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Inferior players in simple games


  • Mika Widgrén

    () (Turku School of Economics and Centre for Economic Policy Research , Rehtorinpellonkatu 3, 20500 Turku, Finland.)

  • Stefan Napel

    () (WIOR, Universität Karlsruhe, D-76128 Karlsruhe, Germany.)


Power indices like those of Shapley and Shubik (1954) or Banzhaf (1965) measure the distribution of power in simple games. This paper points at a deficiency shared by all established indices: players who are inferior in the sense of having to accept (almost) no share of the spoils in return for being part of a winning coalition are assigned substantial amounts of power. A strengthened version of the dummy axiom based on a formalized notion of inferior players is a possible remedy. The axiom is illustrated first in a deterministic and then a probabilistic setting. With three axioms from the Banzhaf index, it uniquely characterizes the Strict Power Index (SPI). The SPI is shown to be a special instance of a more general family of power indices based on the inferior player axiom.

Suggested Citation

  • Mika Widgrén & Stefan Napel, 2001. "Inferior players in simple games," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 209-220.
  • Handle: RePEc:spr:jogath:v:30:y:2001:i:2:p:209-220
    Note: Received: December 1999/Final version: June 2001

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    Cited by:

    1. Montero, Maria & Vidal-Puga, Juan J., 2011. "Demand bargaining and proportional payoffs in majority games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 395-408, March.
    2. Hohnisch, M & Pittnauer, S & Solomon, S & Stauffer, D, 2010. "Socioeconomic interaction and swings in business confidence indicators," Center for Mathematical Economics Working Papers 345, Center for Mathematical Economics, Bielefeld University.
    3. repec:spr:grdene:v:19:y:2010:i:6:d:10.1007_s10726-009-9157-y is not listed on IDEAS
    4. René Brink & Gerard Laan & Valeri Vasil’ev, 2014. "Constrained core solutions for totally positive games with ordered players," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 351-368, May.
    5. Mika Widgrén, 2003. "Enlargements and the Principles of Designing EU - Decision-Making Procedures," CESifo Working Paper Series 903, CESifo Group Munich.
    6. Mika WidgrÚn & Stefan Napel, 2002. "The Power of a Spatially Inferior Player," Homo Oeconomicus, Institute of SocioEconomics, vol. 19, pages 327-343.
    7. Manfred Holler & Stefan Napel, 2005. "Local monotonicity of power: Axiom or just a property?," Quality & Quantity: International Journal of Methodology, Springer, vol. 38(5), pages 637-647, January.
    8. Freixas, Josep & Pons, Montserrat, 2008. "Circumstantial power: Optimal persuadable voters," European Journal of Operational Research, Elsevier, vol. 186(3), pages 1114-1126, May.
    9. Agnieszka Rusinowska, 2010. "The Hoede-Bakker index modified to the Shapley-Shubik and Holler-Packel indices," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00406430, HAL.
    10. Stefan Napel & Mika Widgrén, 2002. "Strategic Power Revisited," CESifo Working Paper Series 736, CESifo Group Munich.
    11. Casajus, André, 2009. "Outside options, component efficiency, and stability," Games and Economic Behavior, Elsevier, vol. 65(1), pages 49-61, January.
    12. Christian Fahrholz & Philipp Mohl, 2004. "EMU-enlargement and the Reshaping of Decision-making within the ECB Governing Council: A Voting-Power Analysis," Eastward Enlargement of the Euro-zone Working Papers wp23, Free University Berlin, Jean Monnet Centre of Excellence, revised 01 Jun 2004.
    13. Montero, Maria, 2017. "Proportional Payoffs in Legislative Bargaining with Weighted Voting: A Characterization," Quarterly Journal of Political Science, now publishers, vol. 12(3), pages 325-346, October.


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