A Study On Non-Bayesian Social Learning Model Based On Structure Analysis

In daily life, people form opinions over various economic, political and social issues which do not have an obvious solution. The information relevant to these issues usually disperses over the large society, while each agent can only observe a tiny piece of the information. In the process of opinion formation, individuals will rely on their perception to the world, their personal experiences and effects of others'views to a degree. Social learning aims to aggregate the decentralized information by the communication among agents. According to the rule of belief update, social learning models can be mainly divided into Bayesian and non-Bayesian. The difference lies in that the former need the agent to infer others'information using Bayesian law.In this paper we consider two special situations based on the non-Bayesian social learning model established by Jadbabaie et al. One is when there are some uninformed agents which can not observe the signals in the social networks, while the other is when there are multi-true states in the society. This paper focus on the study of what conditions are needed to ensure asymptotical learning for all agents, and how would the learning speed be affected.The main contributions made in the paper are as follows:1. We proved both through theory analysis and simulations, that even there are few agents which can observe the signals in the social network, as long as some mild assumptions are satisfied, all agents would learn the true state of the world in the end.2. In non-Bayesian social learning models with uninformed agents, the strategy specifically choosing those hub vertices with large degrees to be those informed agents, can make the learning faster than it is when randomly choose the same amount of agents. Besides, the more heterogeneous the network become, the better the specific selection strategy will be.3. When there are multiple true states in the society, the rule of learning with constant weights can not ensure agents learn asymptotically, instead there is the chaos in the evolution of each agent'belief. In the same situation, we make sure every agent learn its correspondingly true state by designing several rules of weight adjustment, which are also testified through simulations.