A Relation-Algebraic Approach to Simple Games
GATE Working Paper No. 09-13
27 Pages Posted: 23 Jul 2009 Last revised: 15 Apr 2011
Date Written: June 1, 2009
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
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