Research On Inter Regional Emission Reduction Strategy Based On Differential Game Theory

The global environmental pollution caused by carbon emissions is related to various aspects of social production and living,such as rising in sea-levels,the frequency of extreme weather,increasing of the desertification areas and exhausted available energy and so on.It not only affects people's production and life,but also threatens the survival of many species on our planet.In order to jointly deal with the environmental crisis faced by human being,the relevant agencies of the United Nations has set up some operational modes of emission reduction to help countries control the future levels of greenhouse gas emissions,so as to effectively alleviate the environmental problems.These modes include:1.Carbon Tax.By imposing a carbon tax to curb the scale of production,it would promote the transformation of general enterprises to environmental protection enterprises,so as to achieve the purpose of reducing emissions.2.Emissions Trading,ET.In this way,the area which is difficult to complete the task of reducing could buy carbon emission permits from the areas which over fulfill their emission reduction task.3.Joint Implementation,JI.That is,many areas within the developed countries can be regarded as a whole,taking some areas to reduce emissions and some areas to increase emissions,then the emission reduction task can be completed in general.4.Clean Development Mechanism,CDM.It can promote the development of greenhouse gas emissions in developed and developing countries.Compared with the traditional sense of the static game or dynamic game,the differential game can more accurately reflect the actual situation of the game for its unique properties(the set of decision model is continuous set of choices,and participants are influenced by the objective function of state variables),then it is more appropriate for the study of regional carbon emission control problem.This paper is based on the theory of differential game,with the time consistency criterion as the core and the overall rationality and individual rationality as the basic guarantee.It studies the problems of inter regional pollution control,the main contents are as follows:First,the differential game analysis based on the carbon tax regulation.Without considering the influence of political factors,the government's carbon tax policies are studied by constructing the differential game model and the optimal production strategies of enterprises in the face of the government' s dynamic carbon tax policy are analyzed by establishing the Hamilton function.There is a Stackelberg game between the government and the enterprise,the government needs to achieve a dynamic balance through the tax policies to promote regional economic development and control the scale of pollution.Second,the differential game analysis based on the carbon emissions trading system.Considering the situation that several regions form an alliance and an environmental agency or agreement(e.g.Kyoto Protocol)sets standards for each region in the alliance.If the discharge exceeds the standard,the penalty for breach of contract is huge,so all the regions will not default.There is a carbon emissions trading market in the alliance,which is free to buy and sell a certain amount of emissions at any time in the market.The differential game model is established,and the optimal control technique is used to analyze the production and emission of each region during the interval[0,T],and the open-loop or feedback Nash equilibrium solution is given.In addition,the paper proposes a duopoly economic model for the competition of selling emissions permits between two regions in the international market.Two types of demand functions are considered in the paper:The linear demand function case and the cubic demand function case.Third,the differential game based on the analysis of the influence of transboundary pollution.This paper studies a non-cooperative differential game and a cooperative differential game of transboundary industrial pollution between two asymmetric regions.It characterizes the parameter spaces that governments in two neighboring regions can collaborate and gives the feedback Nash equilibrium strategies of governments and industrial firms.By using Hamilton—Jacobi—Bellman equation method to calculate the feedback Nash equilibrium,a subgame-consistent cooperative solution is provided and a payment distribution mechanism is proposed.With such a payment distribution,both governments will receive a higher payoff in a cooperative solution than in a non-cooperative solution at any instant of time during the game.The main difficulties and innovations of the paper can be summed into following four aspects:1.It analyzes the problems of the government carbon tax policy under the condition of the change of the market share of the two kinds of enterprises,such as green enterprises and normal enterprises.It is different from other literatures,this paper sets up the market share of green enterprises in the form of state variables,and it comes to be the optimal control problem with two state variables(another state variable is the cumulative stock of pollution).2.Not only analyzes the carbon emissions trading market transactions,but also examines the market competition in the sale of the right to sell.In the paper,the difference between the selling price and the sales volume of the emission permits is compared in oligopoly market and duopoly market.3.Analysis of the impact of transboundary pollution on the strategy of intergovernmental cooperation.The transboundary pollution damages the regions in two ways:through a global accumulative pollutant and a regional non-accumulative pollutant.In the pollutants of these cases,the former is hard to get rid of and has an accumulative global impact for the environment(For example,greenhouse gases can contribute to global warming),the latter is a non-accumulative regional pollutant and would affect the neighboring areas(For example,acid rain generated by the industrial activities in one area pollutes the soil of neighboring areas).4.A payment distribution mechanism is proposed and a subgame-consistent cooperative solution is provided.With such a payment distribution,the cooperative scheme can be upheld throughout the game horizon,both group optimality and individual rationality are required to be satisfied and it can satisfy the time consistency during the planning period.