Computations on Simple Games Using RelView
Conference paper
Abstract
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.
Keywords
Cooperative Game Coalition Formation Simple Game Winning Coalition Veto Player
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
- 1.
- 2.Banzhaf, J.F.: Weighted voting doesn’t work: A mathematical analysis. Rutgers Law Review 19, 317–343 (1965)Google Scholar
- 3.Berghammer, R., Bolus, S., Rusinowska, A., de Swart, H.: A relation-algebraic approach to simple games. Europ. J. Operat. Res. 210, 68–80 (2011)MathSciNetCrossRefMATHGoogle Scholar
- 4.Berghammer, R., Braßel, B.: Computing and visualizing closure objects using relation algebra and relView. In: Gerdt, V.P., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2009. LNCS, vol. 5743, pp. 29–44. Springer, Heidelberg (2009)CrossRefGoogle Scholar
- 5.Berghammer, R., Neumann, F.: RelView – An OBDD-Based Computer Algebra System for Relations. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V., et al. (eds.) CASC 2005. LNCS, vol. 3718, pp. 40–51. Springer, Heidelberg (2005)CrossRefGoogle Scholar
- 6.Berghammer, R., Rusinowska, A., de Swart, H.: Applying relational algebra and RelView to coalition formation. Europ. J. Operat. Res. 178, 530–542 (2007)CrossRefMATHGoogle Scholar
- 7.Berghammer, R., Rusinowska, A., de Swart, H.: An interdisciplinary approach to coalition formation. Europ. J. Operat. Res. 195, 487–496 (2009)MathSciNetCrossRefMATHGoogle Scholar
- 8.van Deemen, A.: Dominant players and minimum size coalitions. Europ. J. Polit. Res. 17, 313–332 (1989)CrossRefGoogle Scholar
- 9.van Deemen, A.: Coalition formation in centralized policy games. J. Theoret. Polit. 3, 139–161 (1991)CrossRefGoogle Scholar
- 10.Elkind, E., Goldberg, L.A., Goldberg, P.W., Wooldridge, M.: On the computational complexity of weighted voting games. Ann. Math. Artif. Intell. 56, 109–131 (2009)Google Scholar
- 11.Leoniuk, B.: ROBDD-basierte Implementierung von Relationen und relationalen Operationen mit Anwendungen. Diss., Univ. Kiel (2001)Google Scholar
- 12.von Neumann, J., Morgenstern, O.: Theory of games and economic behaviour. Princeton University Press, Princeton (1944)MATHGoogle Scholar
- 13.Peleg, B., Sudhölter, P.: Introduction to the theory of cooperative games. Springer, Heidelberg (2003)CrossRefMATHGoogle Scholar
- 14.Peters, H.: Game theory: A Multi-leveled approach. Springer, Heidelberg (2008)CrossRefMATHGoogle Scholar
- 15.Prasad, K., Kelly, J.S.: NP-completeness of some problems concerning voting games. Int. J. Game Theory 19, 1–9 (1990)MathSciNetCrossRefMATHGoogle Scholar
- 16.van Roozendaal, P.: Centre parties and coalition cabinet formations: a game theoretic approach. Europ. J. Polit. Res. 18, 325–348 (1990)CrossRefGoogle Scholar
- 17.Schmidt, G., Ströhlein, T.: Relations and graphs. Springer, Heidelberg (1993)CrossRefMATHGoogle Scholar
- 18.Taylor, A.D.: Mathematics and politics. Springer, Heidelberg (1995)CrossRefMATHGoogle Scholar
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