Non-Bayesian social learning model with periodically switching structures

In this article, we investigate the dynamics of non-Bayesian social learning model with periodically switching structures. Unlike the strongly connectedness conditions set for the temporal connecting networks of the non-Bayesian social learning to guarantee its convergence in the literature, our model configurations are essentially relaxed in a manner that the connecting networks in every switching duration can be non-strongly connected. Mathematically and rigorously, we validate that, under relaxed configurations, dynamics of our model still converge to a true state of social learning in a particular sense of probability. Additionally, we provide estimations on the convergence rate for successful social learning in our model. Numerically, we demonstrate the efficacy of the analytically established conditions and estimations by using some representative examples with switching structures. We believe that our results could be potentially useful for illustrating the social activities in the real world.

Automated summary

In this article, the dynamics of a non-Bayesian social learning model with periodically switching structures are investigated. Unlike previous studies, the model configurations are relaxed and it is validated that the dynamics of the model still converge to a true state of social learning in a particular sense of probability under such relaxed configurations. Estimations on the convergence rate for successful social learning in the model are provided, and the efficacy of the established conditions and estimations are numerically demonstrated using representative examples with switching structures. These results could potentially be useful for illustrating real-world social activities.