The Second Order Optimality Conditions For Nash Equilibrium Games And Stability Analysis

The non-cooperative game problem is usually solved by the classical Nash equilibrium and the generalized Nash equilibrium.In practical application,the generalized Nash equilibrium can be more detailed,comprehensive description and solve practical problems.This paper mainly discusses the optimality conditions and the stability of the optimal solution of Nash equilibrium problem.Firstly,the first-order optimality condition is simply summed up.Then the second-order optimality condition is discussed in detail by using the nonlinear optimization theory,and then the conclusion is extended to the classical Nash equilibrium problem.At the end of the paper,a slight disturbance is introduced to the original problem,and the stability of the optimal solution is analyzed.The conclusion is that if the original problem satisfies the Jacobian uniqueness condition,then the optimal solution has stability.