Indirect control and power in mutual control structures

Abstract

In a mutual control structure agents exercise control over each other. Typical examples occur in the area of corporate governance: firms and investment companies exercise mutual control, in particular by owning each others' stocks. In this paper we formulate a general model for such situations. There is a fixed set of agents, and a mutual control structure assigns to each subset (coalition) the subset of agents controlled by that coalition. Such a mutual control structure captures direct control. We propose a procedure in order to incorporate indirect control as well: if S controls T , and S and T jointly control R, then S controls R indirectly. This way, invariant mutual control structures result. Alternatively, mutual control can be described by vectors of simple games, called simple game structures, each simple game describing who controls a certain player, and also those simple games can be updated in order to capture indirect control. We show that both approaches lead to equivalent invariant structures.In the second part of the paper, we axiomatically develop a class of power indices for invariant mutual control structures. We impose four axioms with a plausible interpretation in this framework, which together characterize a broad class of power indices based on dividends resulting both from exercising and from undergoing control. By adding an extra condition a unique power index is singled out. In this index, each player accumulates his Shapley-Shubik power index assignments from controlling other players, diminished by the sum of the Shapley-Shubik power index assignments to other players controlling him.

Indirect Control of Corporations: Analysis and Simulations

“…Then in (1999), Turnovec proposed a way of determining the direct and indirect property distribution and the degree of transparency of an ownership structure. Since then, numerous other approaches have been proposed; for example, a reader can find a good and broad literature review of the most relevant references in this topic in Leruth, 2007, 2013;Karos and Peters, 2015;Bertini et al, 2016).…”

“…Mostly, the Shapley-Shubik and Banzhaf indices or their modifications have been applied to measure direct and indirect power/control [see, for example, Shapley, 2003a, 2003b;Leruth, 2007, 2013;Karos and Peters, 2015); for the Banzhaf index, see (Banzhaf, 1965;Penrose, 1946Penrose, , 1952; for Shapley-Shubik, see (Shapley and Shubik, 1954)]. However, there are some approaches that have used other indices.…”

“…Figures 3 and 4 show the shareholding networks with cycles in the graphs. Figure 2 presents the simplified organization chart of the Porsche-Volkswagen corporate structure (from 2008 to 2013) considered in (Karos and Peters, 2015). The players are Porsche Family (1), Qatar (2), Lower Saxony (3), Porsche SE (4), Volkswagen AG (5), Porsche AG (6), and Others (7).…”

Effectivity and power

“…Similarly, economic situations as for instance financial and corporate governance structures may be modelled by simple games, and power indices may be applied in order to obtain some indication of the real influence of firms or investment companies in such situations Leruth, 2007, 2013;Karos and Peters, 2015).…”

Cross-Ownership: A Device for Management Entrenchment?

“…Cross-ownership can also be found in the U.S. mutual fund industry. For instance, 1 This situation corresponds to a two-firm ownership ring or mutual control (Karos and Peters, 2013). In fact, the length of a cross-ownership ring may take any positive integer value.…”