从Stackelberg-Nash均衡视角对动态社交网络系统中的意见分层建模分析  

Analysis of Hierarchical Opinion Modeling in Dynamic Social Network System from the Perspective of Stackelberg Nash Equilibrium

作　　者：闫晓雪 纪志坚[1,2] YAN Xiaoxue;JI Zhijian(School of Automation,Qingdao University,Qingdao 266071;Shandong Key Laboratory of Industrial Control Technology,Qingdao 266071)

机构地区：[1]青岛大学自动化学院,青岛266071 [2]山东省工业控制技术重点实验室,青岛266071

出　　处：《系统科学与数学》2021年第11期3029-3048,共20页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(61873136,62033007,61873146,61703237);山东省泰山学者攀登计划;山东省泰山学者计划(ts20190930)资助课题。

摘　　要：文章基于社交网络系统中的DeGroot模型,对多个体讨论问题时意见在多智能体网络中的演变进行了研究,在此过程中加入Stackelberg-Nash均衡博弈思想,建立了一种分层控制的智能体交互协议和决策机制.首先,从Stackelberg-Nash均衡的角度,对社交网络系统进行分层优化设计,其中制定并研究的分层决策机制是由一个主要智能体和多个次要智能体组成.主要智能体具有产生策略和预设目标的能力,次要智能体会根据博弈策略演变不断自我优化,产生应对方案并传递给主要智能体.然后,主要智能体将次要智能体的方案整合得到最佳解决方案,再将最佳方案与预设目标进行对比,若误差较大,则进一步优化,直至获得最优解决方案.最后,通过仿真验证了意见分层建模的稳定性和收敛性.This paper studies the evolution of opinions when multiple individuals discuss a problem in a multi-agent network,which is based on the DeGroot model in the social network system.In this process,Stackelberg-Nash equilibrium game idea is taken into consideration to establish a hierarchical control agent interaction protocol and decision-making mechanism.Firstly,from the perspective of Stackelberg-Nash equilibrium,we put forward a hierarchical optimization design of the social network system,in which the hierarchical decision-making mechanism developed and studied is composed of one major agent and several minor agents.The major agent has the ability to generate a preset goal and strategies,while the minor agent constantly selfoptimizes according to the evolution of game strategies to generate solutions and pass them to the major agent.Secondly,the major agent integrates the solutions of the minor agents to get the best solution.Then,the best solution is compared with the preset target.If the errors are large,the optimal solution is further optimized until the optimal solution is obtained.Finally,the stability and convergence of the model are verified by simulation.

关 键 词：社交网络 多智能体网络 Stackelberg-Nash均衡(SNG) 意见分层优化 

分 类 号：O157.5[理学—数学] O225[理学—基础数学]