A Model of Influence with a Continuum of Actions

29 Pages Posted: 25 Mar 2010

See all articles by Michel Grabisch

Michel Grabisch

Université Paris I Panthéon-Sorbonne - CERMSEM

Agnieszka Rusinowska

University of Lyon 2 - Groupe d'Analyse et de Théorie Economique (GATE)

Multiple version iconThere are 2 versions of this paper

Date Written: 2010

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.

Keywords: Action, Decision, Influence Index, Unanimous Influence Function, Follower of a Coalition, Kernel, Fixed Point, Linear Influence Function

JEL Classification: C7, D7

Suggested Citation

Grabisch, Michel and Rusinowska, Agnieszka, A Model of Influence with a Continuum of Actions (2010). Available at SSRN: https://ssrn.com/abstract=1572547 or http://dx.doi.org/10.2139/ssrn.1572547

Michel Grabisch (Contact Author)

Université Paris I Panthéon-Sorbonne - CERMSEM ( email )

106-112, Boulevard de l'Hôpital
Paris, 75647
France

Agnieszka Rusinowska

University of Lyon 2 - Groupe d'Analyse et de Théorie Economique (GATE) ( email )

93, chemin des Mouilles
Ecully, 69130
France

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
23
Abstract Views
660
PlumX Metrics