Research On Optimal Control And Consistency Of Opinion Dynamic Games

Nowadays,the epidemic has spread across the globe,which makes the research on the opinion dynamic games especially important.This paper examines opinion dynamic games in an infinite discrete time horizon and divides them into homogeneous opinion dynamic games and general opinion dynamic games according to different social structures.In these models,the dynamic equations of agents’ opinions are linear,and the payoff function of each player is quadratic.Therefore,this is a type of linearquadratic game.The Bellman equation can be used to obtain the feedback Nash Equilibrium of the game and optimal path.This article creatively proposes an opinion dynamic game with an external control and separately examines the above two types of opinion dynamic game.Firstly,this paper considers the homogeneous opinion dynamic games with singleplayer and multi-players,obtains the optimal control of players at each stage by using Bellman method,and gives the optimal path of the evolution of agents’ opinions.Then,the influence of control cost on the mean value of agents’ opinions is analyzed.Secondly,this paper investigates generalized opinion dynamic games with single-player and multi-players,solves the feedback Nash equilibrium and the corresponding optimal path by using Bellman Equation,and discusses the consensus of the optimal path.Finally,using a series of simulation calculations,the influence of the number of players,network structure,and control cost on the convergence speed and consensus of the game is studied.