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Institute
This paper reviews the recent literature on the “social ranking problem”, that is, the problem of converting group rankings into individual rankings. We introduce and categorize existing social ranking methods and we briefly explain their attributes. Three main categories of social ranking methods are identified: lexicographic social rankings, methods based on voting mechanisms, and those inspired by the theory of coalitional games. An open-source R package called socialranking for computing the majority of the existing social rankings is also presented and discussed.
Computing Shapley values for large cooperative games is an NP-hard problem. For practical applications, stochastic approximation via permutation sampling is widely used. In the context of machine learning applications of the Shapley value, the concept of antithetic sampling has become popular. The idea is to employ the reverse permutation of a sample in order to reduce variance and accelerate convergence of the algorithm. We study this approach for the Shapley and Banzhaf values, as well as for the Owen value which is a solution concept for games with precoalitions. We combine antithetic samples with established stratified sampling algorithms. Finally, we evaluate the performance of these algorithms on four different types of cooperative games.
The Asymmetric Public Goods Game (APGG) C++ framework offers an easy to use environment to study game theoretical questions. Specifically, it is designed to address questions in the domain of asymmetric public goods games.
We hereby publish version 1.1.2 of our software APGG (Release for DOI via Zenodo for paper in JOSS, the Journal of Open Source Software).
The Asymmetric Public Goods Game (APGG) C++ framework offers an easy to use environment to study game theoretical questions. Specifically, it is designed to address questions in the domain of asymmetric public goods games. The modular architecture allows for a vast amount of scenarios and setups for experimenting with different public goods games, using easy to change parameters. Users can experiment with well mixed and structured populations as well as with symmetric and asymmetric payoffs. APGG also features group level payoffs and individual payoffs, and different evolutionary selection mechanisms (Miller et al., 1995) and replication schemes. Results are automatically saved in semantic and descriptive structures and can be easily visualized with the included Python scripts. This paper aims to explain the functionality and the structure of the framework, to show the workflow that APGG follows, to present the different modules that are available, and to show how APGG can be used to run experiments with public goods games on example scenarios.
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.
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".
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.
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.
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.