Differential Game Method Research Articles

Study on Watershed Ecological Compensation for Water Pollution Considering Population Flow: A Case Study in the Lower Yellow River Basin

Watershed ecological compensation (WEC) mechanisms can help coordinate the distribution of revenue among different regions and realize the collaborative treatment of water pollution. However, limited research has examined the influence of population flow on the design of ecological compensation mechanisms. In this paper, the differential game method is used to construct a model of water pollution control in upstream and downstream regions with the consideration of population flow. The Lower Yellow River Basin (LYRB), which includes Henan and Shandong Provinces, is taken as a case study, and relevant data are used for simulation analysis. The constraints and population flow factors that influence the establishment of a WEC mechanism between upstream and downstream governments are explored. The results show that (1) the implementation of WEC can stimulate the upstream government’s efforts to treat pollutants, and the amount of pollutants eliminated and the revenue of the upstream and downstream governments increase; (2) with the continuous flow of population from the upstream region to the downstream region, the amount of pollutants eliminated and the revenue of the downstream government decrease; and (3) in the absence of external incentive measures, when the population flow exceeds a certain threshold, the WEC mechanism of the upstream and downstream governments cannot be spontaneously carried out. The conclusions of this study can provide scientific guidance for improving the WEC mechanism between the upstream and downstream governments within a basin.

Research on innovation decisions in industry-university-research cooperation based on differential games

ABSTRACT The lack of innovation power in industry-university-research (IUR) cooperation is one of the important reasons leading to low independent innovation ability in China. Considering the long-term and dynamic nature of IUR innovation effort, the differential game method is used to compare and analyse the optimal decision under four scenarios: independent R&D by enterprises and university-research institutes, tax incentives for enterprises by the government, tax incentives and subsidies by the government, and a Stackelberg game considering the internal cost subsidy of enterprises. The results show that government tax incentives can improve the enthusiasm of enterprises for cooperative innovation, while government subsidies can simultaneously improve the enthusiasm of IUR institutes for cooperative innovation and can enhance the overall benefits of both parties and even the system. When certain conditions are met based on the government’s tax incentive and subsidy policies, the innovation effort, cooperative innovation level and benefits in the Stackelberg game are optimal, and Pareto improvement can be achieved. The optimal benefits of enterprises and university-research institutes, the total benefits of the system, and the optimal trajectory of the cooperative innovation level tend to be stable over time in the four game scenarios.

Cooperative Decisions of a Multi-Agent System for the Target-Pursuit Problem in Manned–Unmanned Environment

With the development of intelligent technology, multi-agent systems have been widely applied in military and civilian fields. Compared to a single platform, multi-agent systems can complete more dangerous, difficult, and heavy tasks. However, due to the limited autonomy of unmanned platforms and the regulatory needs of personnel, multi-agent systems cooperating with manned platforms to perform tasks have been more widely promoted at this stage of development. This paper addresses a differential game method for cooperative decision-making of a multi-agent system cooperating with the manned platform for the target-pursuit problem. The manned platform pursues the target according to a certain trajectory, and its state can be obtained by the multi-agent system. Firstly, for the case that the target moves with a fixed trajectory, the target-pursuit problem in a manned–unmanned environment is viewed in the form of game based on a communication graph among agents. Secondly, strategies of all agents are proposed while maintaining their group cohesion. A set of coupled differential equations is solved to implement strategy calculation. Compared to purely unmanned systems, the strategies combine the advantages of the manned platform and add a reference item, which can achieve team cohesion relatively quickly. Furthermore, a brief analysis is made on the scenarios where the target is in another case or adopts other strategies. Finally, comparative simulations have verified the effectiveness and synergy of the strategy.

Equipment classification based differential game method for advanced persistent threats in Industrial Internet of Things

This paper is dedicated to solving the problem of Advanced Persistent Threat (APT) attack and defense in the Industrial Internet of Things (IIoT). Due to the diversity of IIoT equipment and the inconsistency of protection capabilities, it is difficult for the existing uniform defense strategy and the random defense strategy to achieve ideal results. Considering that both attackers and defenders aim to achieve maximum benefits by paying the minimum cost, as well as the differences between devices, this paper proposes an equipment classification based differential game method for APT in IIoT. Firstly, all equipment is divided into two categories according to their protective capabilities. Secondly, the APT attack and defense process is mathematically described, and the corresponding differential game problem is formulated and analyzed theoretically. Finally, the theoretical results of this method are verified by various experiments, including the comparisons with the uniform defense strategy, the random defense strategy, and the latest model.

Fault-tolerant control for second-order nonlinear systems with actuator faults via zero-sum differential game

Stable operations of control systems play a vital role in mission accomplishments of the second-order nonlinear systems, such as six-axis robots used in intelligent production lines, industrial equipment and control systems. In this paper, a fault-tolerant control scheme is developed for a class of second-order nonlinear control system under actuator bias faults and loss of effectiveness faults via the zero-sum differential game method. Based on the backstepping method, a controller is designed to ensure system tracking performance. Then by the zero-sum differential game method, a fault-tolerant controller is designed for the equivalent error system. Simulation results show the validity of the designed fault-tolerant control scheme.

Modeling forest carbon sink trading with carbon credit using stochastic differential game

Forest carbon sinks integrated into the carbon trading is an important way to solve the funding shortage of carbon emission reduction and is a major measure to achieve carbon sequestration and thereby carbon neutrality. We propose a carbon credit trading mechanism based on forest carbon sinks and build an optimal carbon credit trading model on forest companies and manufacturers. The scale of carbon sink forest and trading price is determined by stochastic differential game method. Reasonable emission reduction responsibilities are set to achieve coordination between forest carbon sequestration and economic development. The results show that farsighted forest company is more likely to participate in carbon credit trade when the total amount of forest carbon sequestration is small, while shortsighted forest company is more likely to participate in carbon credit trade when the total amount of forest carbon sequestration is large. Low emission reduction responsibility in carbon credit trade is conductive to increasing forest carbon sequestration, and improving the enthusiasm of shortsighted forest company to participate in the trade, which reflects the superiority of the proposed carbon credit trading mechanism. This implies that the forest company should undertake low emission reduction responsibilities to achieve a win-win situation for economic and environmental benefits.

Analysis of Multi-Robot Cooperative Hunting Using Differential Game Technique

This research presents two robots cooperative hunting behavior by the use of a differential game method. There are two pursuer robots that are trying to find and then surround another robot prey evader. The purpose of the game is for the two pursuer robots to find the evader simultaneously or when one of the robots finds the evader first it will wait for the other robot to cooperate with it within a specified period of time. We use differential game theory to formulate the problem with a system of an ordinary differential equation. The conditions for the termination of the game were given to be when one of the pursuers catch the evader and the other cooperate with it or when the two pursuers catch it simultaneously.We carefully analyzed all the mathematical equations developed using the ordinary differential equations for the game and present the sufficient conditions that can warrant the two pursuers to catch the evader either simultaneously or one first and then the other cooperates with the first one which will result in termination of the game. We also show mathematically that in the course of the game the robot prey evader tries to prolong the capture time, while the pursuer robots try to shorten the capture time

Finding an optimal selection in diversify combating modes for desertification region

The differential game method effectively reflects the multi-agent, long-term, and dynamic characteristics of combating regional desertification. Considering the differences in the levels of economic development level and governance technology between adjacent areas, three desertification-combating modes are proposed for exploratory purposes. The differential game models of the two regions combating desertification areas are constructed as per the certain level of cooperation, ecological subsidy, and technology transfer modes. The optimal combating mode is found by comparing the equilibrium results. The study demonstrates that when cooperation level dominated by the region with higher economic and governance technology levels is lower than the threshold $ \phi^{*}_{u_2} $ and $ \phi^{*}_{1V} $, the technology transfer mode is optimal, and the level of cooperation does not affect the technology transfer fee. However, when cooperation level is higher than the threshold $ \phi^{*}_{u_2} $ and $ \phi^{*}_{1V} $, the ecological subsidy mode is optimal. Meanwhile, as the dominant region further raises the cooperation level, it can drive the non-dominant region to increase the desertification combating input level. The certain level of cooperation mode is the least efficient of the three modes. However, when compared with the situation of completely independent governance by the two regions, the certain level of cooperation mode can relatively improve the efficiency of regional desertification combating.

Collaborative governance of haze pollution between local governments

Facing the increasingly prominent regional and complex air pollution, the division of labor and cooperation is considered to be a necessary means of haze pollution control. During the collaborative governance of haze pollution, there is a game relationship between local governments in the regional alliance. The governments make choices while playing games and cooperating with each other, based on their own benefits. When the local governments in the regional alliance break the administrative boundaries and cooperate together, what kind of mechanism should be established so that all local governments in the entire regional alliance can actively cooperate is the key to the problem. This paper adopts the differential game method to study the mechanism of collaborative governance of regional haze pollution, according to three situations in the haze control within the regional alliance. The results show that the effort of local governments in the region to control haze is negatively correlated with their governance cost; after the introduction of the supervision, assessment, and punishment (SAP) mechanism, the implementation of legally binding constraints on each subject can make local governments more enthusiastic about haze control, and improve the synergistic benefits of haze control. Multiple co-governance, interactive monitoring, and interest compensation are of great significance to improving the coordinated governance of haze pollution among local governments.

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.

Differential Game Model of Shared Manufacturing Supply Chain Considering Low-Carbon Emission Reduction

In the context of sharing manufacturing, a three-echelon low-carbon supply chain has been established, consisting of the leader-shared manufacturing platform, the follower surplus capacity demander, and the surplus capacity provider. Furthermore, the differential game method is used to determine the best equilibrium strategy for the perfect trajectory of product emission reduction and the ideal profit of supply chain participants in three scenarios: decentralized decision-making, centralized decision-making, and decentralized decision-making based on a two-way cost-sharing contract taking into account the long-term and dynamic nature of emission reduction issues. We compare the three scenarios by using analysis and numerical simulation. The findings show that once the contract was implemented, supply chain members’ levels of effort, product emission reduction, and supply chain system profit reached centralized decision-making levels, achieving the dual Pareto improvement of economic and environmental advantages. The conclusions achieved may be used as a theoretical framework for decision-making by players in the low-carbon supply chain, as well as a collaborative approach.

Knowledge Sharing Strategy and Emission Reduction Benefits of Low Carbon Technology Collaborative Innovation in the Green Supply Chain

Knowledge sharing (KS) in the green supply chain (GSC) is jointly determined by the KS efforts of suppliers and manufacturers. This study uses the differential game method to explore the dynamic strategy of KS and the benefits of emission reduction in the process of low carbon (LC) technology in the GSC. The optimal trajectory of the knowledge stock and emission reduction benefits of suppliers and manufacturers under different strategies are obtained. The validity of the model and the results are verified by numerical simulation analysis, and the sensitivity analysis of the main parameters in the case of collaborative sharing is carried out. The results show that in the case of centralized decision-making, the KS efforts of suppliers and manufacturers are the highest, and the knowledge stock and emission reduction benefits of GSC are also the best. The cost-sharing mechanism can realize the Pareto improvement of GSC’s knowledge stock and emission reduction benefits, but the cost-sharing mechanism can only increase the supplier’s KS effort level. In addition, this study found that the price of carbon trading and the rate of knowledge decay have a significant impact on KS. The study provides a theoretical basis for promoting KS in the GSC and LC technology innovation.

Research on Cooperative Innovation Strategy of Multi-Agent Enterprises Considering Knowledge Innovation and Environmental Social Responsibility

Based on the context of enterprise green innovation ecosystem, this paper discusses the decision-making of knowledge innovation and environmental social responsibility in the multi-agent enterprise R&D innovation system that is composed of core enterprises and satellite enterprises, and it provides a new perspective for comprehensively improving enterprise innovation ability. By using differential game method and considering the joint influence of knowledge innovation and environmental social responsibility, this paper analyzes the cooperative innovation of multi-agent enterprises under a dynamic framework and discusses the decision-making process and optimal returns of core enterprises and satellite enterprises under centralized decision, decentralized decision and Stackelberg master-slave game modes. The conclusions are as follows: (1) When multi-entity enterprise R&D and innovation system moderately fulfill their environmental social responsibilities, their income increases significantly, and the green innovation capability of green innovation ecosystem is enhanced effectively; (2) When the profit ratio of core enterprises is controlled above 1/3, and the subsidy rate of government on satellite enterprises is controlled below 2/3, the green innovation ecosystem is in a balanced state, and the innovation initiative of multi-agent enterprises reaches a high level; (3) Under centralized decision making, the revenue proportion of core enterprises decreases, but the overall revenue of R&D innovation system reaches the Pareto optimum. Finally, the differential game decision-making process is analyzed with an example to verify the validity of the model conclusion, which provides a scientific basis for the knowledge innovation decision of multi-agent enterprise R&D innovation system in the green innovation ecosystem and accelerates the process of carbon neutrality.

Control of Parametrically Perturbed Objects with a Full Information

The objective of this paper was to justify the new synthesis method of stabilizing controller for parametrically perturbed systems, which often appear in mobile robots, aircrafts, engineering objects with non-stationary parameters, intellectual control systems with a self-learning etc. Due to the high complexity and uncertainty of these systems, the classical PID controllers are not applicable and so a full information about the object state vector is used. Controllers obtained in this way allow to minimize the integral quality criterion of the system with the worst case parameter perturbation. For this purpose, the methods of differential games and switching systems theories were applied. Control laws are calculated by using the value function of the corresponding differential game, which can be obtained by solving the Hamilton-Jacobi-Bellman-Isaacs equations. A special set of basic functions was developed to approximate the value function and satisfy the boundary conditions. Finally, controller synthesis for a specific object with a nonstationary parameter is given. It significantly exceeds both the linear and fuzzy controllers in terms of quality. In the task of analyzing system qualitative characteristics under the worst parametric perturbation, our results are compared to the modern direct collocation methods of optimal control. With the same accuracy, proposed method is two times faster for low order systems. To verify that developed controllers can be employed in real time applications, we present computational time and memory usage in the end of the article.

Quality cooperation and retail service supply chain model selection: based on the perspective of service quality concerns

PurposeIn the new retail era, the supply chain synergy produced by quality integration has become the new direction of service supply chain research. The purpose of this paper is to study how to promote the sustainable development of the retail service supply chain (RSSC) by comparing and analyzing the optimal quality behavior, optimal returns, and the combination of conditions and strategies of the participating members of the RSSC.Design/methodology/approachFrom the perspective of quality function development and service quality concern, this paper considers RSSC as a two-level supply chain structure composed of functional service provider and retail service integrator. In this paper, a dynamic optimization model of quality input-cooperation-coordination of RSSC is proposed under two quality cooperation modes of decentralization and integration. This paper adopts the differential game method to compare and analyze the optimal quality behavior, optimal income, forming conditions and strategic combination of the participating members of the RSSC in different situations.Findings(1) Compared with quality dispersion, quality integration has more significant Pareto improvement effect on quality behavior and optimal revenue of RSSC. (2) In the case of quality integration, the optimal revenue obtained by the service sharing model is generally better than that obtained by the retail alliance collaboration model. (3) Benefit distribution ratio and quality cost allocation determine the optimal quality behavior of participating members of the RSSC, and also become the key factors for participating members to choose the collaborative mode in the case of quality integration.Originality/valueBased on the quality function development of RSSC, this paper introduces the concept of steady service quality, and discusses the relationship between the quality cooperation stability and the mode selection of RSSC. This provides a theoretical basis for how to build a RSSC with efficient operation and stable quality.

Robust event-triggered game-based attitude control for on-orbit assembly

On-orbit assembly is important in future space mission. It is a key process to adjust the attitude of substructures before assembling them into the main structure. In this paper, an event-triggered robust differential game is developed for multiple microsatellites fixed on one substructure to control the attitude of the substructure subject to disturbance. By taking disturbance as a special player to game with coordinated microsatellites, the attitude regulation problem is formulated as a robust differential game problem so that each microsatellite can independently calculate its own worst-case control strategy to reject disturbance. Considering the limited computation ability, a set of coupled algebraic equations is derived to obtain analytical expressions of Nash equilibrium strategies of microsatellites. Simultaneously, an event triggering threshold is designed by using the state error to avoid continuous communication and computation of mulitple microsatellites, and Zeno behaviour can be effectively avoided. Numerical simulations verify the effectiveness and stability of the event-triggered robust differential game method for the attitude regulation of the substructure.

A differential game method against attacks in heterogeneous honeynet

The use of honeynet has become relatively common for security researchers and network operators to improve the network security. Thus, study of decision-making against attacks in a heterogeneous honeynet is significantly important for improving the design of honeynet and effectively preventing attacks. This paper establishes a dynamic node-evolutive model under attacks by considering the inherent characteristics and the functional interaction between ordinary nodes and honeypots, based on which the decision-making problem is modeled as a differential game. The existence of the saddle-point involved in the game is validated and the optimal dynamic strategies for the honeynet system and attackers are obtained through the proposed algorithm. The obtained optimal strategies are verified using several random strategies. The effects of the network topology and attack duration on the strategies for both sides and on the overall attack effect are evaluated. The key findings are: a) strategic decision-making should be closely related to the node degree. Specifically, the higher-degree node adapts attack or capture strategy in preference to the lower-degree one, in contrast to the patching strategy. b) a honeynet with higher power-law exponent is beneficial to eliminate attack effects, whereas a higher attack duration can aggravate these effects. The obtained results provide a theoretical foundation to improve the design of honeynet and restrain honeynet attacks.

Linear quadratic differential game approach for attitude takeover control of failed spacecraft

Spacecraft is mostly abandoned after its fuel exhausts or actuator fails. Using microsatellites to implement attitude takeover control for failed spacecraft is a cost efficient way to recycle on-board valuable payloads at a low cost. In order to achieve collaboration between independent microsatellites, a differential game based method is proposed to stabilize the combined spacecraft composed of multiple microsatellites and the failed spacecraft, in which each microsatellite can independently calculate its own control strategy. Firstly, based on the attitude model of combined spacecraft and the performance index function of each microsatellite, the linear quadratic differential game model is formulated. By optimizing individual performance index functions, the control strategies of multiple microsatellites can be obtained. Secondly, in order to find the Nash equilibrium strategies of microsatellites, the coupled Hamilton-Jacobi(HJ) equations are transferred to a set of coupled Riccati differential equations over finite time horizon. In order to avoid computational overhead, a set of coupled algebraic Riccati equations over infinite horizon is also derived, which can be solved easily with high precision by the Lyapunov iterations method. Finally, numerical simulations verify the effectiveness of the differential game method for the attitude takeover control of failed spacecraft.

Optimal guidance against active defense ballistic missiles via differential game strategies

The optimal guidance problem for an interceptor against a ballistic missile with active defense is investigated in this paper. A class of optimal guidance schemes are proposed based on linear quadratic differential game method and numerical solution of Riccati differential equation. By choosing proper parameters, the proposed guidance schemes are able to drive the interceptor to the target and away from the defender simultaneously. Additionally, fuel cost, control saturation, chattering phenomenon and parameters selection were taken into account. Satisfaction of the proposed guidance schemes of the saddle point condition is proven theoretically. Finally, nonlinear numerical examples are included to demonstrate the effectiveness and performance of the developed guidance approaches. Comparison of control performance between different guidance schemes are presented and analysis.

Differential Game Research Based on Industrial Poverty Alleviation in E-Commerce Environment

This paper studies the decision-making of poverty alleviation investment in the supply chain system composed of agricultural suppliers and e-commerce sales platforms. Using the method of differential games, the changes of the equilibrium results of supply chain members in two cases are investigated and compared. The research shows that Under the Nash non-cooperative game situation, government subsidies can improve the degree of poverty alleviation efforts and the optimal benefits of supply chain members. The government subsidy coefficient τ only affects the poverty alleviation efforts and total revenue of agricultural suppliers and e-commerce sales platforms, and has no effect on the promotion efforts of e-commerce sales platforms.