Evolution,Control And Robustness Analysis Of Congestion Game

In various fields,such as economics,sociology and engineering and so on,congestion game has made an important contribution to the study of actual congestion problems.It is a special game in game theory.Congestion games can also be repeated over time,which is called evolutionary congestion game.With the rapid development of economy,the theory and application of evolutionary congestion game has gradually become a hot research field in the academic circles at home and abroad.In evolutionary congestion game,when the numbers of players and strategies are finited,its dynamic evolution process can be equivalent to a finite value logic dynamic system.The semi tensor product of matrix is a powerful tool to deal with the finite logic dynamic system.It can also be used in the research of the finite evolution congestion game.Firstly,the semi tensor product method of matrix is used to study the stabilization of the delay evolution congestion game in this paper.Then,the robustness analysis of the evolution congestion game with attackers is considered.Finally,the robustness analysis of the evolution congestion game with attacking players is discussed.The main research contents are as follows:(1)The control problem of evolutionary congestion game with time delay is investigated.Firstly,utilizing the semi-tensor product method of matrix,the evolutionary congestion game with time delay is described as a logical dynamic system.Based on this,the dynamic behavior of delay evolutionary congestion game is analyzed,and it is proved that the fixed point of the game is Nash equilibrium.Then,for any given initial situation,the necessary and sufficient conditions for global stabilization to Nash equilibrium under open-loop control and state feedback control are presented,and the design process of control is constructed respectively.Finally,numerical examples are presented to show the effectiveness of the theoretical results.(2)The robustness of evolutionary congestion game with attackiers and feasible state constrained set is investigated.Firstly,using the semi-tensor product method of matrix,evolutionary congestion game dynamic system with attackers and controllers is established and is transformed into algebraic form.Then,for any initial profiles in the restricted set of feasible states,the sufficient and necessary conditions of robust reachable equilibrium under open-loop control and state feedback control are presented,and the design process of control is constructed respectively.Finally,numerical examples are presented to show the correctness of the theoretical results.(3)The robustness of evolutionary congestion game with attackers and phenomenon of time delay is investigated.Firstly,using the semi-tensor product method of matrix,delay evolutionary congestion game dynamic system with attackers and controllers is established and is transformed into algebraic form.Then,for any initial profiles,the sufficient and necessary conditions of globally robust reachable equilibrium under openloop control and state feedback control are presented,and the design process of control is constructed respectively.Finally,numerical examples are presented to show the effectiveness of the theoretical results.