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A model of influence with a continuum of actions

  • Michel Grabisch

    ()

    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • Agnieszka Rusinowska

    ()

    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

We generalize a two-action (yes-no) model of influence to a framework in which every player has a continuum of actions, among which he has to choose one. 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 a measure of such a positive influence of a coalition on a player. Several unanimous influence functions in this generalized framework are considered. Also the set of fixed points under a given influence function is analyzed. Furthermore, we study linear influence functions and discuss their convergence. For a linear unanimous function, we find necessary and sufficient conditions for the existence of the positive influence of a coalition on a player, and we calculate the value of the influence index. We also introduce a measure of a negative influence of a coalition on a player.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number hal-00666821.

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Date of creation: 2011
Date of revision:
Publication status: Published, Journal of Mathematical Economics, 2011, 47, 576-587
Handle: RePEc:hal:cesptp:hal-00666821
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00666821
Contact details of provider: Web page: http://hal.archives-ouvertes.fr/

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  1. Bolger, Edward M, 1993. "A Value for Games with n Players and r Alternatives," International Journal of Game Theory, Springer, vol. 22(4), pages 319-34.
  2. Cont, Rama & Löwe, Matthias, 2010. "Social distance, heterogeneity and social interactions," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 572-590, July.
  3. Borm, P.E.M. & van den Brink, J.R. & Slikker, M., 2000. "An Iterative Procedure for Evaluating Digraph Competitions," Research Memorandum 788, School of Economics and Management.
  4. 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.
  5. Bolger, E M, 1986. "Power Indices for Multicandidate Voting Games," International Journal of Game Theory, Springer, vol. 15(3), pages 175-86.
  6. Agnieszka Rusinowska & Michel Grabisch, 2010. "A model of influence with an ordered set of possible actions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00519413, HAL.
  7. Dan S. Felsenthal & Moshé Machover, 2002. "Models and Reality: the Curios Case of the Absent Abstention," Homo Oeconomicus, Institute of SocioEconomics, vol. 19, pages 297-310.
  8. 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.
  9. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer, vol. 18(1), pages 39-43, March.
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  11. Edward M. Bolger, 2000. "A consistent value for games with n players and r alternatives," International Journal of Game Theory, Springer, vol. 29(1), pages 93-99.
  12. Abdou, J, 1988. "Neutral Veto Correspondences with a Continuum of Alternatives," International Journal of Game Theory, Springer, vol. 17(2), pages 135-64.
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