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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 article deals with measuring indirect control in complex corporate shareholding networks using the concept of power indices from cooperative game theory. We focus on the approaches by Mercik-Łobos and Stach-Mercik which measure the control power of all firms involved in shareholding networks with algorithms based on the raw Johnston index. We point out how these approaches can be generalized replacing the raw Johnston index by various other power indices in a modular fashion. We further extend the algorithmic framework by investigating more than one regression and present requirements for software and modelling. Finally, we test the new framework of generalized implicit power indices for a network with 21 players and discuss how properties of the underlying power index like efficiency or null player removability influence the measurements of indirect control.
Package ‘rSRD’
(2023)
We provide an implementation for Sum of Ranking Differences (SRD),
a novel statistical test introduced by Héberger (2010)
<doi:10.1016/j.trac.2009.09.009>. The test allows the comparison of
different solutions through a reference by first performing a rank
transformation on the input, then calculating and comparing the distances
between the solutions and the reference - the latter is measured in the
L1 norm. The reference can be an external benchmark (e.g. an established
gold standard) or can be aggregated from the data. The calculated distances,
called SRD scores, are validated in two ways, see Héberger and Kollár-Hunek
(2011) <doi:10.1002/cem.1320>. A randomization test (also called permutation
test) compares the SRD scores of the solutions to the SRD scores of randomly
generated rankings. The second validation option is cross-validation that
checks whether the rankings generated from the solutions come from the same
distribution or not. For a detailed analysis about the cross-validation
process see Sziklai, Baranyi and Héberger (2021) <arXiv:2105.11939>. The
package offers a wide array of features related to SRD including the computation
of the SRD scores, validation options, input preprocessing and plotting tools.
We study the efficient computation of power indices for weighted voting games using the paradigm of dynamic programming. We survey the state-of-the-art algorithms for computing the Banzhaf and Shapley–Shubik indices and point out how these approaches carry over to related power indices. Within a unified framework, we present new efficient algorithms for the Public Good index and a recently proposed power index based on minimal winning coalitions of the smallest size, as well as a very first method for computing the Johnston indices for weighted voting games efficiently. We introduce a software package providing fast C++ implementations of all the power indices mentioned in this article, discuss computing times, as well as storage requirements.