Design Of Resource Distribution For Dynamic Systems Based On Congestion Game

In recent years,the game theoretic control of dynamic system has been applied more and more deeply in the fields of electricity market transaction,computer network,military strategy and road traffic.The problem of resource allocation,such as cost sharing and welfare allocation,lies in finding effective methods to optimize the allocation of resources,so that the entire dynamic system can reach the overall optimality.The congestion game has a fixed model,which has great application prospects in solving the problem of resource allocation in dynamic systems.As a powerful tool to study the mapping and dynamic processes on finite sets,semi-tensor product of matrices has significant practical value in resource allocation based on game theory.In this paper,we consider a facility-based system,such as road transportation,power stations and power users,etc,that can be considered as such a system.Based on the previous studies,we apply the congestion game approach to further study the problem of collaborative control and resource allocation in dynamic systems.This provides a theoretical basis for optimizing resource allocation.The main work and specific research contents of this paper are as follows:1.Considering the design optimization problem of facility-cost functions under the condition of separable objective function.By using semi-tensor product of matrices,the congestion game is transformed into a matrix form.By designing suitable facility-cost functions,a sufficient and necessary condition for transforming a facility-based general system into a congestion game is given,so that the given system performance can be as system's potential function.By using the properties that the potential game will eventually converge to the Nash equilibrium point,the dynamic evolution of the system is studied to ensure that the resource allocation of the whole system achieves the global optimum when each user optimizes its own payoff functions.2.In the case of the inseparable objective function,a kind of nearest separable congestion game is considered and applied to the design of the facility-cost functions of the facility-based general system.When only part of the facility-cost functions can be designed and the facility's bearing capacity is limited,the sufficient and necessary conditions for transforming the system into a congestion game under these two kinds of constraints are analyzed.For the case that the facility-cost functions has both solution and no solution,the dynamic equivalence of the game is used to discuss the conditions that the system achieves the global optimum.Under the condition of linear weighted congestion game,the parameters of the linear facility-cost functions of the facility-based linear weighted system are optimized and designed to realize the optimal control of system resources.Through the strategy of myopic best response adjustment and Lyapunov's method,the dynamic and potential-based stability of the system are analyzed to illustrate the feasibility of the design method.