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2 Operations Research and Decisions

2 2021

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Measurement of control power in corporate networks

Stach Izabella, Mercik Jacek

Operations Research and Decisions

2021

Vol. 31, No. 1

98--121

This paper discusses some game-theoretical methods for measuring indirect control in complex corporate shareholding networks. The methods use power indices to estimate the direct and indirect control in shareholding structures. Some of these methods only estimate the control power of investors (firms without shareholdings), and only a few measure the control power of all firms involved in shareholding networks (which means investors and stock companies). None of them takes measuring the importance of mutual connections (edges in the networks) into consideration; thus we focus in particular on an extension of these methods in this paper to measure both the control-power of the firms involved in complex shareholding structures (represented by nodes in networks) and the importance (power) of linkages between the firms as elements of a whole corporate shareholding network. More precisely, we apply our approaches to a theoretical example of a corporate network. Moreover, we continue the considerations about reasonable properties for indirect control measurement. Some ideas of new properties are proposed. The paper also provides a brief review of the literature concerning the topic.

Computing power indices for weighted voting games via dynamic programming

Staudacher Jochen, Kóczy László Á., Stach Izabella, Filipp Jan, Kramer Marcus, Noffke Till, Olsson Linuss, Pichler Jonas, Singer Tobias

Operations Research and Decisions

2021

Vol. 31, No. 2

123--145

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.