Opinion dynamics in multi-agent systems with binary decision exchanges

Opinion dynamics in social networks has been widely studied in recent years, mostly by considering exchanges of opinions among neighboring agents. This paper addresses a scenario where the agents make decisions repeatedly on two hypotheses and where agents only exchange decisions. Motivated by the Bayesian models in the literature of human cognition, we model this learning procedure by the Bayes' rule. The social belief of each agent is defined to be the posterior of one of the hypotheses conditioned on the information it obtained from the society. We show that under certain conditions, once the social belief evolves to some region, the agent will refuse to change its belief. We demonstrate the asymptotical properties of the proposed model by computer simulations.