Computations on Simple Games Using RelView

  • Rudolf Berghammer
  • Agnieszka Rusinowska
  • Harrie de Swart
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6885)

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
  2. 2.
    Banzhaf, J.F.: Weighted voting doesn’t work: A mathematical analysis. Rutgers Law Review 19, 317–343 (1965)Google Scholar
  3. 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. 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. 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. 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. 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. 8.
    van Deemen, A.: Dominant players and minimum size coalitions. Europ. J. Polit. Res. 17, 313–332 (1989)CrossRefGoogle Scholar
  9. 9.
    van Deemen, A.: Coalition formation in centralized policy games. J. Theoret. Polit. 3, 139–161 (1991)CrossRefGoogle Scholar
  10. 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. 11.
    Leoniuk, B.: ROBDD-basierte Implementierung von Relationen und relationalen Operationen mit Anwendungen. Diss., Univ. Kiel (2001)Google Scholar
  12. 12.
    von Neumann, J., Morgenstern, O.: Theory of games and economic behaviour. Princeton University Press, Princeton (1944)MATHGoogle Scholar
  13. 13.
    Peleg, B., Sudhölter, P.: Introduction to the theory of cooperative games. Springer, Heidelberg (2003)CrossRefMATHGoogle Scholar
  14. 14.
    Peters, H.: Game theory: A Multi-leveled approach. Springer, Heidelberg (2008)CrossRefMATHGoogle Scholar
  15. 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. 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. 17.
    Schmidt, G., Ströhlein, T.: Relations and graphs. Springer, Heidelberg (1993)CrossRefMATHGoogle Scholar
  18. 18.
    Taylor, A.D.: Mathematics and politics. Springer, Heidelberg (1995)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Rudolf Berghammer
    • 1
  • Agnieszka Rusinowska
    • 2
  • Harrie de Swart
    • 3
  1. 1.Institut für InformatikUniversität KielKielGermany
  2. 2.Centre d’Economie de la Sorbonne, CNRS – Université Paris IParisFrance
  3. 3.Department of PhilosophyTilburg UniversityTilburgThe Netherlands

Personalised recommendations