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Banzhaf Measures for Games with Several Levels of Approval in the Input and Output

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Abstract

An axiomatic characterization of ‘a Banzhaf score’ notion is provided for a class of games called (j,k) simple games with a numeric measure associated to the output set, i.e., games with n players, j ordered qualitative alternatives in the input level and k possible ordered quantitative alternatives in the output. Three Banzhaf measures are also introduced which can be used to determine a player's ‘a priori’ value in such a game. We illustrate by means of several real world examples how to compute these measures.

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Authors and Affiliations

  1. Department of Applied Mathematics III and Polytechnic School of Manresa, Polytechnic University of Catalonia, Spain

    Josep Freixas

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  1. Josep Freixas
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Correspondence to Josep Freixas.

Additional information

Research partially supported by Grant BFM 2003-01314 of the Science and Technology Spanish Ministry and the European Regional Development Fund.

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Freixas, J. Banzhaf Measures for Games with Several Levels of Approval in the Input and Output. Ann Oper Res 137, 45–66 (2005). https://doi.org/10.1007/s10479-005-2244-9

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  • DOI: https://doi.org/10.1007/s10479-005-2244-9

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