Differential Game Analysis of Transboundary Pollution Based on Competitive Pricing

A differential game analysis of multipollutant transboundary pollution in river basin

A fuzzy differential game theory is proposed to solve the n-person (or n-player) nonlinear differential noncooperative game and cooperative game (team) problems, which are not easily tackled by the conventional methods. In the paper, both noncooperative and cooperative quadratic differential games are considered. First, the nonlinear stochastic system is approximated by a fuzzy model. Based on the fuzzy model, a fuzzy controller is proposed to deal with the noncooperative differential game in the sense of Nash equilibrium strategies or with the cooperative game in the sense of Pareto-optimal strategies. Using a suboptimal approach, the outcomes of the fuzzy differential games for both the noncooperative and the cooperative cases are parameterized in terms of an eigenvalue problem. Since the state variables are usually unavailable, a suboptimal fuzzy observer is also proposed in this study to estimate the states for these differential game problems. Finally, simulation examples are given to illustrate the design procedures and to indicate the performance of the proposed methods.

A fuzzy differential game theory is proposed to solve the N-person (or N-player) nonlinear differential noncooperative and cooperative (team) game problems, which are not easily tackled by the conventional methods. In this study, both noncooperative and cooperative quadratic differential game are considered. First, the nonlinear stochastic system is approximated by a stochastic fuzzy model. Based on the stochastic fuzzy model, a fuzzy observer-based controller is proposed to deal with the noncooperative differential game in the sense of Nash equilibrium strategies or cooperative (team) game in the sense of Pareto-optimal strategies. Using the suboptimal approach, the outcome of the fuzzy differential game for both noncooperative and cooperative game is parameterized in terms of the eigenvalue problem (EVP). Linear matrix inequality (LMI) techniques are employed to solve these problems from the convex optimization perspective.

This paper analyzes a dynamic Stackelberg differential game model of watershed transboundary water pollution abatement and discusses the optimal decision-making problem under non-cooperative and cooperative differential game, in which the accumulation effect and depreciation effect of learning-by-doing pollution abatement investment are taken into account. We use dynamic optimization theory to solve the equilibrium solution of models. Through numerical simulation analysis, the path simulation and analysis of the optimal trajectory curves of each variable under finite-planning horizon and long-term steady state were carried out. Under the finite-planning horizon, the longer the planning period is, the lower the optimal emission rate is in equilibrium. The long-term steady-state game under cooperative decision can effectively reduce the amount of pollution emission. The investment intensity of pollution abatement in the implementation of non-cooperative game is higher than that of cooperative game. Under the long-term steady state, the pollution abatement investment trajectory of the cooperative game is relatively stable and there is no obvious crowding out effect. Investment continues to rise, and the optimal equilibrium level at steady state is higher than that under non-cooperative decision making. The level of decline in pollution stock under finite-planning horizon is not significant. Under the condition of long-term steady state, the trajectories of upstream and downstream pollution in the non-cooperative model and cooperative model are similar, but cooperative decision-making model is superior to the non-cooperative model in terms of the period of stabilization and steady state.

A differential game analysis of multi-regional coalition for transboundary pollution problems

Transboundary water institutions in action

Spatial vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative dynamic games

The purpose of the paper is to assess the current state of prices and price relations in the agricultural sector of Russia. The authors analyzed the dynamics of prices of agricultural products, industrial products, food products, and processing industry, consumer prices in the period 2014–2018. The authors consider the cost structure of agricultural production, which is the basis of balanced price relationships. The study showed that the increase in prices of agricultural producers in recent years was significantly less than in other sectors of the economy. This leads to an increase in disproportions and to a decrease in the financial stability of agricultural producers. The most significant disproportions in price relations are formed in the sale of food products in retail trade. The study compares the average prices of agricultural producers in Russia with the prices of producers in the countries leading in terms of exports of these products in the world. Such a comparison allows to determine that crop production (wheat and sunflower seeds) has a price competitiveness in the world market. The authors provide a number of proposals to improve price relations in the agricultural sector of Russia. The proposals are aimed at the balanced development of agriculture: in the sphere of relations between agricultural producers and resource-providing industries, in the field of production, as well as in the field of ensuring the balance of supply and demand.

The energy consumption disparity is an important factor affecting product pricing. The risk and the cost of new energy products are generally higher than those of traditional energy products, which results in conflicting pricing strategies between manufacturers and retailers. Applying the concepts from dynamic cooperative game theory, such as improved Shapley value, in this paper, we have studied the optimal pricing strategies of manufacturers and retailers in a cooperative and a noncooperative game. Based on policies and market conditions in China, we have used a logistic regression model to determine the impact of product sales, devised pricing strategies affected by the relevant government tax, and subsidy policy. The results show that, first, under the basic condition in which the manufacturer obtains profit, the optimal pricing of the retailer in a noncooperative game is more than that in a cooperative game. Second, the differential coefficient of the energy consumption of the two products in the cooperative game is greater than that in the noncooperative game. Third, the cooperative game not only plays an incentivizing role for retailers in setting reasonable prices of new energy products but also encourages manufacturers, producing a greater difference of energy consumption between traditional energy products and new energy products, which further reduces the consumption of new energy products. Finally, the strategies of sharing the green marketing costs by manufacturers and retailers can improve the total profits of the supply chain in addition to their own.

The purpose of this study was to investigate international cooperation on pollution control between asymmetric countries under uncertainty. We considered any two countries that are asymmetric with respect to their technological level and the amount of environmental damage they incur. Production processes result in the emission of pollutants that are added to the existing pollution stock common to both countries. The stock of pollution evolves stochastically, according to the geometric Brownian motion. The governments of the two countries set their pollutant emission levels at the Markov perfect equilibrium to maximize their expected net present value of social welfare. In addition, they set their pollutant emission levels at cooperative equilibrium to maximize the sum of their expected net present value of social welfare.In cooperative stochastic differential games, a credible cooperative agreement must be subgame consistent. Subgame consistency ensures extension of an optimal policy to a later starting time, and any possible state brought about by prior optimal behaviour of the governments remains optimal.We considered a cooperative game in which the governments of two countries agree to maximize and divide the sum of their expected net present value of social welfare in a way that shares the gain from their cooperation proportional to the relative sizes of their expected non-cooperative net present value of social welfare at every instant of time. In conclusion, the country with a higher technological level or that incurs lower environmental damage obtains a larger instantaneous payoff at the subgame consistent solution.JEL Classification: F18, L13, Q58

Spectrum sharing in cognitive radio networks is essential to ensure effective communication between secondary users. Game theory is suitable to be applied to the spectrum sharing strategies since it considers strategic interactions between users. There are two types of games based on the ability to communicate between users: cooperative game and non-cooperative game. In this paper, the two spectrum sharing methods using cooperative and non-cooperative games are analyzed and compared. The numerical analysis shows that both the cooperative game and the non-cooperative game have their own best operation environment, in terms of the secondary user population.

PurposeThe government plays an important role in the financing process of small and medium enterprises (SMEs), but the current government-enterprise cooperation (GEC) mechanism cannot well solve the financing problem of SMEs. In addition, since government-enterprise cooperation is a long-term dynamic process, this study aims to explore the cooperation strategy between the government and core enterprises in supply chain finance (SCF) under the dynamic structure.Design/methodology/approachConsidering both parties have the characteristics of disappointment aversion, our research constructs a game theory model of government subsidy and the effort of the enterprise to implement SCF based on differential game and studies different game strategies in the non-cooperative game, the Stackelberg game and the cooperative game.FindingsOur findings show that the government subsidy can significantly spur the enterprise in the supply chain to implement SCF. We also find that the limitation of the government subsidy exists. In addition, the optimal strategy, the optimal benefit and the total benefit of the financing system formed by the government and the enterprise in the cooperative game are better than those in the non-cooperative game. Pareto optimality is achieved.Research limitations/implicationsThe limitations of this paper are: (1) In theory, this paper only takes the government and enterprise as game subjects without considering other participants in the supply chain. In addition, only disappointment aversion is taken into consideration while in reality the participants often exhibit multiple behavior preferences. (2) In methodology, only the numerical solution is given through the solution algorithm and all parameters are assumed to be determined as time changes for the convenience of calculation.Practical implicationsThe government can motivate enterprises in the supply chain to implement SCF by providing subsidies. However, it should be noted that excessive subsidy will make the enterprise dependent on the government and as a result, decrease the effort level to implement SCF. Thus, it is necessary for the government to keep track of the business conditions of the enterprise to make a subsidy strategy. In addition, the government can reduce the impact of disappointing aversion by making more targeted policies and taking risk management measures.Social implicationsOn one hand, it is necessary for the government to keep track of the business conditions of the enterprise to make a subsidy strategy. In addition, the government can reduce the impact of their own disappointing aversion by making more targeted policies and adopting risk management measures. On the other, it is important for the enterprise to improve the regulatory mechanism and optimize the compensation structure of decision-makers to inhibit the impact of decision-makers' disappointing aversion.Originality/valueThis study is the first to investigate the mechanism of GEC in the setting of SCF based on a differential game. Furthermore, our study provides a theoretical basis for the government and enterprises to cooperate in SCF.

Much of the literature on international environmental agreements uses static models, although most important transboundary pollution problems involve stock pollutants. The few papers that study IEAs using models of stock pollutants do not allow for the possibility that membership of the IEA may change endogenously over time. In this paper we analyse a simple infinite-horizon version of the Barrett (1994) model, in which unit damage costs increase with the stock of pollution, and countries decide each period whether to join an IEA. We show that there exists a steady-state stock of pollution with corresponding steady-state IEA membership, and that if the initial stock of pollution is below (above) steady-state then membership of the IEA declines (rises) as the stock of pollution tends to steady-state. As we increase the parameter linking damage costs to the pollution stock, initial and steady-state membership decline; in the limit, membership is small and constant over time.

In this paper, we develop a differential game model of transboundary pollution which incorporates abatement investments and clean technology innovations under the influence of learning by doing. We consider clean technology as an endogenous variable that can be improved though technology investment, and region’s cost function depends not only on the R&D investment but also influenced on the accumulation of experience. Our focus is on the investment behavior in clean technology and the impact of learning by doing on optimal decisions of the regional. We also study the general solutions of the dynamic systems and discuss the results with numerical examples under both the noncooperative game and the cooperative game. Results show that clean technology innovation and emission reduction experience accumulation can increase the region’s future revenues; the improvement of the learning rate and knowledge accumulation growth rate of clean technology can promote regional’ transformation toward a cleaner mode of production; both regions achieve higher levels of clean technology and lower pollution stocks in cooperative games.

6 - Cross-border resource management: methods