Research On The Problem Of Producer Game Under Different Carbon Emission Reduction Mechanisms

Greenhouse gas emissions cause global warming and bring serious disasters and impacts to mankind.It is found that the main factor leading to global warming is high carbon emissions.Reducing carbon emissions is an effective means to curb global warming.Therefore,many countries and regions have taken a series of measures to limit carbon emissions,which will affect the production decisions of producers.In this paper,based on the clean development mechanism and carbon tax carbon trading mechanism in the carbon emission reduction mechanism,we take optimal control and differential game as the theoretical basis,and the numerical method of partial differential equation as the research tool,the optimal decision-making of producers under multiple carbon emission reduction mechanisms is studied.Specific studies are summarized as follows:Firstly,the impact of dynamically changing emission reduction technology on the game results of two adjacent regions is studied.We regard emission reduction technology as an endogenous variable that can be changed by investment,consider the production decisions of two adjacent regions,and establish a differential game model to maximize the income of producers.The HJB equation satisfied by the value function is derived and an analytical solution of the equation is obtained.From this,the value function of producers,the optimal output,the optimal investment level,and the evolution path of emission reduction technology and pollution stock with time are given.The results show that:regional output increases with the progress of emission reduction technology,and emissions and air pollution stock first increase and then decrease with the progress of emission reduction technology.When two adjacent regions invest in R&D of emission reduction technologies,the income of each region is affected by the emission reduction technologies of both sides.When two regions do not invest in emission reduction technologies at the same time,regardless of the change of production efficiency and pollution damage,the regional income of investing in emission reduction technologies increases with the increase of output,and the regional income of not investing in emission reduction technologies decreases with the increase of output.Therefore,Investment in emission reduction technologies can effectively reduce the "free riding"behavior in carbon emission reduction actionsSecondly,based on the investment in emission reduction technology,the influence of"learning by doing" effect on the game of two symmetrical transboundary pollution regions is studied.Experience accumulation can reduce investment costs and affect production decisions.In this paper,we establishes a transboundary pollution differential game model of cooperation and noncooperation between two adjacent regions,and the maximum principle is used to solve and analyze the model.The results show that:there is an admissible set of parameters,compared with the noncooperative game,the regional output is lower,the emission reduction technology is cleaner,the air pollution stock is less,and the regional net income is higher under the cooperative game.Near the steady-state equilibrium solution,The investment level of emission reduction technology,experience accumulation,emission reduction technology and pollution stock are all decrease with the evolution of time.Parameter analysis shows that the larger of the growth rate of knowledge accumulation,the smaller of the pollution stock,and the impact of all parameters on emission reduction technology is weak.At the same time,the accumulation of emission reduction experience and the progress of emission reduction technology can increase the region’s net profit.Thirdly,we consider the multiplayer game problem,the influence of price competition on the two symmetrical transboundary pollution regions is studied.Different emission reduction technologies will affect the price of products,and then affect the production decisions of producers.A differential game model of transboundary pollution under price competition is established.The maximum principle is used to solve and analyze the model.The results show that:for each region,compared with noncooperative game,the product price is higher,the output is lower,the total air pollution stock is lower,and the regional net income is higher in cooperation game.The parameter analysis shows that for each region,the product price decreases,the output increases,the income increases,and the pollution stock in the air decreases with the progress of emission reduction technology;the product price decreases,the output increases and the air pollution stock increases when the price competition is strengthened.The progress of emission reduction technology has a positive impact on regional decision-making,while price competition will lead to lose of income for both sides.Finally,the impact of the compound emission reduction mechanism of carbon tax and carbon trading-on the game of infinite producers is studied.We design a carbon emission reduction mechanism framework of carbon tax and carbon trading,and establish a mean field game model to analyze the optimal decision of producers.The HJB equation and Kolmogorov equation satisfied by the model are derived by using the idea of mean field.The step-by-step difference method is used to solve the equations,and the effectiveness of the numerical method is proved.By analyzing the evolution of three different types of distribution functions which representing the initial emission state of producers with time,the optimal decision of producers is obtained.The results show that under the compound carbon emission reduction mechanism,each producer tends to choose a different emission level from other producers when producers are in production intensive areas,each producer selects an emission level similar to the initial state when the distribution of producers is relatively uniform.Numerical analysis shows that under the compound carbon emission mechanism,carbon tax has a great impact on the initial carbon emission right,and carbon trading price has a great impact on the overall carbon emission.