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This paper discusses some game-theoretical methods for measuring indirect control in complex corporate shareholding networks. The methods use power indices in order 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 take 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 in order 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 started in Mercik and Stach (Transactions on Computational Collective Intelligence XXXI, LNCS 11290: 64–79, 2018) 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.

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