Stochastic Noncooperative Game With Production And Transportation For Multi-firm Under Traffic Network

The non-cooperative game problem is one of the important research proposed in the twentieth century.It is also the core of game theory and has a very wide range of applications,such as economics,finance,social sciences,psychology,and computation science and so on.However,the reality has many uncertainties,such as weather conditions,traffic,and customer demand and so on.Researchers regard them as random environment.The deterministic noncooperative game problem could not describe and solve these problems truthfully,so it becomes no longer applicable.In this case,the stochastic non-cooperative game takes stochastic environment into account,which is based on the non-cooperative game theory to help decision makers resist future uncertainty and make appropriate decisions.Stochastic non-cooperative game problem can be extended to two-stage or even multi-stage problems and is worth deeply research.Meanwhile,the uncertainties of market environment can bring a degree of risk.Because different kinds of decision makers have different risk tolerance,we need to control risk.The paper studies two-stage stochastic non-cooperative game from the following two aspects.(1)The study of two-stage stochastic non-cooperative game problem which participants are risk-neutral.In this part,we consider a class of multi-firm stochastic non-cooperative game with production and transportation in multi-market,in which the participants are risk-neutral.First,according to the description of game,we establish the optimization problem of competitors,study Karush-Kuhn-Tucker(KKT)conditions of such game problems,and transform these twostage stochastic non-cooperative game problems into two-stage stochastic variational inequalities.At the same time,the existence analysis of the equilibrium solution of the problem is given.Then the two-stage stochastic variational inequalities are solved by the Progressive hedging method(PHM).Finally,the solution results are interpreted and analyzed.(2)The study of two-stage stochastic non-cooperative game problem which participants are risk-averse.In the second part,we study the stochastic non-cooperative game with production and transportation in multi-market,in which the participants are risk-averse.In other words,the risk measure is used to measure market risk when we establish model.Firstly,the model is constructed according to the problem description,and the risk measure CVaR is used to control risk.Then we transforme it into a two-stage stochastic variational inequality.The objective of optimization problem with CVaR becomes nonsmooth and bring some difficulties to direct calculation.We use the smooth function to approximate the original problem.Under this situation,PHM can be used to solve it and we can get the equilibrium solution.Finally,the equilibrium solutions obtained from the two parts are compared to analyze the impact of decision makers' risk attitudes on decision-making.