A relation-algebraic approach to simple games

Simple games are a powerful tool to analyze decision - making and coalition formation in social and political life. In this paper, we present relation-algebraic models of simple games and develop relational specifications for solving some basic problems of them. In particular, we test certain fundamental properties of simple games and compute specific players and coalitions. We also apply relation algebra to determine power indices. This leads to relation-algebraic specifications, which can be evaluated with the help of the BDD-based tool RelView after a simple translation into the tool's programming language. In order to demonstrate the visualization facilities of RelView, we consider an example of the Catalonian Parliament after the 2003 election.Relation algebra ; RelView ; simple game ; winning coalition ; swinger ; dominant player ; central player ; power index

A Relation-algebraic Approach to Simple Games

Simple games are a powerful tool to analyze decision-making and coalition formation in social and political life. In this paper, we present relation-algebraic models of simple games and develop relational algorithms for solving some basic problems of them. In particular, we test certain fundamental properties of simple games (being monotone, proper, respectively strong) and compute specific players (dummies, dictators, vetoers, null players) and coalitions (minimal winning coalitions and vulnerable winning coalitions). We also apply relation-algebra to determine central and dominant players, swingers and power indices (the Banzhaf, Holler-Packel and Deegan-Packel indices). This leads to relation-algebraic specifications, which can be executed with the help of the BDD-based tool RelView after a simple translation into the tool's programming language. In order to demonstrate the visualization facilities of RelView we consider an example of the Catalonian Parliament after the 2003 election.relation algebra; RelView; simple game; winning coalition; swinger; dominant player; central player; power index

Computing Tournament Solutions using Relation Algebra and REL VIEW

We describe a simple computing technique for the tournament choice problem. It rests upon a relational modeling and uses the BDD-based computer system RelView for the evaluation of the relation-algebraic expressions that specify the solutions and for the visualization of the computed results. The Copeland set can immediately be identified using RelView's labeling feature. Relation-algebraic specifications of the Condorcet non-losers, the Schwartz set, the top cycle, the uncovered set, the minimal covering set, the Banks set, and the tournament equilibrium set are delivered. We present an example of a tournament on a small set of alternatives, for which the above choice sets are computed and visualized via RelView. The technique described in this paper is very flexible and especially appropriate for prototyping and experimentation, and as such very instructive for educational purposes. It can easily be applied to other problems of social choice and game theory.Tournament, relational algebra, RelView, Copeland set, Condorcet non-losers, Schwartz set, top cycle, uncovered set, minimal covering set, Banks set, tournament equilibrium set.

Applying relational algebra and RelView to coalition formation

We present an application of relational algebra to coalition formation. This leads to specifications, which can be executed with the help of the RelView tool after a simple translation into the tool's programming language. As an example we consider a simplification of the situation in Poland after the 2001 elections.RelView; relational algebra; coalition formation; feasible government; dominance; stable government

Computations on Simple Games using RelView

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.relational algebra ; RelView ; simple games

Negotiating a stable government - an application of bargaining theory to a coalition formation model

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.stable government; bargaining game; subgame perfect equilibrium

An Interdisciplinary Approach to Coalition Formation

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.Graph theory; RelView; relational algebra; dominance; stable government

Applying Relation Algebra and RelView to Measures in aSocial Network

We present an application of relation algebra to measure players' ‘strength' in a social network with influence between players. In particular, we deal with power, success, and influence of a player as measured by the Hoede-Bakker index, its generalization and 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 BDDbased tool RelView after a simple translation into the tool's programming language. As an example we consider the present Dutch parliament.RelView ; relation algebra ; social network ; the Hoede-Bakker index ; influence index ;follower ; kernel

Applying relational algebra and RelView to measures in a social network

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.RelView; relation algebra; social network; Hoede-Bakker index; influence index