scholarly journals Some Results on the Control of Polluting Firms According to Dynamic Nash and Stackelberg Patterns

Economies ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 77
Author(s):  
George E. Halkos ◽  
George J. Papageorgiou
Keyword(s):  
Differential Games ◽  
Stackelberg Game ◽  
Pollution Abatement ◽  
Control Policy ◽  
Open Loop ◽  
Social Planner ◽  
Nash Game ◽  
State Variable ◽  
Polluting Firms ◽  
Analytical Expressions

In this paper we model the conflict between the group of polluting firms in a country and any social planner in the same country who attempts to control the volume of emissions generated during the production process. Both players of the game have their own control policies, i.e., the rate of emissions on behalf of the polluting firms and the rate of pollution control (e.g., pollution abatement or environmental taxation) on behalf of the home country. The common state variable of the model is the number of polluting firms, which aims to be minimized via the country’s control policy, but on the polluters’ side it is beneficial to be maximized. Regarding the game model, its setup belongs to the special class of differential games, which are called ‘state separable differential games’. An important property of these games is that the open-loop Nash equilibrium coincides with the Markovian (closed-loop) equilibrium and, in the case of hierarchical moves, analytical solutions are easily obtained. The game proposed here is analyzed for both types of equilibrium, i.e., Nash and Stackelberg. In the simultaneous move game (i.e., the Nash game) we find the equilibrium’s analytical expressions of the controls for both players, as well as the stationary value of the stock of polluting firms. A sensitivity analysis of the model’s crucial variables takes place. In the hierarchical move game (i.e., the Stackelberg game) we find the equilibrium values of the controls, as well as of the state variable. As a result, a comparison between the two types of equilibrium for the game takes place. The analysis of the comparison reveals that the conflict is more intensive (since both controls have greater values) for the case in which the polluting firms act as the leader in the hierarchical move game.

scholarly journals The role of nonzero conjectural variation in pollution abatement and output in the design of emission taxes

2021 ◽  
pp. 1-24
Author(s):  
Luis Gautier
Keyword(s):  
Pollution Abatement ◽  
Emission Taxes ◽  
International Context ◽  
Cooperative Equilibrium ◽  
Emissions Taxes ◽  
Conjectural Variations ◽  
Polluting Firms ◽  
Global Emissions

Abstract The presence of nonzero conjectural variations in pollution abatement and output make emission taxes less effective with respect to reducing emissions. This has implications for the characterization of the optimal emission tax, particularly in an international context where there are large asymmetries in pollution intensities. A higher degree of collusion in output between polluting firms results in higher emissions taxes in the non-cooperative equilibrium. In contrast, a higher degree of collusion in abatement between polluting firms results in lower emissions taxes in the non-cooperative equilibrium. These results rely on the presence of nonzero conjectural variations and large asymmetries in pollution intensities across countries. The analysis is relevant to the design of international environmental policy, including cases where countries face increasing global competition and damages from rising global emissions.

scholarly journals Demand Subsidy versus Production Regulation: Development of New Energy Vehicles in a Competitive Environment

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1280
Author(s):  
Zixuan Wang ◽  
Xiuzhang Li
Keyword(s):  
Social Welfare ◽  
Stackelberg Game ◽  
Positive Impact ◽  
Consumer Preference ◽  
Social Planner ◽  
Environmental Preferences ◽  
The Social ◽  
New Energy ◽  
Vehicle Market ◽  
New Energy Vehicles

In the competitive market environment, the growth of new energy vehicles (NEVs) faces many obstacles. Demand subsidy or production regulation-related policies are widely used to promote the development of NEVs. A comparative analysis of the effects of the two types of policies on the competitive vehicle market requires further study. To fill this gap, we investigate which type of policy is more preferable from the perspective of the social planner. In this paper, we construct a Stackelberg game with a welfare-maximizing social planner and two profit-maximizing manufacturers producing NEVs and fuel vehicles (FVs), respectively. Interestingly, although both types of policies can increase the quantity of NEVs, demand subsidy also promotes the growth of total vehicles at the same time; in contrast, production regulation reduces the total vehicles. Moreover, compared with the benchmark that no policy intervention, demand subsidy generally improves social welfare, while production regulation improves social welfare only with high consumer preference for NEVs. Nevertheless, production regulation always has a positive impact on the environment, whereas demand subsidy may have a positive impact only when the NEV is very environment friendly. The numerical results show that consumer environmental preferences and the regulation of environmental impact determine which type of policy dominates the other.

scholarly journals A stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises under uncertain environment

2018 ◽  
Vol 16 (1) ◽  
pp. 607-622 ◽  
Author(s):  
Shi Yin ◽  
Baizhou Li
Keyword(s):  
Differential Game ◽  
Cooperative Game ◽  
Stackelberg Game ◽  
Innovation System ◽  
Stochastic Differential Game ◽  
Low Carbon ◽  
Nash Game ◽  
Low Carbon Economy ◽  
Collaborative Innovation ◽  
Technology Level

AbstractConsidering the fact that the development of low carbon economy calls for the low carbon technology sharing between interested enterprises, this paper study a stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises. In the paper, we consider the random interference factors that include the uncertain external environment and the internal understanding limitations of decision maker. In the model, superior enterprises and inferior enterprises are separated entities, and they play Stacklberg master-slave game, Nash non-cooperative game, and cooperative game, respectively. We discuss the feedback equilibrium strategies of superior enterprises and inferior enterprises, and it is found that some random interference factors in sharing system can make the variance of improvement degree of low carbon technology level in the cooperation game higher than the variance in the Stackelberg game, and the result of Stackelberg game is similar to the result of Nash game. Additionally, a government subsidy incentive and a special subsidy that inferior enterprises give to superior enterprises are proposed.

scholarly journals Managing a 5G mobile phone supply chain under the impact of strategic consumers: A two-period game analysis and applications

2021 ◽  
Author(s):  
Qin Zhang ◽  
Zijian He ◽  
Junhai Ma
Keyword(s):  
Supply Chain ◽  
Mobile Phone ◽  
Stackelberg Game ◽  
Great Influence ◽  
Purchasing Behavior ◽  
Optimal Price ◽  
Nash Game ◽  
Strategic Consumers ◽  
Game Analysis ◽  
The Impact

Consumers' strategic purchasing behavior has a great influence on the pricing and sales of new products. In order to study the impact of strategic consumers on the sales of 5G mobile phones, we establish a two-period pricing model. The supply chain contains two manufacturers, a communications operator and a mobile phone retailer. Cases where two manufacturers have the same or different pricing rights are researched by using the Stackelberg game and the Nash game model. Our research results are as follows:(1) We obtain the optimal 5G communication fees in two periods and find out how they change with the proportion of consumers changing. (2) We figure out the profits of the supply chain in two periods and analyze them. We find that the communication operator earns more than the others most of the time. (3) We investigate how the proportion of strategic consumer impact on supply chain profits and conclude that the optimal price and demand in a period will decrease as the proportion of consumers who only purchase products in the other period increases.

One-Player Differential Games

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Dynamical System ◽  
Differential Games ◽  
Continuous Time ◽  
Information Structure ◽  
Dynamic Games ◽  
State Feedback ◽  
Open Loop ◽  
Linear Quadratic ◽  
Time Dynamic ◽  
Termination Time

This chapter focuses on one-player continuous time dynamic games, that is, the optimal control of a continuous time dynamical system. It begins by considering a one-player continuous time differential game in which the (only) player wants to minimize either using an open-loop policy or a state-feedback policy. It then discusses continuous time cost-to-go, with the following conclusion: regardless of the information structure considered (open loop, state feedback, or other), it is not possible to obtain a cost lower than cost-to-go. It also explores continuous time dynamic programming, linear quadratic dynamic games, and differential games with variable termination time before concluding with a practice exercise and the corresponding solution.

scholarly journals Linear-Quadratic Stackelberg Game for Mean-Field Backward Stochastic Differential System and Application

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Kai Du ◽  
Zhen Wu
Keyword(s):  
Optimal Control ◽  
Differential System ◽  
Optimization Problems ◽  
Stackelberg Game ◽  
Mean Field ◽  
Open Loop ◽  
Stackelberg Equilibrium ◽  
Linear Quadratic ◽  
Stackelberg Differential Game ◽  
Lq Optimal Control

This paper is concerned with a new kind of Stackelberg differential game of mean-field backward stochastic differential equations (MF-BSDEs). By means of four Riccati equations (REs), the follower first solves a backward mean-field stochastic LQ optimal control problem and gets the corresponding open-loop optimal control with the feedback representation. Then the leader turns to solve an optimization problem for a 1×2 mean-field forward-backward stochastic differential system. In virtue of some high-dimensional and complicated REs, we obtain the open-loop Stackelberg equilibrium, and it admits a state feedback representation. Finally, as applications, a class of stochastic pension fund optimization problems which can be viewed as a special case of our formulation is studied and the open-loop Stackelberg strategy is obtained.

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