STP-based Potential Game And Its Application

Potential game,as a special type of game in non-cooperative game,is one of the most important research fields in game theory.It has many good properties,especially the property of converging to pure Nash equilib-rium point under evolution makes it popular,and has been widely used in economy,power,transportation and some other fields.Based on the semi-tensor product(STP)of matrices,this thesis studies the dynamics and convergence of delayed hyper-networked evolutionary potential game,and the specific application of potential game in traffic congestion system.The main contents are listed as follows:In Chapter 1,we mainly introduce the research status of potential game and STP of matrices.In Chapter 2,we present some preliminaries including the definition and properties of STP of matrices,and the related knowledge of game theory.In Chapter 3,we study the dynamics and convergence of delayed hyper-networked evolutionary potential game.A new game model,named delayed hyper-networked evolutionary game(HNEG),is proposed as the generalization of network evolutionary game.The model considers the time delay of information transmission and the multi-people in fundamental network game simultaneously,which makes the model more practical.Based on the STP of matrices,the systematic theoretic framework is provided for the combination of potential game and delayed HNEG,and we give the specific steps to analyze the dynamics and convergence.Moreover,considering the efficiency and reality about updating process,based on the myopic best response adjustment rule(MBRAR),we define a new strategy updating rule named as delayed group-based sequential MBRAR.And we prove that the game can converge to one of the pure Nash equilibrium trajectories under this rule.In Chapter 4,the potential game control theory is applied to the traffic congestion system.We study the road congestion pricing problem in traffic system.When traffic managers solve the problem of road congestion,they can't make complete regulations and constraints on the route selection of travelers.Travelers aim at optimizing their own utilities in the absence of a centralized management.In this chapter,we consider the problem that how to design a reasonable congestion price when the global function of traffic system is given,so that the travelers' route selection can just make the global function reach the optimum.Based on the STP of matrices,this problem is transformed into the optimization problem of network congestion game.A sufficient and necessary condition is proposed to guarantee that the global function can be transformed into the potential function of network congestion game.Then detailed procedures are obtained to design the road congestion price when conversion can be established.This chapter provides a new method to establish congestion pricing mechanism,which is helpful to optimize the operation of urban traffic network.In Chapter 5,a brief conclusion is presented to end this work,also the prospect for the work is made.