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A model of influence with a continuum of actions

  • Michel Grabisch

    ()

    (Université Paris I Panthéon-Sorbonne, Centre d'Economie de la Sorbonne, 106-112 Bd de l'Hôpital, 75013 Paris, France)

  • Agnieszka Rusinowska

    ()

    (GATE, CNRS UMR 5824 - Université de Lyon, 93 Chemin des Mouilles - B.P. 167, 69131 Ecully Cedex, France)

In the paper, we generalize a two-action (yes-no) model of influence to a framework in which every player has a continuum of actions and he has to choose one of them. We assume the set of actions to be an interval. Each player has an inclination to choose one of the actions. Due to influence among players, the final decision of a player, i.e., his choice of one action, may be different from his original inclination. In particular, a coalition of players with the same inclination may influence another player with different inclination, and as a result of this influence, the decision of the player is closer to the inclination of the influencing coalition than his inclination was. We introduce and study a measure of such a positive influence of a coalition on a player. Several unanimous influence functions in this generalized framework are considered. Moreover, we investigate other tools for analyzing influence, like the concept of a follower of a given coalition, its particular case - a perfect follower, and the kernel of an influence function. We study properties of these concepts. Also the set of fixed points under a given influence function is analyzed. Furthermore, we study linear influence functions. We also introduce a measure of a negative influence of a coalition on a player.

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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 1004.

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Length: 29 pages
Date of creation: 2010
Date of revision:
Handle: RePEc:gat:wpaper:1004
Contact details of provider: Postal: 93, chemin des Mouilles - B.P.167 69131 - Ecully cedex
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Web page: http://www.gate.cnrs.fr/

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  1. Borm, P.E.M. & van den Brink, J.R. & Slikker, M., 2002. "An iterative procedure for evaluating digraph competitions," Other publications TiSEM 40ae2ec2-efdb-48f6-905c-5, Tilburg University, School of Economics and Management.
  2. Michel Grabisch & Agnieszka Rusinowska, 2008. "A model of influence in a social network," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00344457, HAL.
  3. 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.
  4. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00308741, HAL.
  5. Yang, J.-H. Steffi, 2009. "Social network influence and market instability," Journal of Mathematical Economics, Elsevier, vol. 45(3-4), pages 257-276, March.
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  12. Wu-Hsiung Huang, 2009. "Is a continuous rational social aggregation impossible on continuum spaces?," Social Choice and Welfare, Springer, vol. 32(4), pages 635-686, May.
  13. Michel Grabisch & Agnieszka Rusinowska, 2008. "A model of influence in a social network," Documents de travail du Centre d'Economie de la Sorbonne b08066, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  14. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence with an ordered set of possible actions," Theory and Decision, Springer, vol. 69(4), pages 635-656, October.
  15. Bolger, E M, 1986. "Power Indices for Multicandidate Voting Games," International Journal of Game Theory, Springer, vol. 15(3), pages 175-86.
  16. Edward M. Bolger, 2002. "Characterizations of two power indices for voting games with r alternatives," Social Choice and Welfare, Springer, vol. 19(4), pages 709-721.
  17. Cont, Rama & Löwe, Matthias, 2010. "Social distance, heterogeneity and social interactions," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 572-590, July.
  18. Wu-Hsiung Huang, 2004. "Is proximity preservation rational in social choice theory?," Social Choice and Welfare, Springer, vol. 23(3), pages 315-332, December.
  19. Josep Freixas & William S. Zwicker, 2003. "Weighted voting, abstention, and multiple levels of approval," Social Choice and Welfare, Springer, vol. 21(3), pages 399-431, December.
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  21. Lorenz, Jan, 2005. "A stabilization theorem for dynamics of continuous opinions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 217-223.
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