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A relation-algebraic approach to simple games

Author

Listed:
  • Rudolf Berghammer

    () (Institut für Informatik - Universitat Kiel)

  • Stefan Bolus

    (Institut für Informatik - Universitat Kiel)

  • Agnieszka Rusinowska

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne)

  • Harrie De Swart

    () (Faculteit Wijsbegeerte-Logica en taalanalyse - Universiteit van Tilburg)

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 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.

Suggested Citation

  • Rudolf Berghammer & Stefan Bolus & Agnieszka Rusinowska & Harrie De Swart, 2011. "A relation-algebraic approach to simple games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00574767, HAL.
  • Handle: RePEc:hal:cesptp:hal-00574767
    DOI: 10.1016/j.ejor.2010.09.006
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00574767
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    References listed on IDEAS

    as
    1. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    2. Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2010. "Applying relation algebra and RelView to measures in a social network," European Journal of Operational Research, Elsevier, vol. 202(1), pages 182-195, April.
    3. Annick Laruelle & Federico Valenciano, 2001. "Shapley-Shubik and Banzhaf Indices Revisited," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 89-104, February.
    4. Lorenzo-Freire, S. & Alonso-Meijide, J.M. & Casas-Mendez, B. & Fiestras-Janeiro, M.G., 2007. "Characterizations of the Deegan-Packel and Johnston power indices," European Journal of Operational Research, Elsevier, vol. 177(1), pages 431-444, February.
    5. Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2007. "Applying relational algebra and RelView to coalition formation," European Journal of Operational Research, Elsevier, vol. 178(2), pages 530-542, April.
    6. Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2009. "An interdisciplinary approach to coalition formation," European Journal of Operational Research, Elsevier, vol. 195(2), pages 487-496, June.
    7. Federico Valenciano & Annick Laruelle, 2000. "- Shapley-Shubik And Banzhaf Indices Revisited," Working Papers. Serie AD 2000-02, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    8. Prasad, K & Kelly, J S, 1990. "NP-Completeness of Some Problems Concerning Voting Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 1-9.
    9. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    10. Bolus, Stefan, 2011. "Power indices of simple games and vector-weighted majority games by means of binary decision diagrams," European Journal of Operational Research, Elsevier, vol. 210(2), pages 258-272, April.
    11. R J Johnston, 1978. "On the measurement of power: some reactions to Laver," Environment and Planning A, Pion Ltd, London, vol. 10(8), pages 907-914, August.
    12. Klinz, Bettina & Woeginger, Gerhard J., 2005. "Faster algorithms for computing power indices in weighted voting games," Mathematical Social Sciences, Elsevier, vol. 49(1), pages 111-116, January.
    13. Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2010. "Applying relation algebra and RelView to measures in a social network," European Journal of Operational Research, Elsevier, vol. 202(1), pages 182-195, April.
    14. Alonso-Meijide, J.M. & Casas-Mendez, B. & Holler, M.J. & Lorenzo-Freire, S., 2008. "Computing power indices: Multilinear extensions and new characterizations," European Journal of Operational Research, Elsevier, vol. 188(2), pages 540-554, July.
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    Cited by:

    1. Bolus, Stefan, 2011. "Power indices of simple games and vector-weighted majority games by means of binary decision diagrams," European Journal of Operational Research, Elsevier, vol. 210(2), pages 258-272, April.
    2. Rudolf Berghammer & Agnieszka Rusinowska & Harrie de Swart, 2011. "Computations on Simple Games using REL VIEW," Documents de travail du Centre d'Economie de la Sorbonne 11014, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. repec:hal:journl:hal-00633859 is not listed on IDEAS
    4. Freixas, Josep & Kurz, Sascha, 2013. "The golden number and Fibonacci sequences in the design of voting structures," European Journal of Operational Research, Elsevier, vol. 226(2), pages 246-257.
    5. Agnieszka Rusinowska & Rudolf Berghammer & Harrie De Swart & Michel Grabisch, 2011. "Social networks: Prestige, centrality, and influence (Invited paper)," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00633859, HAL.

    More about this item

    Keywords

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

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