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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.

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Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 30 (2001)
Issue (Month): 2 ()
Pages: 209-220

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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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