| Game theory is a powerful tool to simulate the interaction between two or more independent decision makers in a competitive environment.It is widely used in economics.In the second chapter,a Cournot game model with multiple dimensions and multiple objectives is proposed.Under the assumption of complete information static non-cooperative game,each player in the game makes decisions in multiple domains and pursues multiple goals simultaneously.In this paper,vector-valued Kyfan inequality and cone theory are used to prove the existence of the weak Pareto-Nash equilibrium of the model.Then the lexicographical equilibrium solution is obtained by the sequential quadratic programming algorithm combined with fmincon function.As an application of the conclusions,we discuss the game problem when three companies compete for the production output of two products and pursue profit maximization and environmental impact minimization,and obtain the lexicographical equilibrium solution.The traditional multi-objective game theory studies the problem that the players consider the benefits of multiple objectives at the same time.In these cases,however,the payoff is an exact value,ignoring the disturbance caused by inaccurate or inaccurate information.Therefore,in chapter 3,we use interval number to measure the uncertainty of return value,put forward a two-matrix multi-objective game model of return value of interval value,and solve the problem.Firstly,the interval dual-matrix multi-objective game problem is transformed into the interval multi-objective optimization problem.Secondly,the relative theory of interval analysis is introduced to construct the comparative relation between interval vectors.Based on the improvement of multi-objective fireworks algorithm,the fireworks algorithm for solving interval multi-objective optimization problem is obtained.The weak Pareto-Nash equilibrium solution of the interval bimatrices multi-objective game problem is obtained numerically by using this algorithm.Finally,considering that the solution results are not accurate enough,there are problems such as time complexity of the algorithm.The theory of G exact efficient solution is introduced,and by refining the solution set and results in the iterative process,the equilibrium solution set of weak Pareto-Nash refinement is obtained.This shows the practicability and effectiveness of the method. |
