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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.

Indirect Control of Corporations: Analysis and Simulations

Stach I.

Decision Making in Manufacturing and Services

2017

Vol. 11, no. 1-2

31--51

This paper is devoted to the concept of indirect control in corporate shareholding networks. This topic is important in financial economics. Since shareholding size does not actually reflect an investor’s power-control in corporate shareholding networks, diverse approaches to measuring the control-power of investors has been proposed. We focus in particular on a game-theoretical approach; specifically the model of Denti and Prati (2001) and its implementation to control sharing analysis and simulation in shareholding networks thanks to the computer program „Control Sharing Simulation”.

On Public Values and Power Indices

Bertini C., Stach I.

Decision Making in Manufacturing and Services

2015

Vol. 9, no. 1

9--25

In this paper, we analyze some values and power indices from a different point of view that are well-defined in the social context where the goods are public. In particular, we consider the Public Good index (Holler, 1982), the Public Good value (Holler and Li, 1995), the Public Help index (Bertini et al., 2008), the König and Bräuninger index (1998) also called the Zipke index (Nevison et al., 1978), and the Rae index (1969). The aims of this paper are: to propose an extension of the Public Help index to cooperative games; to introduce a new power index with its extension to a game value; and to provide some characterizations of the new index and values.