Simulation And Analysis Of Social Learning Model Besed On Expert Agents

This paper mainly discusses the social learning model based on expert agents on complex networks and the model analysis.Social learning is a crossing field including complex network, sociology, economy and sociology, becoming more and more popular and important. This topic is becoming a trend.The paper mainly discusses about the modeling, proof and simulation research of social network based on expert agents. The model based on expert agents combines the virtue of Bayesian learning and Non-Bayesian learning, which has good swiftness and convergence. And we compare and analyze this model to other models.Firstly, we research the background of social learning and analyze the approach of home and abroad researchers, including the concept of social learning, the research approach and main papers.It is discussed in the background of social learning and proposed the social learning model and its systematic analysis, including the convergence analysis and the convergence speed analysis.This paper introduces a model that agents use an information updating rule combining non-Bayesian learning and Bayesian learning in a social network. The research is about convergence analysis and convergence speed analysis.The convergence analysis includes Bayesian update and Non-Bayesian update. Information from some distinguishing individuals aggregates through the network so that every agent could collect enough information about the true belief. The observation from expert Bayesian agents will drive the average belief of the true belief in the network converge with possibility of 1 as time grows to infinite. In this process, we compare to 2 classic model of the research and showed the superiority of this model. In the convergence analysis, we discuss the theorem and its proof, which backed our assumption.Suppose1) The network is a strongly connected directed graph, the connection matrix A is a random matrix.2) There exists at least one expert agent used by Bayesian update rule.3) There exists at least one agent with positive prior belief(not alleging to be expert agent)4) There exists a "Good" action.Thus the true belief all agents of the network will converge to 1 when time grows to infinite with a possibility of 1.This model answers the three basic questions of social learning, and can be applied to many practical problems according to the theorem above. So it has a virtue of both theoretical and practical.In the convergence speed analysis, we quantify the analysis of the model and summarize the factors which will affect the convergence of the network and how to fuel the convergence. The factors include:1. Network structure2. The number of expert agents3. The position of expert agents4. The possibility of the expert to choose a "Good" actionThen, these factors are sorted according to their influence and we give a solution how to accelerate the convergence of the network.Next, by the tools of network evolution and forecast analysis in some practical examples, the theory and application of this paper is shown.Finally, we summarize the paper and make a conclusion.