A study of the dynamic of influence through differential equations∗

Emmanuel Maruani; Michel Grabisch; Agnieszka Rusinowska

RAIRO - Operations Research (2012)

  • Volume: 46, Issue: 1, page 83-106
  • ISSN: 0399-0559

Abstract

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The paper concerns a model of influence in which agents make their decisions on a certain issue. We assume that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. An innovative and important element of the model with respect to other studies of this influence framework is the introduction of weights reflecting the importance that one agent gives to the others. These importance weights can be positive, negative or equal to zero, which corresponds to the stimulation of the agent by the ‘weighted’ one, the inhibition, or the absence of relation between the two agents in question, respectively. The exhortation obtained by an agent is defined by the weighted sum of the opinions received by all agents, and the updating rule is based on the sign of the exhortation. The use of continuous variables permits the application of differential equations systems to the analysis of the convergence of agents’ decisions in long-time. We study the dynamic of some influence functions introduced originally in the discrete model, e.g., the majority and guru influence functions, but the approach allows the study of new concepts, like e.g. the weighted majority function. In the dynamic framework, we describe necessary and sufficient conditions for an agent to be follower of a coalition, and for a set to be the boss set or the approval set of an agent. equations to the influence model, we recover the results of the discrete model on on the boss and approval sets for the command games equivalent to some influence functions.

How to cite

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Maruani, Emmanuel, Grabisch, Michel, and Rusinowska, Agnieszka. "A study of the dynamic of influence through differential equations∗." RAIRO - Operations Research 46.1 (2012): 83-106. <http://eudml.org/doc/276397>.

@article{Maruani2012,
abstract = {The paper concerns a model of influence in which agents make their decisions on a certain issue. We assume that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. An innovative and important element of the model with respect to other studies of this influence framework is the introduction of weights reflecting the importance that one agent gives to the others. These importance weights can be positive, negative or equal to zero, which corresponds to the stimulation of the agent by the ‘weighted’ one, the inhibition, or the absence of relation between the two agents in question, respectively. The exhortation obtained by an agent is defined by the weighted sum of the opinions received by all agents, and the updating rule is based on the sign of the exhortation. The use of continuous variables permits the application of differential equations systems to the analysis of the convergence of agents’ decisions in long-time. We study the dynamic of some influence functions introduced originally in the discrete model, e.g., the majority and guru influence functions, but the approach allows the study of new concepts, like e.g. the weighted majority function. In the dynamic framework, we describe necessary and sufficient conditions for an agent to be follower of a coalition, and for a set to be the boss set or the approval set of an agent. equations to the influence model, we recover the results of the discrete model on on the boss and approval sets for the command games equivalent to some influence functions.},
author = {Maruani, Emmanuel, Grabisch, Michel, Rusinowska, Agnieszka},
journal = {RAIRO - Operations Research},
keywords = {Social network; inclination; importance weight; decision; influence function; differential equations; social network},
language = {eng},
month = {5},
number = {1},
pages = {83-106},
publisher = {EDP Sciences},
title = {A study of the dynamic of influence through differential equations∗},
url = {http://eudml.org/doc/276397},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Maruani, Emmanuel
AU - Grabisch, Michel
AU - Rusinowska, Agnieszka
TI - A study of the dynamic of influence through differential equations∗
JO - RAIRO - Operations Research
DA - 2012/5//
PB - EDP Sciences
VL - 46
IS - 1
SP - 83
EP - 106
AB - The paper concerns a model of influence in which agents make their decisions on a certain issue. We assume that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. An innovative and important element of the model with respect to other studies of this influence framework is the introduction of weights reflecting the importance that one agent gives to the others. These importance weights can be positive, negative or equal to zero, which corresponds to the stimulation of the agent by the ‘weighted’ one, the inhibition, or the absence of relation between the two agents in question, respectively. The exhortation obtained by an agent is defined by the weighted sum of the opinions received by all agents, and the updating rule is based on the sign of the exhortation. The use of continuous variables permits the application of differential equations systems to the analysis of the convergence of agents’ decisions in long-time. We study the dynamic of some influence functions introduced originally in the discrete model, e.g., the majority and guru influence functions, but the approach allows the study of new concepts, like e.g. the weighted majority function. In the dynamic framework, we describe necessary and sufficient conditions for an agent to be follower of a coalition, and for a set to be the boss set or the approval set of an agent. equations to the influence model, we recover the results of the discrete model on on the boss and approval sets for the command games equivalent to some influence functions.
LA - eng
KW - Social network; inclination; importance weight; decision; influence function; differential equations; social network
UR - http://eudml.org/doc/276397
ER -

References

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