Nash Balance Realization Based On Swarm Intelligence And Reinforcement Learning

In this paper,we mainly focus on to solve Nash equilibrium based on swarm intelligence algorithm and reinforcement learning algorithm.First,we introduced immune memory,self-evolution,information sharing mechanism into quantum particle swarm optimization algorithm,then Co-evolutionary immune quantum particle swarm optimization(CIQPSO)algorithm is presented.It proved that the algorithm converges by introducing probability density selection function.Second,the Co-evolutionary immune quantum particle optimization algorithm was used to solve the n-person non-cooperative finite game and the generalized game Nash equilibrium problem.Finally,from the perspective of reinforcement learning,this paper try to solve multi-agent stochastic game's Nash equilibrium by using reinforcement learning algorithm.This paper is organized as follows:Chaper 1 is the preface,which mainly introduces the research background and significance of game theory,the research status of swarm intelligence algorithm and game learning.In chapter 2,we mainly study the Co-evolutionary immune quantum particle swarm optimization(CIQPSO)algorithm to solve n-person non-cooperative finite game.We introduced information sharing,self-evolution and immune memory into quantum particle swarm optimization algorithm to obtain a new CIQPSO algorithm,the algorithm maintained the diversity of the population by probability density selection,and the convergence properties of the CIQPSO algorithm is proved.The numerical results illustrate that the algorithm is effective.In chapter 3,we mainly study to solve the generalized game Nash equilibrium problem by using the CIQPSO algorithm.First,the GNEP is turned into the nonlinear complementarity problem by using the Karush-Kuhn-Tucker(KKT)condition.Then,the nonlinear complementarity problem is converted into the nonlinear equations problem by using the complementarity function method.Finally,For the nonlinear equation equilibrium problem,we use the CIQPSO algorithm to solve by constructing an appropriate fitness function,the numerical results show that the algorithm is effective.In chapter 4,We consider the realization of Nash equilibrium in a class of multiagent stochastic game.Through Python to simulate and calculate the process of Nash equilibrium of the multi-agent in a specific environment based on the idea of reinforcement learning;the multi-armed bandit game's Nash equilibrium is solved by the stochastic gradient algorithm with benchmark item and the planning game's Nash equilibrium is solved by using the value function iteration algorithm.In 5 chapter,we are the summary and prospect of the whole paper.