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Modifying the Hoede-Bakker index to the Shapley-Shubik and Holler-Packel indices

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  • Agnieszka Rusinowska

    () (University of Lyon, Lyon, F-69003, France; CNRS, UMR 5824, GATE, Ecully, F-69130, France; ENS LSH, Lyon, F-69007, France ; Centre Leon Berard, Lyon, F-69003, France)

Abstract

Abstract. In the paper, we present some modifications of the Hoede-Bakker index defined in a social network in which players may influence each other. Due to influences of the other actors, the final decision of a player may be different from his original inclination. These modifications are defined for an arbitrary probability distribution over all inclination vectors. In particular, they concern a situation in which the inclination vectors may be not equally probable. Furthermore, by assuming special probability distributions over all inclination vectors, we construct modifications of the Hoede-Bakker index that coincide with the Shapley-Shubik index and with the Holler-Packel index, respectively.

Suggested Citation

  • Agnieszka Rusinowska, 2007. "Modifying the Hoede-Bakker index to the Shapley-Shubik and Holler-Packel indices," Working Papers 0729, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
  • Handle: RePEc:gat:wpaper:0729
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    1. Agnieszka Rusinowska, 2007. "The not-preference-based Hoede-Bakker index," Working Papers 0704, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
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    Keywords

    Hoede-Bakker index; inclination vector; probability distribution; Shapley-Shubik index;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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