A study of the dynamic of influence through differential equations

The paper concerns a model of influence in which agents make their decisions on a certain issue. It is assumed 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. The use of continuous variables permits the application of differential equations systems to the analysis of the convergence of agents’ decisions in long-time. In particular, by applying the approach based on differential equations to the influence model, we recover the results of the discrete model on classical influence functions, and the results on the boss and approval sets for the command games equivalent to some influence functions.