A Relation-algebraic Approach to Simple Games

Rudolf Berghammer (), Agnieszka Rusinowska and Harrie de Swart ()
Additional contact information
Rudolf Berghammer: Institut fur Informatik, Christian-Albrechts-Universitat Kiel Olshausenstraße 40, 24098 Kiel, Germany
Harrie de Swart: Department of Philosophy, Tilburg University P.O. Box 90153, 5000 LE Tilburg, The Netherlands

No 913, Working Papers from Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon

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 speciï¬ cations, 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 (search for similar items in EconPapers)
JEL-codes: C63 C65 C71 C88 D72 (search for similar items in EconPapers)
Pages: 27 pages
Date: 2009
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ftp://ftp.gate.cnrs.fr/RePEc/2009/0913.pdf (application/pdf)

Related works:
Journal Article: A relation-algebraic approach to simple games (2011)
Working Paper: A relation-algebraic approach to simple games (2011)
Working Paper: A relation-algebraic approach to simple games (2011)
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