Calculation And Implementation Of Nash Equilibrium Based On Swarm Intelligence Algorith

In this dissertation,we focus on the calculation and realization of Nash equilibrium by using swarm intelligence algorithms.It mainly includes the study of using the improved differential evolution algorithms to solve Nash equilibrium,seeking Nash equilibrium is equivalent to solving nonlinear equations,and the rational paths realization for Nash equilibrium.The full text is divided into six chapters,and the specific content includes:In Chapter 1,we briefly summarize the research background and significance of calculation and realization of Nash equilibrium and its related issues.The research status of the solving Nash equilibrium,solving Nash equilibrium is equivalent to solving equations,and realizing Nash equilibrium.Finally,it expounds on the main research contents,innovations,and the basic framework of the research.In Chapter 2,we introduce some basic concepts,properties,and relevant conclusions in this dissertation.It includes the concepts and properties of stochastic functional and stochastic process,the basic concepts and related properties of the Nash equilibrium in9)-person non-cooperative game,and the concepts,principles,and operation processes of swarm intelligence algorithms.In Chapter 3,solving the Nash equilibrium by using the improved differential evolution algorithms is studied.First,according to the equivalence between a Nash equilibrium and a solution of some optimization problems,an adaptive differential particle swarm algorithm is proposed to solve the single-objective game.Second,we study the extended type of single-objective game,that is,the multi-objective game in multi-conflict situations.According to the concept of the multi-objective game in multi-conflict situations,an integrated game model under the multi-objective is established.Then,based on multi-objective optimization,the multi-objective integrated game model is transformed into the single-objective integrated game model by using the Entropy Weight Method.And an adaptive differential particle swarm algorithm based on the simulated annealing algorithm is proposed to solve the integrated game model.Finally,the efficiency of the proposed improved algorithms in solving Nash equilibrium is verified by computing single-objective games and multi-objective games in multi-conflict situations.In Chapter 4,we investigate the fact that solving Nash equilibrium is equivalent to solving nonlinear equations.First,the necessary condition for solving Nash equilibrium of the general game is given.Further,the equivalence theorem that Nash equilibrium of9)-person finite non-cooperative game is equivalent to the solution of nonlinear equations is presented,which provides a new method for solving Nash equilibrium.Second,a new algorithm for solving the equations,an adaptive differential evolution algorithm based on the cultural algorithm,is proposed.The algorithm is based on the bilevel evolutionary mechanism of the culture algorithm.The adaptive differential evolution algorithm is introduced into the population evolution space of the cultural algorithm.The implicit information in the population space is extracted,summarized,and stored in the belief space of the cultural algorithm,and guides the evolution of the population space in the form of knowledge,to accelerate the convergence of population evolution and enhance the adaptability of the algorithm.In the theoretical analysis,the finite Markov chain is used to prove that the algorithm weakly converges to the optimal global solution in probability,which provides a favorable theoretical guarantee for solving the Nash equilibrium.Finally,it is verified that solving Nash equilibrium by solving nonlinear equations is efficient.The proposed algorithm has certain advantages in terms of convergence speed and global optimization by solving several classical games.In Chapter 5,we mainly study the rational paths realization for Nash equilibrium.Based on the bounded rationality of the players and inspired by game learning,two methods are proposed to realize Nash equilibrium.One method is to realize Nash equilibrium based on the best response dynamics.First,according to the optimal response dynamics and strategic interactions of the players,an objective function with rationality is established to realize Nash equilibrium.Second,an adaptive differential evolution algorithm based on a relaxation strategy is proposed to realize the Nash equilibrium.Then,the algorithm’s convergence is proved by using the method of stochastic function,which provides a theoretical guarantee for realizing Nash equilibrium.Finally,by simulating the prisoner’s dilemma game and a three-oligopoly Cournot game,we found that the research method and algorithm can quickly realize Nash equilibrium,which is a new and effective method to realize Nash equilibrium.The other is an iterative method based on the rationality of the players and the individual’s best interests.This method uses the characteristics that the correction strategy of the players tends to Nash equilibrium,and the advantage of the individual’s optimal response strategy to guide the players to move in the direction of increasing profits,so that the players have the power and tendency to realize Nash equilibrium.Finally,the effectiveness of the method to realize Nash equilibrium is verified by simulating two matrix games,which provides a reference for future research on the realization of Nash equilibrium.In chapter 6,we briefly summarize the results of this dissertation and look forward to some future research prospects.