It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems kn...It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.展开更多
China is a country with the most water consumption, so it is lack of water resources.Industry has brought serious water pollution while driving economic development, which leads to the destruction of ecological enviro...China is a country with the most water consumption, so it is lack of water resources.Industry has brought serious water pollution while driving economic development, which leads to the destruction of ecological environment. With the improvement of environmental awareness, many scholars have shifted their research direction to how to improve the ecological environment. Most studies consider the whole system as a "black box", regardless of its internal structure. Therefore, a method to identify inefficiency is necessary and some suggestions for optimization are given. In this paper,a two-stage undesirable fixed-sum output data envelopment analysis(DEA) model is proposed. The industrial chemical oxygen demand(COD) emission during 2011–2015 are adjusted, and the efficiency values are calculated by heuristic search algorithm. The efficiency of 30 provinces and cities is divided into eastern, central and western regions. The model can identify the inefficient stage in industrial system, and find the source of low efficiency in the system. The analysis shows that the efficiency of eastern region is the highest, while the overall efficiency is inclined to the pollutant treatment stage.Finally, the paper puts forward some suggestions for the low efficiency areas, which can save water while ensuring economic benefits, and provide new direction for water pollution reduction and improve the ecological environment.展开更多
With the development of China’s economy,environmental pollution has become cumulatively serious.The primary source of environmental pollution is thermal power generation,which has attracted the attention of governmen...With the development of China’s economy,environmental pollution has become cumulatively serious.The primary source of environmental pollution is thermal power generation,which has attracted the attention of governments and academia in recent years.To effectively reduce environmental pollution,research should study how to constrain the undesirable output of thermal power plants,that is,to limit the total undesirable output of the plants to a certain fixed sum.However,few studies have suggested that these undesirable outputs should be fixed-sum outputs.Moreover,no previous research publication about thermal power plants has analyzed their environmental performance changes.To address these gaps,a novel Malmquist-DEA approach is proposed for evaluate the environmental performance of thermal power plants in this paper.This approach generalizes the equilibrium efficient frontier DEA model with fixed-sum undesirable outputs and incorporates the model into the Malmquist productivity index(MPI).The authors apply this approach to the analysis of provincial thermal power plant environmental performance in China and analyze such plants’trends based on panel data from2011 to 2014.The empirical research shows that the environmental performance of regional thermal power plants was positively affected by efficiency change and negatively affected by technical change.Finally,the authors provide policy suggestions based on our findings.展开更多
文摘It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.
基金Supported by Doctoral Research Startup Fund of Anhui University of Finance&Economics (85051)。
文摘China is a country with the most water consumption, so it is lack of water resources.Industry has brought serious water pollution while driving economic development, which leads to the destruction of ecological environment. With the improvement of environmental awareness, many scholars have shifted their research direction to how to improve the ecological environment. Most studies consider the whole system as a "black box", regardless of its internal structure. Therefore, a method to identify inefficiency is necessary and some suggestions for optimization are given. In this paper,a two-stage undesirable fixed-sum output data envelopment analysis(DEA) model is proposed. The industrial chemical oxygen demand(COD) emission during 2011–2015 are adjusted, and the efficiency values are calculated by heuristic search algorithm. The efficiency of 30 provinces and cities is divided into eastern, central and western regions. The model can identify the inefficient stage in industrial system, and find the source of low efficiency in the system. The analysis shows that the efficiency of eastern region is the highest, while the overall efficiency is inclined to the pollutant treatment stage.Finally, the paper puts forward some suggestions for the low efficiency areas, which can save water while ensuring economic benefits, and provide new direction for water pollution reduction and improve the ecological environment.
基金supported by the National Natural Science Foundation of China under Grant Nos.72071192,71671172the Anhui Provincial Quality Engineering Teaching and Research Project under Grant No.2020jyxm2279+2 种基金the Anhui University and Enterprise Cooperation Practice Education Base Project under Grant No.2019sjjd02Teaching and Research Project of USTC(2019xjyxm019,2020ycjg08)the Fundamental Research Funds for the Central Universities(WK2040000027)。
文摘With the development of China’s economy,environmental pollution has become cumulatively serious.The primary source of environmental pollution is thermal power generation,which has attracted the attention of governments and academia in recent years.To effectively reduce environmental pollution,research should study how to constrain the undesirable output of thermal power plants,that is,to limit the total undesirable output of the plants to a certain fixed sum.However,few studies have suggested that these undesirable outputs should be fixed-sum outputs.Moreover,no previous research publication about thermal power plants has analyzed their environmental performance changes.To address these gaps,a novel Malmquist-DEA approach is proposed for evaluate the environmental performance of thermal power plants in this paper.This approach generalizes the equilibrium efficient frontier DEA model with fixed-sum undesirable outputs and incorporates the model into the Malmquist productivity index(MPI).The authors apply this approach to the analysis of provincial thermal power plant environmental performance in China and analyze such plants’trends based on panel data from2011 to 2014.The empirical research shows that the environmental performance of regional thermal power plants was positively affected by efficiency change and negatively affected by technical change.Finally,the authors provide policy suggestions based on our findings.
