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A model of influence with a continuum of actions

Author

Listed:
  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Agnieszka Rusinowska

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

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.

Suggested Citation

  • Michel Grabisch & Agnieszka Rusinowska, 2011. "A model of influence with a continuum of actions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00666821, HAL.
    • Handle: RePEc:hal:cesptp:hal-00666821
    DOI: 10.1016/j.jmateco.2011.08.004
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    Cited by:

    1. Rusinowska, Agnieszka & Taalaibekova, Akylai, 2019. "Opinion formation and targeting when persuaders have extreme and centrist opinions," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 9-27.
    2. Agnieszka Rusinowska & Rudolf Berghammer & Harrie de Swart & Michel Grabisch, 2011. "Social networks: Prestige, centrality, and influence (Invited paper)," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00633859, HAL.
    3. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, vol. 2(1), pages 1-33, March.

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    JEL classification:

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

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