Two Stage Stochastic Programming Model With Equilibrium Constraints For Capital Tax Competition

We can witness many random affairs happenning in our daily lives. In recent years, how to found reasonable model and solve the model with practical algorithm are the hot spots in the field of optimization. In this paper, we take the random factors of international capital compe-tition into account to found a stochastic programming model with some equilibrium constraints and use the SAA method to analyze the convergence quality of the model’s Nash stationary points. Finally we make a simple numerical test for the model with evaluation function method. This paper provides a theoretical basis from being "competition only " to " cooperative com-petition" in the international capital competition. Our main work as following:Chapter one we introduce the background of this paper, and give a brief overview of the domestic and foreign literature about capital tax competition.Chapter two we display some concepts of mathematical programming and some conven-tions for the following model foundation and problem solving.Chapter three is the model foundation. Considering the tax in the international competi-tion we expect to maximize the benefit function to built a stochastic programming model, and discuss the existence and uniqueness of the problem’s solution.Chapter four we characterize the first-order equilibrium conditions of the original problem with Clarke subdifferential,and then discuss the convergence properties and converging rate of the stability points.Chapter five is the numerical experiments.According to the convergence theory discussed in the chapter four, we adopt the method about multiple objective programming based on some reasonable assumptions for this model and gives the numerical results by using tool Matlab.