The possibility of bargaining among EU members, or among political parties in a little municipali... more The possibility of bargaining among EU members, or among political parties in a little municipality, the contractual value of thousandths of an apartment building, the weight of a block of shares of a company, the vote of the International Olympic Committee members can be described with the same mathematical models: the power indices. A feature common to the above is the possibility, for each «player», to obtain certain majorities by a coalition with other players. The study of power indices allows the construction of efficient models for forecasting, simulation, optimization and regulations in several fields: political, economic, financial and so on. This paper summarizes some results obtained on the matter, in the Universities of Bergamo and AGH in and give some ideas for further developments.
We outline certain problems, still open before us, concerning the appli-cation of power indices t... more We outline certain problems, still open before us, concerning the appli-cation of power indices to politics and finance.
A solution is proposed to the problem of assigning seats to new countries applying for membership... more A solution is proposed to the problem of assigning seats to new countries applying for membership of the European Parliament. This solution is obtained by weighting the populations and GDP of all members. A strategy of optimization for each single country is also suggested.
Various methods to measure power control of firms in corporate shareholding structures are introd... more Various methods to measure power control of firms in corporate shareholding structures are introduced. This paper is a study of some game-theoretical approaches for measuring direct and indirect control in complex corporate networks. We concentrate on the comparison of methods that use power indices to evaluate the control-power of firms involved in complex corporate networks. More precisely, we only thoroughly analyze the Karos and Peters and the Mercik and Lobos approaches. In particular, we consider the rankings of firms given by the considered methods and the meaning of the values assigned by the power indices to the stock companies presented in corporate networks. Some new results have been obtained. Specifically, taking into account a theoretical example of a corporate shareholding structure, we observe the different rankings of investors and stock companies given by the Φ index introduced by Karos and Peters in 2015 and the implicit index introduced by Mercik and Lobos in 2016. Then, some brief considerations about the reasonable requirements for indirect control measurement are provided, and some ideas of modifying the implicit index are undertaken. The paper also provides a short review of the literature of the game-theoretical approaches to measure control power in corporate networks.
This paper discusses some game-theoretical methods that use power indices for measuring the indir... more This paper discusses some game-theoretical methods that use power indices for measuring the indirect control power of firms and mutual connections in complex corporate shareholding networks. Only a few of the methods considered in the literature so far measure the control power of all firms involved in shareholding networks; meanwhile, none of them regard measuring the importance of linkages. The intention of this article is first to propose a modification of the Mercik-Łobos and Mercik-Stach methods using the Banzhaf index to measure the direct and indirect control of investors and stock companies. Second, having already estimated the control power of nodes (firms) in a network, we consider the relationship of this power to the power of the linkages that connect the companies in directed networks. Then, we present our own idea of how such link’s power can be measured. We regard to the power of the link in relation to the firms as well as (more significantly) in relation to the entire corporate network.
The paper presents a solution to the problem of cost allocation for a communication network in wh... more The paper presents a solution to the problem of cost allocation for a communication network in which the connection values between two nodes are defined by a fuzzy utility function. The utility function can refer to both existing communication nodes and new node proposals. For the allocation mechanism, the authors used the fuzzy Shapley value built on a complete coalition of all paths connecting the root of the tree with all nodes of the given network.
The possibility of bargaining among EU members, or among political parties in a little municipali... more The possibility of bargaining among EU members, or among political parties in a little municipality, the contractual value of thousandths of an apartment building, the weight of a block of shares of a company, the vote of the International Olympic Committee members can be described with the same mathematical models: the power indices. A feature common to the above is the possibility, for each «player», to obtain certain majorities by a coalition with other players. The study of power indices allows the construction of efficient models for forecasting, simulation, optimization and regulations in several fields: political, economic, financial and so on. This paper summarizes some results obtained on the matter, in the Universities of Bergamo and AGH in and give some ideas for further developments.
We outline certain problems, still open before us, concerning the appli-cation of power indices t... more We outline certain problems, still open before us, concerning the appli-cation of power indices to politics and finance.
A solution is proposed to the problem of assigning seats to new countries applying for membership... more A solution is proposed to the problem of assigning seats to new countries applying for membership of the European Parliament. This solution is obtained by weighting the populations and GDP of all members. A strategy of optimization for each single country is also suggested.
Various methods to measure power control of firms in corporate shareholding structures are introd... more Various methods to measure power control of firms in corporate shareholding structures are introduced. This paper is a study of some game-theoretical approaches for measuring direct and indirect control in complex corporate networks. We concentrate on the comparison of methods that use power indices to evaluate the control-power of firms involved in complex corporate networks. More precisely, we only thoroughly analyze the Karos and Peters and the Mercik and Lobos approaches. In particular, we consider the rankings of firms given by the considered methods and the meaning of the values assigned by the power indices to the stock companies presented in corporate networks. Some new results have been obtained. Specifically, taking into account a theoretical example of a corporate shareholding structure, we observe the different rankings of investors and stock companies given by the Φ index introduced by Karos and Peters in 2015 and the implicit index introduced by Mercik and Lobos in 2016. Then, some brief considerations about the reasonable requirements for indirect control measurement are provided, and some ideas of modifying the implicit index are undertaken. The paper also provides a short review of the literature of the game-theoretical approaches to measure control power in corporate networks.
This paper discusses some game-theoretical methods that use power indices for measuring the indir... more This paper discusses some game-theoretical methods that use power indices for measuring the indirect control power of firms and mutual connections in complex corporate shareholding networks. Only a few of the methods considered in the literature so far measure the control power of all firms involved in shareholding networks; meanwhile, none of them regard measuring the importance of linkages. The intention of this article is first to propose a modification of the Mercik-Łobos and Mercik-Stach methods using the Banzhaf index to measure the direct and indirect control of investors and stock companies. Second, having already estimated the control power of nodes (firms) in a network, we consider the relationship of this power to the power of the linkages that connect the companies in directed networks. Then, we present our own idea of how such link’s power can be measured. We regard to the power of the link in relation to the firms as well as (more significantly) in relation to the entire corporate network.
The paper presents a solution to the problem of cost allocation for a communication network in wh... more The paper presents a solution to the problem of cost allocation for a communication network in which the connection values between two nodes are defined by a fuzzy utility function. The utility function can refer to both existing communication nodes and new node proposals. For the allocation mechanism, the authors used the fuzzy Shapley value built on a complete coalition of all paths connecting the root of the tree with all nodes of the given network.
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Papers by Izabella Stach