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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.
The article studies the efficient computation of the Public Good index defined by Manfred Holler in 1982 (and also known as the Holler index or as the Holler–Packel index) as well as variations of that power index defined in scientific works by Manfred Holler allowing for precoalitions among subsets of players. Starting from the state-of-the-art algorithm for computing the Public Good index for weighted voting games the paper presents a framework for fast algorithms for six variants of the Public Good index with precoalitions. The study discusses implementations of the Public Good indices with precoalitions in C++, reviews computing times, and points out that the new algorithms are applicable for large numbers of 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 ‘CoopGame’
(2019)
The theory of cooperative games with transferable utility offers useful insights into the way parties can share gains from cooperation and secure sustainable agreements, see e.g. one of the books by Chakravarty,Mitra and Sarkar (2015, ISBN:978-1107058798) or by Driessen (1988,ISBN:978-9027727299) for more details. A comprehensive set of tools for cooperative game theory with transferable utility is provided. Users can create special families of cooperative games, like e.g. bankruptcy games,cost sharing games and weighted voting games. There are functions to check various game properties and to compute five different set-valued solution concepts for cooperative games. A large number of point-valued solution concepts is available reflecting the diverse application areas of cooperative game theory. Some of these point-valued solution concepts can be used to analyze weighted voting games and measure the influence of individual voters within a voting body. There are routines for visualizing both set-valued and point-valued solutions in the case of three or four players.
This document gives a few use cases for the EvolutionaryGames package. EvolutionaryGames provides basic concepts of evolutionary game theory, like e.g. finding evolutionary stable strategies and computing and drawing evolutionarily stable sets as well as phase diagrams for various evolutionary dynamics for single-population games with two, three and four different phenotypes.
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.
The purpose of this paper is to introduce new methods to measure the indirect control power of firms in complex corporate shareholding structures using the concept of power indices from cooperative game theory. The proposed measures vary in desirable properties satisfied, as well as in the bargaining models of power indices used to construct them. Hence, they can be used to produce different pictures of the coalitional strength of firms in control of other firms in mutual shareholding networks with the presence of cycles. Precisely, in the framework of Karos and Peters from 2015, ten power indices substitute the original Shapley and Shubik power index in a modular fashion. In this way, we obtain a set of new measures called aggregated indices. The float shareholders typically hold less than 5 percent of the outstanding shares, which is an uncertain element of indirect control in complex shareholding structures. The fuzzy number seems appropriate to model these shareholders’ behavior. The novelty is that we model the behavior of float using Z-fuzzy numbers. The new methods are tested in an example.
The article belongs to the Special Issue "Decision Optimization in Information Theory and Game Theory" of the journal "Entropy".
The aim of the article is to propose a new method of valuation of a company, considering its ownership relations with other companies. For this purpose, the concept of the Shapley value from cooperative game theory is used as the basis for assessing such dependent companies. The paper presents proposals for Shapley value calculation algorithms for our model. We expand our model by discussing personal relations in addition to ownership relations and point out how intuitionistic fuzzy sets may be helpful in this context. As a result, we propose two new expanded models. In the first probabilistic model, we apply Pearson’s correlation coefficient, in the second, we use a correlation coefficient between intuitionistic fuzzy sets to determine the personal relationships. Finally, we present and interpret results for a real-world economic network with 17 companies.
We study the efficient computation of power indices for weighted voting games with precoalitions amongst subsets of players (reflecting, e.g., ideological proximity) using the paradigm of dynamic programming. Starting from the state-of-the-art algorithms for computing the Banzhaf and Shapley–Shubik indices for weighted voting games, we present a framework for fast algorithms for the three most common power indices with precoalitions, i.e., the Owen index, the Banzhaf–Owen index and the symmetric coalitional Banzhaf index, and point out why our new algorithms are applicable for large numbers of players. We discuss implementations of our algorithms for the three power indices with precoalitions in C++ and review computing times, as well as storage requirements.