Exploration-imitation competition in well-mixed and structured populations

Social physics is the mathematical study of how the flow of ideas can change the behavior of individuals. Models in social physics include processes for searching after new ideas and dispersing them inside the population. The present paper makes use of exploration and imitation processes for the mentioned purpose. A new type of imitation is employed here, in which the imitant strategy is not simply replaced by role model strategy, but rather moves toward it. Our exploration process is additive Gaussian noise. To study these processes, we both analyze and simulate the strategy distribution function. By combining exploration and soft imitation, the width of the strategy distribution function becomes stationary. In this model, regular imitation is a particular limit of soft imitation, where an imitant copies the role model, through which the stationary width of the distribution function disappears. As the network causes complex behavior, soft imitation and exploration have been studied in some complex networks as well. Simulation results show that for a small world, scale-free, random regular, and random network, and by selected parameters in this research, distribution function width reaches stationary states.