Abstract
In this chapter the mathematical bulk of the thesis is presented. The aim of having an exhaustive account of the methods results in the extensive scope of the chapter. As networks find their mathematical embodiment in adjacency matrices (see Appendix B), most of the formalism is comprised of linear-algebraic manipulations.
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Notes
- 1.
Brioschi et al. (1989) use the value of the net assets.
- 2.
A list of acronyms can be found in front matter of this book.
- 3.
Treasury shares may have come from a repurchase of shares by the firm from shareholders or they may have never been issued to the public. These shares do not pay dividends and have no voting rights, see also Fig. 1.4.
- 4.
\(\mathrm{diag }(\mathrm{diag }(A)) = \mathrm{diag }(A)\), \(\mathrm{diag }(A+B) = \mathrm{diag }(A) + \mathrm{diag }(B)\), and \(\mathrm{diag }(I) = I\).
- 5.
This was also observed in Eq. (2.75).
- 6.
- 7.
It is not clear if this difference should be understood as an error in the computation or if simply \({\mathop {\nu }\limits ^{^{\circ }}}^\mathrm{int }\) is just another legitimate variant to the theme of integrated value.
- 8.
Meaning on the basis of all direct and indirect paths in the network.
References
H. Almeida, S.Y. Park, M. Subrahmanyam, D. Wolfenzon, Beyond cash flow and voting rights: valuation and performance of firms in complex ownership structures. Working paper, New York University Stern School of Business, 2007
S. Baldone, F. Brioschi, S. Paleari, Ownership measures among firms connected by cross-shareholdings and a further analogy with input-output theory, in 4th JAFEE international conference on investment and derivatives, 1998
J.F. Banzhaf, Weighted voting doesn’t work: a mathematical analysis. Rutgers Law Rev. 19, 317–343 (1965)
S. Battiston, Inner structure of capital control networks. Physica A 338(1–2), 107–112 (2004)
P. Bonacich, Factoring and weighting approaches to status scores and clique identification. J. Math. Sociol. 2(1), 113–120 (1972)
P. Bonacich, Power and centrality: a family of measures. Am. J. Sociol. 92(5), 1170–1182 (1987)
P. Bonacich, P. Lloyd, Eigenvector-like measures of centrality for asymmetric relations. Soc. Netw. 23(3), 191–201 (2001)
S.P. Borgatti, Centrality and network flow. Soc. Netw. 27(1), 55–71 (2005)
S.P. Borgatti, R. Everett, A graph-theoretic perspective on centrality. Soc. Netw. 28(4), 466–484 (2006)
F. Brioschi, S. Paleari, How much equity capital did the Tokyo stock exchange really raise. Finan. Eng. Japan. Mark. 2(3), 233–258 (1995)
F. Brioschi, L. Buzzacchi, M.G. Colombo, Risk capital financing and the separation of ownership and control in business groups. J. Bank. Finance 13(1), 747–772 (1989)
A. Chapelle, Separation of ownership and control: where do we stand? Corp. Ownersh. Control 2(2), (2005)
A. Chapelle, A. Szafarz, Controlling firms through the majority voting rule. Physica A 355, 509–529 (2005)
Y.H. Chen, Voting power, control rents and corporate governance: an integrated analysis of owner control and corporate governance. SSRN eLibrary, 2004
S. Claessens, S. Djankov, The separation of ownership and control in East Asian corporations. J. Finan. Econ. 58(1–2), 81–112 (2000)
Y. Crama, L. Leruth, L.D.R. Renneboog, Corporate control concentration measurement and firm performance. Discussion paper, Tilburg University, 2003. http://ideas.repec.org/p/dgr/kubtil/200317.html
J. Cubbin, D. Leech, The effect of shareholding dispersion on the degree of control in British companies: theory and measurement. Econ. J. 93(370), 351–369 (1983)
H. Demsetz, K. Lehn, The structure of corporate ownership: causes and consequences. J. Polit. Econ. 93(6), 1155–1177 (1985)
B. Derrida, H. Flyvbjerg, Multivalley structure in Kauffman’s model: analogy with spin glasses. J. Phys. A.19, 1003–1008 (1986)
D. Flath, Indirect shareholding within Japan’s business groups. Econ. Lett. 38(2), 223–227 (1992)
L.C. Freeman, Centrality in social networks conceptual clarification. Soc. Netw. 1, 215–239 (1978)
L.C. Freeman, Going the wrong way on a one-way street: centrality in physics and biology. J. Soc. Struct. 9(2), (2008)
J.B. Glattfelder, S. Battiston, Backbone of complex networks of corporations: the flow of control. Phys. Rev. E 80(3), 36104 (2009)
M. Goergen, M. Martynova, L. Renneboog, Corporate governance convergence: evidence from takeover regulation reforms in Europe. Oxford Rev. Econ. Policy 21(2), 243–268 (2005)
O.C. Herfindahl, Copper Costs and Prices: 1870–1957 (John Hopkins University Press, Baltimore, 1959)
C.H. Hubbell, An input-output approach to clique identification. Sociometry 28(4), 377–399 (1965)
R. La Porta, F. Lopez de Silanes, A. Shleifer, Corporate ownership around the world. J. Finan. 54(2), 471–517 (1999)
D. Leech, Corporate ownership and control: a new look at the evidence of Berle and Means. Oxford Econ. Pap. 39(3), 534–551 (1987a)
D. Leech, Ownership concentration and the theory of the firm: a simple-game-theoretic approach. J. Ind. Econ. 35(3), 225–240 (1987b)
D. Leech, The relationship between shareholding concentration and shareholder voting power in British companies: a study of the application of power indices for simple games. Manage. Sci. 34(4), 509–527 (1988)
D. Leech, Computation of power indices. The Warwick Economics Research Paper Series (TWERPS) 644, University of Warwick, Department of Economics, 2002a. URL http://ideas.repec.org/p/wrk/warwec/644.html
D. Leech, An empirical comparison of the performance of classical power indices. Polit. Stud. 50(1), 1–22 (2002b)
D. Leech, J. Leahy, Ownership structure, control type classifications and the performance of large British companies. Econ. J. 101(409), 1418–1437 (1991)
W.W. Leontief, Input-Output Economics (Oxford University Press, Oxford, 1966)
S. Prigge, The performance of shareholder influence measures: an empirical assessment of share in votes, Banzhaf index, and Shapley-Shubik index. SSRN eLibrary, 2007
G. Rohwer, U. Pötter, Transition Data Analysis User’s Manual (Ruhr-University, Bochum, 2005)
F. Schweitzer, G. Fagiolo, D. Sornette, F. Vega-Redondo, A. Vespignani, D.R. White, Economic networks: the new challenges. Science 325(5939), 422 (2009)
M. Serrano, M. Boguñá, A. Vespignani, Extracting the multiscale backbone of complex weighted networks. Proc. Nat. Acad. Sci. 106(16), 6483 (2009)
L.S. Shapley, M. Shubik, A method for evaluating the distribution of power in a committee system. Am. Polit. Sci. Rev. 48(3), 787–792 (1954)
The Deminor Group. Application of the one share—one vote principle in Europe. Technical report, A report prepared for Association of British Insurers by Deminor, 2005. http://www.abi.org.uk/Bookshop/
S. Vitali, J.B. Glattfelder, S. Battiston, The network of global corporate control. PloS ONE 6(10), e25995 (2011)
E. Wigner, The unreasonable effectiveness of mathematics in the natural sciences. Commun. Pure Appl. Math. 13(1), 222–237 (1960)
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Glattfelder, J.B. (2013). The Main Methodology: Computing Control in Ownership Networks. In: Decoding Complexity. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33424-5_2
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