, Poland. The authors thank two anonymous reviewers for their careful reading of the manuscript and their helpful comments and suggestions.

Author information

Authors and Affiliations

  1. Fakultät Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435, Kempten, Germany

    Jochen Staudacher & Linus Olsson

  2. AGH University of Science and Technology, Al. Mickiewicza 30, 30-059, Kraków, Poland

    Izabella Stach

Authors
  1. Jochen Staudacher
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Linus Olsson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Izabella Stach
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jochen Staudacher .

Editor information

Editors and Affiliations

  1. Institute of Informatics, Wroclaw University of Technology, Wroclaw, Poland

    Ngoc Thanh Nguyen

  2. Faculty of Information and Communication Technology, Swinburne University of Technology, Hawthorn, Victoria, VIC, Australia

    Ryszard Kowalczyk

  3. WSB University in Wroclaw, Wroclaw, Poland

    Jacek Mercik

  4. University of Lower Silesia, Wroclaw, Poland

    Anna Motylska-Kuźma

Ethics declarations

Conflict of Interest

The authors declare no conflicts of interest.

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer-Verlag GmbH Germany, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Staudacher, J., Olsson, L., Stach, I. (2022). Algorithms for Measuring Indirect Control in Corporate Networks and Effects of Divestment. In: Nguyen, N.T., Kowalczyk, R., Mercik, J., Motylska-Kuźma, A. (eds) Transactions on Computational Collective Intelligence XXXVII. Lecture Notes in Computer Science(), vol 13750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-66597-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-66597-8_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-66596-1

  • Online ISBN: 978-3-662-66597-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation