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Measuring influence among players with an ordered set of possible actions

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Author Info

  • Michel Grabisch

    ()
    (Université Paris I Panthéon-Sorbonne, CERMSEM, 106-112 Bd de l’Hôpital, 75013 Paris, France)

  • 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

In the paper, we introduce and study generalized weighted influence indices of a coalition on a player, where players have an ordered set of possible actions. Each player has an inclination to choose one of the actions. Due to influence of a coalition of other players, a final decision of the player may be different from his original inclination. An influence in such situations is measured by the general weighted influence index. In a particular case, the decision of the player may be closer to the inclination of the influencing coalition than his inclination was. The weighted influence index which captures such a case is called the positive weighted influence index. We also consider the negative weighted influence index, where a final decision of the player goes farther away from the inclination of the influencing coalition. Some special cases of the weighted influence indices, called a possibility influence index and an equidistributed influence index, are also defined. We consider different influence functions and study their properties. A set of followers and a set of a conditional followers of a given coalition are defined, and their properties are analyzed. We define the concepts of success, decisiveness, luck, and failure for the multi-choice model of influence.

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Bibliographic Info

Paper provided by Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure in its series Working Papers with number 0801.

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Length: 20 pages
Date of creation: 2008
Date of revision:
Handle: RePEc:gat:wpaper:0801

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Keywords: decisiveness; follower of a coalition; influence function; influence indices; success;

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References

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  1. repec:hal:cesptp:halshs-00142479 is not listed on IDEAS
  2. Agnieszka Rusinowska, 2007. "The not-preference-based Hoede-Bakker index," Working Papers 0704, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  3. MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer, vol. 26(3), pages 335-351.
  4. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April.
  5. Agnieszka Rusinowska & Michel Grabisch, 2007. "Influence Indices," Working Papers 0705, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  6. Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer, vol. 24(1), pages 171-197, January.
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  1. repec:hal:cesptp:halshs-00445126 is not listed on IDEAS
  2. repec:hal:cesptp:halshs-00344805 is not listed on IDEAS
  3. Michel Grabisch & Agnieszka Rusinowska, 2008. "Measuring influence in command games," Documents de travail du Centre d'Economie de la Sorbonne b08078, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

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