Modeling CO₂ Emission Under Global Warming By Differential Game

Global warming(GW)is now recognized as a significant threat to sustainable development,and carbon dioxide(CO2)is by far the most important of the "GHGs".It is produced by the burning of fossil fuels,and other human activities.With the increase of amount of greenhouse gases,led to a rise in the sea level,extreme climate change,species extinction and other natural phenomena.These disasters is given brought huge losses to human life.Therefore,to reduce emissions,reduce the negative effects from greenhouse gases is the focus problem of global sustainable development today.For a country,the government can pass laws and regulations to achieve the goal of emission reduction.But for two or more countries,there is no capability for higher-level enforcement,e.g.,no world government to enforce the rules.In this case,For a country,the government may formulate laws and regulations,achieve the goal of emission reduction.After providing some introductory background material,we introduce a benchmark dynamic game within which to study the GW problem.We model the GW process as a dynamic differential game in which the players are countries,who benefit from production and produce emissions of greenhouse gases,and the state variable is the stock of greenhouse gases.Additionally,the model allows for population growth and technology change and regard population growth as Logistic growth model.For this model,we derive a bench-mark equilibrium termed the cooperative equilibrium,and the noncooperative equilibrium.We make use of stochastic optimal control theory and dynamic principle to derive the system of Hamilton-Jacobi-Bellman(HJB)equations satisfied by the value functions for the cooperative and the noncooperative games,respectively,and then propose a so-called fitted finite volume method to solve it.We shall see that the two countries make the decision whether cooperation after weight the emission lever and value function.We get the boundary of cooperation and noncooperation.We can adjust the cooperation strategy with time.