A Relation-Algebraic Approach to Simple Games

GATE Working Paper No. 09-13

27 Pages Posted: 23 Jul 2009 Last revised: 15 Apr 2011

See all articles by Rudolf Berghammer

Rudolf Berghammer

University of Kiel

Agnieszka Rusinowska

University of Lyon 2 - Groupe d'Analyse et de Théorie Economique (GATE)

Harrie De Swart

Tilburg University - Department of Philosophy

Date Written: June 1, 2009

Abstract

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.

Keywords: relation algebra, RelView, simple game, winning coalition, swinger, dominant player, central player, power index

JEL Classification: C71, C88, C63, C65, D72

Suggested Citation

Berghammer, Rudolf and Rusinowska, Agnieszka and De Swart, Harrie, A Relation-Algebraic Approach to Simple Games (June 1, 2009). GATE Working Paper No. 09-13, Available at SSRN: https://ssrn.com/abstract=1436975 or http://dx.doi.org/10.2139/ssrn.1436975

Rudolf Berghammer (Contact Author)

University of Kiel ( email )

Olshausenstr. 40
D-24118 Kiel, Schleswig-Holstein 24118
Germany

Agnieszka Rusinowska

University of Lyon 2 - Groupe d'Analyse et de Théorie Economique (GATE) ( email )

93, chemin des Mouilles
Ecully, 69130
France

Harrie De Swart

Tilburg University - Department of Philosophy ( email )

Postbus 90153
Tilburg, DC Noord-Brabant 5000 LE
Netherlands

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