Differential game analysis of joint emission reduction decisions under mixed carbon policies and CEA.

To understand joint emission reduction (JER) of upstream and downstream firms under a low-carbon operational environment, this study incorporates green technology, remanufacturing, low-carbon promotion, consumer environmental awareness (CEA), and mixed carbon policies (carbon tax + cap-and-trade) into a dynamic framework to investigate JER decisions of the upstream manufacturer and the downstream retailer. Applying the differential game theory, we consider low-carbon goodwill as the state variable and explore members' optimal decisions in four cases, namely, idealized case, noncooperative case, unilateral cost-sharing contract (UCSC) case, and bilateral cost-sharing contract (BCSC) case. Our results show that the noncooperative case leads to a loss of efficiency in joint emission reduction. Although the BCSC is more advantageous than the UCSC in improving the efficiency of JER, a profit redistribution mechanism needs to be included, and the profit distribution ratio should be controlled within a certain interval. Only in this situation do both parties prefer the BCSC. Additionally, the impact of mixed carbon policies and CEA on JER decisions, low-carbon goodwill, profits, and coordination are fully discussed, and it is found that in the face of stricter mixed carbon policies, the downstream retailer plays a moderating role only in cooperative cases. Several practical implications are concluded for JER, contract design, CEA, and carbon policies. Governments and firms can benefit from our research by gaining a deeper understanding of JER.

Dynamic pollution management strategies and coordination in aquatic product supply chain under eco-compensation: Perspective of extreme weather crisis.

The ecological compensation mechanism emerges as a solution to reduce pollution for aquatic product supply chain. To comprehend the dynamic pollution management strategies and coordination under the ecological compensation mechanism, this study develops a stochastic differential game between farmers and firms from the perspective of extreme weather crisis. The subjects' optimal decisions are explored in three cases including cooperative case, noncooperative case, and land transfer-cost sharing contract case. Then we simulate theoretical results and illustrate a case study to demonstrate the applicability of ecological compensation collaboration. The results indicate that the extreme weather crisis changes the evolutionary trend and steady state of pollution accumulation. Moreover, the land transfer-cost sharing contract could realize the Pareto improvement in high-risk environment especially after the crisis. But its coordination relies on the ecological compensation coefficient, which gets larger with the interval of [4.9,6.3] after the crisis, compared to the range of [4,5.4] before the crisis. Notably, the contract and ecological compensation mechanism exhibit a complementary relationship in response to the crisis. The findings could provide new inspirations for aquatic product supply chain to balance production and environmental protection.

Sustainable Optimal Control for Switched Pollution-Control Problem with Random Duration.

Considering the uncertainty of game duration and periodic seasonal fluctuation, an n-player switched pollution-control differential game is modeled to investigate a sustainable and adaptive strategy for players. Based on the randomness of game duration, two scenarios are considered in this study. In the first case, the game duration is a random variable, Tf, described by the shifted exponential distribution. In the second case, we assumed that players' equipment is heterogeneous, and the i-th player's equipment failure time, Tfi, is described according to the shifted exponential distribution. The game continues until a player's equipment breaks down. Thus, the game duration is defined as Tf=min{Tf1,…,Tfn}. To achieve the goal of sustainable development, an environmentally sustainable strategy and its corresponding condition are defined. By using Pontryagin's maximum principle, a unique control solution is obtained in the form of a hybrid limit cycle, the state variable converges to a stable hybrid limit cycle, and the total payoff of all players increases and then converges. The results indicate that the environmentally sustainable strategy in the n-player pollution-control cooperative differential game with switches and random duration is a unique strategy that not only ensures profit growth but also considers environmental protection.

Collaborative Innovation Strategy of Supply Chain in the Context of MCU Domestic Substitution : A Differential Game Analysis.

The domestic substitution of the IC (the Integrated Circuit) industry improves economic efficiency and is significant in ensuring national security, which has gradually become an essential strategy for countries worldwide. Based on the background of domestic substitution of integrated circuits, we select a typical component Micro Controller Unit) as the research object, construct a three-level supply chain game model under different scenarios in a dynamic architecture, and analyze the game problem of collaborative innovation of the MCU supply chain. We fully consider the impact of factors such as time, cost and the innovation and collaborative innovation efforts of various supply chain members on the level of domestic substitution. Moreover, we put forward a two-part pricing + cost-sharing contract to achieve supply chain coordination. We found that: (1) Collaborative innovation of the supply chain in the centralized decision-making scenario achieves the highest level, followed by the cost-sharing scenario; (2) The two-part pricing + cost-sharing contract can help achieve supply chain coordination; (3) The trend of the MCU domestic substitution level with manufacturing cost is U-shaped, which means the increase of manufacturing cost may have a positive impact on the process of domestic substitution.

A Nonlinear Finite-Time Robust Differential Game Guidance Law.

In this paper, a robust differential game guidance law is proposed for the nonlinear zero-sum system with unknown dynamics and external disturbances. First, the continuous-time nonlinear zero-sum differential game problem is transformed into solving the nonlinear Hamilton-Jacobi-Isaacs equation, a time-varying cost function is developed to reflect the fixed terminal time, and the robust guidance law is developed to compensate for the external disturbance. Then, a novel neural network identifier is designed to approximate the unknown nonlinear dynamics with online weight tuning. Subsequently, an online critic neural network approximator is presented to estimate the cost function, and time-varying activation functions are considered to deal with the fixed final time problem. An adaptive weight tuning law is given, where two additional terms are added to ensure the stability of the closed-loop nonlinear system and so as to meet the terminal cost at a fixed final time. Furthermore, the uniform ultimate boundedness of the closed-loop system and the critic neural network weights estimation error are proven based upon the Lyapunov approach. Finally, some simulation results are presented to demonstrate the effectiveness of the proposed robust differential game guidance law for nonlinear interception.

Cost-benefit allocation of collaborative carbon emissions reduction considering fairness concerns-A case study of the Yangtze River Delta, China.

As the country with the highest carbon emissions, the main focus of China has become carbon reduction. At present, the governance of carbon reduction is mainly based on the division of administrative regions, which leads to the governance inefficiency and high costs because of spatial spillover and regional mobility of carbon emissions. The need for collaborative governance to promote carbon reduction performance has been recognized. However, because of differences in both costs and benefits between developed and less developed regions, a clear cost and benefit allocation mechanism must be established first. Fairness is very important when all members are to actively participate in collaborative carbon emission reduction efforts. In this paper, one of the regions renowned for collaborative governance-the Yangtze River Delta region-is used as example, and a cost-benefit allocation mechanism is constructed that incorporates members' fairness concerns. The carbon emission efficiency, carbon reduction efforts, and total carbon emission amount are compared under two scenarios: a cost-sharing scenario and a centralized decision-making scenario. The results indicate that, compared with the centralized decision-making scenario, the cost-sharing scenario achieved greater regional carbon reduction efforts, a higher carbon emission efficiency, and more total emissions. Furthermore, under the cost-sharing scenario, in less developed regions, fairness concerns increase carbon emission efficiency and total carbon emissions. The fairness concern in developed regions reduces the profit proportion, while the fairness concern in less developed region increases the profit proportion. The impact of fairness concern on carbon reduction is stronger in developed regions.

Decision analysis of international joint prevention and control of public health emergencies.

COVID-19 has caused huge losses to countries around the world, and it will not end in a short time. The lack of motivation for international joint prevention and control is one of the important reasons for the global pandemic of COVID-19. How to improve the efforts and level of international joint prevention and control has become an urgent problem to be solved. Considering the long-term and dynamic nature of international joint prevention and control, the differential game method is used to compare and analyze the optimal decisions of countries in the three scenarios of spontaneous governance, external subsidies and internal cost sharing. The results show that the optimal prevention and control efforts of countries are negatively correlated with discount rates, prevention and control cost coefficients, decay rate and risk factors. It is positively correlated with the impact degree of social benefits, the impact degree of prevention and control efforts on the level of joint prevention and control, the distribution ratio of social benefits, and the impact degree of prevention and control level on social benefits. The prevention and control efforts, joint prevention and control level, social benefits and system benefits under spontaneous governance are the lowest and highest under the internal cost sharing. The internal cost sharing will only be carried out when social benefits distribution ratio obtained reach a certain threshold. This study provides decision-making support for the joint prevention and control of countries to defeat COVID-19 under the normalization of the epidemic.

Prevention schemes for future pandemic cases: mathematical model and experience of interurban multi-agent COVID-19 epidemic prevention.

To enhance the effectiveness of epidemic prevention (EP) in urban sustainability transformation, joint prevention and control mechanism should be established to prevent and control the COVID-19 epidemic. The interurban multi-agent EP strategy, as a key component of this mechanism, includes the spontaneous EP model, the superior leading EP model, and the collaborative EP model. In this study, firstly, the theoretical mechanism of the interurban multi-agent EP strategy was analyzed. Then, we proposed a three-party differential game model including factors such as the risk coefficient for the virus infection and EP experience teaching. Finally, prevention strategies, prevention efficiency, and prevention losses were compared under the three models based on theoretical analysis and numerical analysis. The results of this study are as follows. COVID-19 EP should be guided by a model of central government (CG) leadership, interurban collaboration, and social participation. The CG and urban governments (UGs) should comprehensively carry out COVID-19 EP from various aspects, including EP experience teaching, mass EP comfort, the utilization rate of EP funds, and the ability to implement strategies. During the course of the COVID-19 EP, when the CG and UGs transition from spontaneous EP model to a higher-level EP model, the UG's EP efforts will be enhanced. Under the collaborative EP model, the CG and UGs undergo the highest levels of EP effort. Compared with spontaneous EP model, the superior leading EP model can promote a Pareto improvement for all parties. From the perspective of total loss, the collaborative EP model is superior to the other two EP models. This study not only provides practical guidance for coordinating interurban relationships and enabling multi-agents to fully form joint forces, but also provides theoretical support for the establishment of an interurban joint EP mechanism under unified leadership.

Optimal Inter-Organization Control of Collaborative Advertising with Myopic and Far-Sighted Behaviors.

This paper investigates the optimal inter-organization control of collaborative advertising considering the myopic and far-sighted behaviors. Taking a two-echelon supply chain as an example, four kinds of differential game models including myopic Stackelberg game, far-sighted Stackelberg game, myopic cooperative game and far-sighted cooperative game are studied. The results show that the optimal advertising efforts of both manufacturer and retailer in the myopic situation decrease with time. But they remain constant in the far-sighted situation. The Pareto improvement applies to both game players from the non-cooperative game to the cooperative game. The numerical analyses are conducted to further investigate the theoretical results and to guide the inter-organization control of collaborative advertising in practice.

Readmission treatment price and product quality in the hospital sector.

In this paper, we study the effect of readmission treatment payment in a dynamic framework characterised by competition among hospitals and sluggish beliefs of patients concerning the service quality. We find that the effect of readmission treatment payment depends on the interplay between the effect of quality in lowering readmissions and its effect on future demand. When the readmission occurrence strongly depends on the service quality, the higher the readmission treatment payment for hospitals, the lower the incentive to provide quality. Instead, when readmission depends barely on quality, the readmission payment acts as the treatment price for first admissions, and thus it reinforces the incentive to provide quality. We also show that the detrimental effect of readmission payments on quality are fed by a high degree of demand sluggishness, that is, by situation where current quality has modest effect on future demand changes. Our findings are robust to different equilibrium concepts of the differential game (i.e., open-loop and state-feedback). The results suggest that a discounted regulated price for readmission can be an effective (and cost-free) policy tool to improve health care quality, especially when the market is characterised by sluggish beliefs about quality.

A Pre-Trained Fuzzy Reinforcement Learning Method for the Pursuing Satellite in a One-to-One Game in Space.

In order to help the pursuer find its advantaged control policy in a one-to-one game in space, this paper proposes an innovative pre-trained fuzzy reinforcement learning algorithm, which is conducted in the x, y, and z channels separately. Compared with the previous algorithms applied in ground games, this is the first time reinforcement learning has been introduced to help the pursuer in space optimize its control policy. The known part of the environment is utilized to help the pursuer pre-train its consequent set before learning. An actor-critic framework is built in each moving channel of the pursuer. The consequent set of the pursuer is updated through the gradient descent method in fuzzy inference systems. The numerical experimental results validate the effectiveness of the proposed algorithm in improving the game ability of the pursuer.

Resource Allocation in Cognitive Radio Wireless Sensor Networks with Energy Harvesting.

The progress of science and technology and the expansion of the Internet of Things make the information transmission between communication infrastructure and wireless sensors become more and more convenient. For the power-limited wireless sensors, the life time can be extended through the energy-harvesting technique. Additionally, wireless sensors can use the unauthored spectrum resource to complete certain information transmission tasks based on cognitive radio. Harvesting enough energy from the environments, the wireless sensors, works as the second users (SUs) can lease spectrum resource from the primary user (PU) to finish their task and bring additional transmission cost to themselves. To minimize the overall cost of SUs and to maximize the spectrum profit of the PU during the information transmission period, we formulated a differential game model to solve the resource allocation problem in the cognitive radio wireless sensor networks with energy harvesting, considering the SUs as the game players. By solving the proposed resource allocation game model, we found the open loop Nash equilibrium solutions and feedback Nash equilibrium solutions for all SUs as the optimal control strategies. Ultimately, series numerical simulation experiments have been made to demonstrate the rationality and effectiveness of the game model.

Optimal Power Control in Wireless Powered Sensor Networks: A Dynamic Game-Based Approach.

In wireless powered sensor networks (WPSN), it is essential to research uplink transmit power control in order to achieve throughput performance balancing and energy scheduling. Each sensor should have an optimal transmit power level for revenue maximization. In this paper, we discuss a dynamic game-based algorithm for optimal power control in WPSN. The main idea is to use the non-cooperative differential game to control the uplink transmit power of wireless sensors in WPSN, to extend their working hours and to meet QoS (Quality of Services) requirements. Subsequently, the Nash equilibrium solutions are obtained through Bellman dynamic programming. At the same time, an uplink power control algorithm is proposed in a distributed manner. Through numerical simulations, we demonstrate that our algorithm can obtain optimal power control and reach convergence for an infinite horizon.

Decision model for binary safety management behavior in a supply chain under digital scenarios: A study based on differential game theory.

The purpose of this study is to expand and deepen research in the field of safety production, explore the role of enterprises as decision-making entities in safety production, analyze the role of different types of decision-making behaviors in the process of enterprise safety production, and provide certain theoretical guidance for multi-agent decision-making in safety production. By summarizing and comparing the existing dual system of supply chain safety management, this study proposes dividing supply chain safety management into the two categories of safety organization and safety research and development (safety R&D) in the context of digitalization. Differential equations are established to describe a two-level supply chain safety management problem including manufacturers and suppliers. The research results show that, compared with the Nash equilibrium, when there are strong manufacturers involved in safety management cooperation, the manufacturer's safety R&D subsidy to suppliers improves the total revenue of the supply chain. When the manufacturer's safety organization supervision efficiency is high, the Stackelberg equilibrium is lower. It is a Pareto improvement for the manufacturer to supervise the supplier's safety organization to the Nash equilibrium. In the case of dual safety cooperation in the supply chain, when there are strong manufacturers, R&D subsidies have a crowding out effect on the safety organization cooperation. Finally, based on the example analysis, relevant suggestions are put forward for supply chain safety management.

Dynamic strategy for low-carbon supply chain considering retailers competition and technological innovation.

This paper discusses how managers adjust their strategies to allocate relevant resources more effectively and maximize economic benefits when major technological changes are predicted for the future. For a supply chain system consisting of a single manufacturer and two competing retailers as the research object. First, random stop model is applied to portray the impact of technological innovation on the decision-making of supply chain members. On this basis, differential game models for supply chain members are constructed based on different cooperation modes, including centralized, decentralized, and retailers alliance. Second, we solve and compare the optimal decision-making, emissions reduction, low-carbon goodwill, and profit levels before and after technological innovation in different modes. Finally, we design a bilateral cost-sharing contract to achieve coordination. Results demonstrate that: (1) Before the success of technological innovation, when a higher probability of success and uplift rate is predicted can incentivize supply chain members' emissions reduction and low-carbon promotion inputs; (2) In the presuccess period of technological innovation, members' independent decision-making (decentralized decision-making) can optimize the retailer's low-carbon promotional inputs under certain conditions. In contrast, the optimality of decentralized decision-making after technological innovation depends only on the influence of competition intensity. (3) The bilateral cost-sharing contract designed in this paper can optimize supply chain-related inputs and performance levels to achieve perfect coordination within the supply chain system, given that specific preconditions are satisfied.

Neural network optimal control for tripartite UAV confrontation systems based on fuzzy differential game.

The neural network optimal control strategy based on a fuzzy differential game is proposed for the tripartite UAV confrontation systems consisting of the attackers, defenders, and targets. Firstly, the tripartite UAV mutual confrontation model is constructed and a nonlinear differential control system is established. Secondly, combining the fuzzy evaluation method and differential game theory, the tripartite UAV are divided into two parts of the confrontation game: attackers-defenders and attackers-targets. The optimal control strategies for the attackers, defenders and targets parties are derived separately. Then, the tripartite UAV game model is considered to be difficult to solve directly. The evaluation neural network is introduced to approximate the optimal value function using an adaptive dynamic programming method. The convergence of the evaluation neural network weights and the stability of the nonlinear differential control system are proved by using Lyapunov stability theory. Finally, the effectiveness of the tripartite UAV confrontation game control strategy designed in this paper is verified by simulation.

Analyzing the influence of government policy on building carbon emission reduction based on differential game.

With the continuous growth of low-carbon economy and people's increasing preference for low-carbon products, the building carbon emission reduction (CER) has been highly concerned by the government. Therefore, in this study, we establish a game model through differential game to analyze the impact of government policies on building's CER. We get: (1) Compared with the carbon tax policy, the government policy combining carbon tax and cost subsidy is more conducive to reducing carbon emissions; (2) For the three government policies, when the cost subsidy rate is lower than a fixed value, the government policy combining carbon tax and cost subsidy is the optimal strategy for building's CER. When the cost subsidy rate is greater than a fixed value, the cost subsidy policy is the best strategy for building's CER.

Reducing carbon emissions in prefabricated buildings supply chains: a focus on component manufacturing processes.

The construction sector accounts for 23% of CO 2 emissions from global economic activity, with China responsible for nearly 41%. Although China has vigorously promoted the development of prefabricated buildings (PBS) in pursuit of cleaner production, the carbon emissions from prefabricated component factories (PCF) should not be underestimated. So, the focus of this research was on how to promote the decarbonization of PCF. Based on the carbon trading market mechanism, the carbon emissions trading tax and revenue tax collection, the authors established a differential game model consisting of the local government and the PCF, studied the equilibrium solutions under different decision models, and analyzed the roles of the two tax systems, carbon trading revenue, and market preferences. The results are as follows: (1) The PCF's low-carbon technology (LCT) innovation efforts can be directly affected by the carbon price, component price, and tax rate and indirectly affected by influencing the local government's efforts. Besides, the local government and the PCF strategies can be changed through the central government's regulation of carbon prices and tax rates. (2) PCF should set reasonable prices for components, improving economic efficiency and the LCT stocks. (3) Cost-sharing contracts can encourage PCF to increase their LCT innovation, which is conducive to increasing the optimal benefits of the PCF. (4) The local government cannot be motivated by cost-sharing contracts. They can increase their optimal benefits only if the cost-sharing coefficient is below a threshold or if the environmental benefits from low-carbon production are above a specific value.

Attitude control of a 3-DoF quadrotor platform using a linear quadratic integral differential game approach.

In this study, a linear quadratic integral differential game approach is applied to regulate and track the Euler angles for a quadrotor experimental platform using two players. One produces commands for each channel of the quadrotor and another generates the worst disturbance based on the mini-maximization of a quadratic criterion with integral action. For this purpose, first, the attitude dynamics of the platform are modeled and its parameters are identified based on the Nonlinear Least Squares Trust-Region Reflective method. The performance of the proposed controller is evaluated for regulation and tracking problems. The ability of the controller is also examined in the disturbance rejection. Moreover, the influence of uncertainty modeling is studied on the obtained results. Then, the performance of the proposed controller is compared with the classic Proportional Integral Derivative, Linear Quadratic Regulator, and Linear Quadratic Integral Regulator. The results demonstrate the effectiveness of the Game Theory on the Linear Quadratic Regulator approach when the input disturbance occurs.

A novel hybrid LFC scheme for multi-area interconnected power systems considering coupling attenuation.

In this paper, a hybrid load frequency control (LFC) scheme is proposed for multi-area interconnected power systems to decouple the intricate double control objectives, by dividing all subareas into the responsible areas and the free areas. The LFC in the responsible area has the function of regulating both the local frequency and the tie-line power, while the control objective of the LFC in the free area is thus simplified to regulate the local frequency only. Then, addressing the complex network coupling and uncertain dynamics, an integrated LFC controller is proposed for the free areas, which consists of two parts, namely, the coupling attenuation baseline controller and the disturbance compensation controller. The coupling attenuation baseline controller satisfying the predefined bounded L2-Gain condition is derived based on the solution to a multi-player zero-sum differential game. Additionally, a novel generalized integral observer is designed to estimate the system's integrated disturbance, and the corresponding disturbance compensation controller is derived. After that, the ultimately uniformly bounded (UUB) stability of the integrated LFC controller combining baseline controller and disturbance compensation controller is proven rigorously. Finally, the performance superiority of the proposed hybrid LFC scheme is validated by the simulations in challenging operating modes.