A relation-algebraic approach to simple games

Rudolf Berghammer (1) , Stefan Bolus (1) , Agnieszka Rusinowska (2) , Harrie de Swart (3)

1 Institut für Informatik
2 CES - Centre d'économie de la Sorbonne
3 Faculteit Wijsbegeerte-Logica en taalanalyse

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.

Mots clés: Relation algebra; RelView; simple game; winning coalition; swinger; dominant player; central player; power index

Domaines: Economies et finances

Rudolf Berghammer, Stefan Bolus, Agnieszka Rusinowska, Harrie de Swart. A relation-algebraic approach to simple games. European Journal of Operational Research, 2011, 210 (1), pp.68-80. ⟨10.1016/j.ejor.2010.09.006⟩. ⟨hal-00574767⟩