121 research outputs found
Sub-coalitional egalitarian and solidarity values
No full textThis paper regards some measures for sharing (public) goods or budgets among members with different participation quotas in a binary decisionmaking process. The main characteristic of such measures is that they should have elements of solidarity with those who have a weak quota of participation in the process. These measures seem appropriate for deals that require solidarity, which contrasts with the classical power indices such as the Shapley and Shubik index or the Banzhaf index. Moreover, we provide a new representation for two
power indices—the Public Help Index ξ (proposed by Bertini and Stach in 2015) and the particularization of the solidarity value proposed by Nowak and Radzik in 1994—the ψ index—in a simple game using null player free winning coalitions.
As it is known, a set of null player free winning coalitions unequivocally determines a simple game. Finally, we compare considered power indices considering some properties in simple games
On public values and power indices
No full textIn 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
Guest editorial (to Special Issue on Game Theory and Applications)
No full textThis special issue of Decision Making in Manufacturing and Services is devoted to Game Theory and Applications and related topics. The origin of the issue is the 10th Spain-Italy-Netherlands Meeting on Game Theory (SING10), which took place on 7th-9th July, 2014. The conference was hosted by the Faculty of Management at AGH University of Science and Technology in Kraków, Poland (main organizer was Izabella Stach).
The history of the SING meetings started at the beginning of the 1980s with the first meetings held in Italy. Then, subsequently, meetings were added in Spain, the Netherlands and Poland. Nowadays SING is one of the most important international meetings on game theory organized each year in a European country.
The SING10 meeting in 2014 attracted more than one hundred and ninety scientist from five continents. More about the SING meetings and in particular about SING10 can be funded in Gambarelli (2011) and Bertini et al. (2014).
The submitted papers (139 presentations, 135 in parallel sessions and 4 in plenary sessions) covered a variety of topics on game theory and its applications. This special issue collects some surveys on recent results in different fields, presented in the conference
A general formulation of power indices
No full textThe research presented in this paper has the aim of comparing different power indices for achieving a global vision and formulate a general power index. This general index, suitably set in, make it possible to obtain a wide range of specific indices. The objective is to achieve a global vision and obtain a tool which will better associate the adapted model to all real situation. In this way it is simpler to compare the different models and identify their particular characteristics
Solidarity Measures
No full textThis paper regards some measures for sharing (public) goods or budgets among members with different participation quotas in a binary decisionmaking process. The main characteristic of such measures is that they should have elements of solidarity with those who have a weak quota of participation in the process. These measures seem appropriate for deals that require solidarity, which contrasts with the classical power indices such as the Shapley and Shubik
index or the Banzhaf index. Moreover, we provide a new representation for two power indices—the Public Help Index ξ (proposed by Bertini and Stach in 2015) and the particularization of the solidarity value proposed by Nowak and Radzik in 1994—the ψ index—in a simple game using null player free winning coalitions.
As it is known, a set of null player free winning coalitions unequivocally determines a simple game. Finally, we compare considered power indices considering some properties in simple games
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