A model of inﬂuence with a continuum of actions
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.
|Date of creation:||2009|
|Publication status:||Published in Working Paper GATE 2010-04. 2009|
|Note:||View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00464460|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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