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

Assessing Antithetic Sampling for Approximating Shapley, Banzhaf, and Owen Values

“…For our sampling algorithms, it is safe to assume that sampling the characteristic function (of the TU game to be approximated) is the most costly part of the computation. Hence, we always plot the number of samples per player (x-axis) against the mean squared error (mse, y-axis) (12).…”

“…Modern applications of cooperative game theory reach far beyond the fair allocation of benefits. For example, models and solution concepts from cooperative game theory are employed for understanding voting power in committees [3][4][5], as well as for analyzing genetic networks [6,7], terrorist networks [8][9][10], or complex shareholding networks [11,12]. However, for n players the number of coalitions grows exponentially and this makes efficient computations on cooperative games challenging.…”

Aggregated Power Indices for Measuring Indirect Control in Complex Corporate Networks with Float Shareholders

“…The game theory approach to measuring the indirect control power of firms as elements of a whole corporate network is known in the literature on the subject. Many scholars proposed methods based on power indices for measuring the indirect control power of a firm in an ownership network; see Gambarelli and Owen (1994) [ 4 ], Turnovec (1999) [ 5 ], Hu and Shapley (2003) [ 6 , 7 ], Leech (2002) [ 8 ], Crama and Leruth (2007, 2013) [ 3 , 9 ], Karos and Peters (2015) [ 1 ], Mercik and Lobos (2016) [ 10 ], Levy and Szafarz (2017) [ 11 ], Mercik and Stach (2018) [ 12 ], Stach, Mercik, and Bertini (2020) [ 13 ], Staudacher, Olsson, and Stach (2021) [ 14 ], Stach and Mercik (2021) [ 15 ], Staudacher, Olsson, and Stach (2022) [ 16 ], and Stach, Mercik, and Bertini (2023) [ 17 ], for examples. The reader can find the comparisons of some of these approaches in [ 18 , 19 , 20 ] and [ 12 ].…”