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International audience ; In this paper, we apply bargaining theory to a certain model of coalition formation. The notions of a feasible government and a stable government are central in the model considered. By a government, we mean a pair consisting of a majority coalition and a policy supported by this coalition. The aim of this paper is to establish which stable government should be created if more than one stable government exists or, in case there is no stable one, which feasible government should be formed if more than one feasible government exists. Several bargaining procedures leading to the choice of one stable (or feasible) government are proposed. We define bargaining games in which only parties belonging to at least one stable (or feasible) government bargain over the creation of a government. We consider different bargaining costs. We investigate subgame perfect equilibria of the bargaining games defined. It turns out that the prospects of a party depend on the procedure applied, and on the bargaining costs assumed. We also apply the coalition formation model to the Polish Parliament after the 2001 elections and apply the different bargaining games for the creation of a government to this example.

International audience ; In this paper, we apply bargaining theory to a certain model of coalition formation. The notions of a feasible government and a stable government are central in the model considered. By a government, we mean a pair consisting of a majority coalition and a policy supported by this coalition. The aim of this paper is to establish which stable government should be created if more than one stable government exists or, in case there is no stable one, which feasible government should be formed if more than one feasible government exists. Several bargaining procedures leading to the choice of one stable (or feasible) government are proposed. We define bargaining games in which only parties belonging to at least one stable (or feasible) government bargain over the creation of a government. We consider different bargaining costs. We investigate subgame perfect equilibria of the bargaining games defined. It turns out that the prospects of a party depend on the procedure applied, and on the bargaining costs assumed. We also apply the coalition formation model to the Polish Parliament after the 2001 elections and apply the different bargaining games for the creation of a government to this example.

International audience ; In this paper, we apply bargaining theory to a certain model of coalition formation. The notions of a feasible government and a stable government are central in the model considered. By a government, we mean a pair consisting of a majority coalition and a policy supported by this coalition. The aim of this paper is to establish which stable government should be created if more than one stable government exists or, in case there is no stable one, which feasible government should be formed if more than one feasible government exists. Several bargaining procedures leading to the choice of one stable (or feasible) government are proposed. We define bargaining games in which only parties belonging to at least one stable (or feasible) government bargain over the creation of a government. We consider different bargaining costs. We investigate subgame perfect equilibria of the bargaining games defined. It turns out that the prospects of a party depend on the procedure applied, and on the bargaining costs assumed. We also apply the coalition formation model to the Polish Parliament after the 2001 elections and apply the different bargaining games for the creation of a government to this example.

Simple games are a powerful tool to analyze decision-making and coalition formation in social and political life. In this paper we present relational models of simple games and develop relational algorithms for solving some game-theoretic basic problems. The algorithms immediately can be transformed into the language of the Computer Algebra system RelView and, therefore, the system can be used to solve the problems and to visualize the results of the computations.

Simple games are a powerful tool to analyze decision-making and coalition formation in social and political life. In this paper we present relational models of simple games and develop relational algorithms for solving some game-theoretic basic problems. The algorithms immediately can be transformed into the language of the Computer Algebra system RelView and, therefore, the system can be used to solve the problems and to visualize the results of the computations.

International audience ; We present an application of relation algebra to measure agents' 'strength' in a social network with influence between agents. In particular, we deal with power, success, and influence of an agent as measured by the generalized Hoede-Bakker index and its modifications, and by the influence indices. We also apply relation algebra to determine followers of a coalition and the kernel of an influence function. This leads to specifications, which can be executed with the help of the BDD-based tool RelView after a simple translation into the tool's programming language. As an example we consider the present Dutch parliament.

International audience ; We present an application of relation algebra to measure agents' 'strength' in a social network with influence between agents. In particular, we deal with power, success, and influence of an agent as measured by the generalized Hoede-Bakker index and its modifications, and by the influence indices. We also apply relation algebra to determine followers of a coalition and the kernel of an influence function. This leads to specifications, which can be executed with the help of the BDD-based tool RelView after a simple translation into the tool's programming language. As an example we consider the present Dutch parliament.

International audience ; A stable government is by definition not dominated by any other government. However, it may happen that all governments are dominated. In graph-theoretic terms this means that the dominance graph does not possess a source. In this paper we are able to deal with this case by a clever combination of notions from different fields, such as relational algebra, graph theory and social choice theory, and by using the computer support system RelView for computing solutions and visualizing the results. Using relational algorithms, in such a case we break all cycles in each initial strongly connected component by removing the vertices in an appropriate minimum feedback vertex set. In this way we can choose a government that is as close as possible to being un-dominated. To achieve unique solutions, we additionally apply the majority ranking recently introduced by Balinski and Laraki. The main parts of our procedure can be executed using the RelView tool. Its sophisticated implementation of relations allows to deal with graph sizes that are sufficient for practical applications of coalition formation.

International audience ; A stable government is by definition not dominated by any other government. However, it may happen that all governments are dominated. In graph-theoretic terms this means that the dominance graph does not possess a source. In this paper we are able to deal with this case by a clever combination of notions from different fields, such as relational algebra, graph theory and social choice theory, and by using the computer support system RelView for computing solutions and visualizing the results. Using relational algorithms, in such a case we break all cycles in each initial strongly connected component by removing the vertices in an appropriate minimum feedback vertex set. In this way we can choose a government that is as close as possible to being un-dominated. To achieve unique solutions, we additionally apply the majority ranking recently introduced by Balinski and Laraki. The main parts of our procedure can be executed using the RelView tool. Its sophisticated implementation of relations allows to deal with graph sizes that are sufficient for practical applications of coalition formation.

International audience ; A stable government is by definition not dominated by any other government. However, it may happen that all governments are dominated. In graph-theoretic terms this means that the dominance graph does not possess a source. In this paper we are able to deal with this case by a clever combination of notions from different fields, such as relational algebra, graph theory and social choice theory, and by using the computer support system RelView for computing solutions and visualizing the results. Using relational algorithms, in such a case we break all cycles in each initial strongly connected component by removing the vertices in an appropriate minimum feedback vertex set. In this way we can choose a government that is as close as possible to being un-dominated. To achieve unique solutions, we additionally apply the majority ranking recently introduced by Balinski and Laraki. The main parts of our procedure can be executed using the RelView tool. Its sophisticated implementation of relations allows to deal with graph sizes that are sufficient for practical applications of coalition formation.

International audience ; A stable government is by definition not dominated by any other government. However, it may happen that all governments are dominated. In graph-theoretic terms this means that the dominance graph does not possess a source. In this paper we are able to deal with this case by a clever combination of notions from different fields, such as relational algebra, graph theory and social choice theory, and by using the computer support system RelView for computing solutions and visualizing the results. Using relational algorithms, in such a case we break all cycles in each initial strongly connected component by removing the vertices in an appropriate minimum feedback vertex set. In this way we can choose a government that is as close as possible to being un-dominated. To achieve unique solutions, we additionally apply the majority ranking recently introduced by Balinski and Laraki. The main parts of our procedure can be executed using the RelView tool. Its sophisticated implementation of relations allows to deal with graph sizes that are sufficient for practical applications of coalition formation.

International audience ; In this paper, a model of political consensus is introduced. Parties try to reach consensus in forming a government. A government is defined as a pair consisting of a winning coalition and a policy supported by this coalition, where a policy consists of policies on given issues. A party evaluates all governments the party belongs to with respect to some criteria. We allow the criteria to be of unequal importance to a party. These criteria concern winning coalitions and policy issues. Parties may be advised to adjust their preferences, i.e., to change their evaluation concerning some government(s) or/and the importance of the criteria, in order to obtain a better political consensus.

International audience ; In this paper, a model of political consensus is introduced. Parties try to reach consensus in forming a government. A government is defined as a pair consisting of a winning coalition and a policy supported by this coalition, where a policy consists of policies on given issues. A party evaluates all governments the party belongs to with respect to some criteria. We allow the criteria to be of unequal importance to a party. These criteria concern winning coalitions and policy issues. Parties may be advised to adjust their preferences, i.e., to change their evaluation concerning some government(s) or/and the importance of the criteria, in order to obtain a better political consensus.

International audience ; In this paper, a model of political consensus is introduced. Parties try to reach consensus in forming a government. A government is defined as a pair consisting of a winning coalition and a policy supported by this coalition, where a policy consists of policies on given issues. A party evaluates all governments the party belongs to with respect to some criteria. We allow the criteria to be of unequal importance to a party. These criteria concern winning coalitions and policy issues. Parties may be advised to adjust their preferences, i.e., to change their evaluation concerning some government(s) or/and the importance of the criteria, in order to obtain a better political consensus.