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A model of influence with a continuum of actions

Author

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  • 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)

Abstract

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.

Suggested Citation

  • Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence with a continuum of actions," Working Papers 1004, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
  • Handle: RePEc:gat:wpaper:1004
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    References listed on IDEAS

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    Keywords

    action; decision; influence index; unanimous influence function; follower of a coalition; kernel; fixed point; linear influence function;

    JEL classification:

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

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