Article ID: | iaor20127600 |
Volume: | 46 |
Issue: | 1 |
Start Page Number: | 83 |
End Page Number: | 106 |
Publication Date: | Jan 2012 |
Journal: | RAIRO - Operations Research |
Authors: | Grabisch Michel, Rusinowska Agnieszka, Maruani Emmanuel |
Keywords: | decision, programming: dynamic, differential equations |
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,