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This study considered the dynamic equilibrium decision-making problem in a three-level supply chain comprising a manufacturer, a recycler and an echelon utilization (EchU) enterprise under the condition of cost-sharing coordination.

This study constructed a differential game model based on cost-sharing coordinated decision-making among a manufacturer, a recycler and an EchU enterprise operating under a cost subsidy. The study determined the optimal equilibrium strategies and evolutionary characteristics of subsidy mechanisms in a closed-loop supply chain. Finally, this study numerically simulated the path evolution process of vehicle battery EchU, the profit of each stakeholder and the sensitivity of parameters and verified the influences of various parameters on the overall structure and path.

The results show that a cost subsidy policy has a moderating effect on the EchU decision-making process and supply chain profit. The effect of that policy increases over time.

This study determined the equilibrium decision-making of enterprises in a closed-loop vehicle battery supply chain from a dynamic perspective, as well as the combined effects of government subsidy policies and cost-sharing coordination mechanisms.

The results have important guiding significance for coordination and cooperation between enterprises in closed-loop supply chains, for their decision-making and for the development of government subsidies.

This study considered the effects of government subsidies on closed-loop supply chains and the introduction of an EchU market to a closed-loop vehicle battery supply chain.

The purpose of the study is to investigate strategies for enhancing pollution oversight by local governments while reducing government-enterprise collusion (GEC) levels. Additionally, the factors influencing pollution control efforts at incineration plants are explored. Potential approaches to improving them and for effectively reducing waste incineration pollution are suggested.

The authors examined the most effective methods for mitigating incineration-related pollution and preventing collusion and developed a differential game model involving interactions between local governments and incineration plants. The findings of this work have significant policy implications for central governments worldwide seeking to regulate waste incineration practices.

The results indicate that, first, elevating environmental assessment standards can incentivize local governments to improve their oversight efforts. Second, collusion between incineration plants and local governments can be deterred by transferring benefits from the plants to the local government, while increased supervision by the central government and the enforcement of penalties for collusion can also mitigate collusion. Third, both central and local governments can bolster their supervisory and penalty mechanisms for instances of excessive pollution, encouraging incineration plants to invest more in pollution control. Finally, when the central government finds it challenging to detect excessive incineration-related pollution, enhancing rewards and penalties at the local government level can be a viable alternative.

This study stands out by considering the dynamic nature of pollutants. A differential game model is constructed which captures the evolving dynamics between local governments and incineration plants, offering insights regarding the prevention of collusion from a dynamic perspective. The findings may provide a valuable reference for governments as they develop and enforce regulations while motivating incineration plants to actively engage in reducing waste-incineration pollution.

As the quality of the environment decreases, enterprises and consumers' awareness of environmental protection is constantly improving. More and more enterprises begin to increase their investment in carbon emission reduction and attract environmentally friendly consumers to buy low-carbon products through advertising. The purpose of this paper is to utilize a realistic differential game model to provide dynamic carbon emission reduction strategies, advertising strategies and cooperation methods for complex supply chain members from a long-term perspective.

This paper uses the extend Vidale-Wolfe model (V-W model) to discuss the dynamic joint emission reduction strategy in the supply chain.

(1) When consumers' awareness of environmental protection increases, on the whole, carbon emission reduction and profit of products show an upward trend. (2) From a long-term perspective, the manufacturer's advertising subsidy to one of the retailers is the best choice. If the strength of the two retailers is unbalanced, the manufacturer will choose to cooperate with the dominant retailer. (3) Advertising, as a marketing means for retailers to promote low-carbon products, can alleviate the adverse effects of prisoner's dilemma in a semi-cooperative state, but it cannot achieve the Pareto optimization result.

This paper focuses on the analysis of the situation that when the manufacturer is the leader and thinks that consumers are active advocates of low-carbon products.

The results of this paper can provide theoretical basis for the joint emission strategy of supply chain members in low-carbon environment.

Although green logistics has become a new focus of cooperation between government and enterprises under environmental constraints, how local governments formulate subsidy policies to effectively guide the green transformation of regional logistics and how to facilitate the reasonable cost-sharing are rather critical. This paper will deeply explore the dynamic process of the tripartite participation (government, platform, and logistics enterprises) in the selection of regional green logistics strategy, and reveal the evolutionary game relationship of the three parties.

To explore the dynamics involving the government, platform and logistics enterprises for the green logistic transformation, and reveal the evolutionary gaming among the three parties, based on the bounded rationality premise, this study constructs the tripartite asymmetric evolutionary game models, uses the stability theorem of differential equation to explore the evolution and stability strategy of the system in different cases and explicates the paths of influence on the tripartite behaviors via simulations.

Results of this study indicate that there exist stable equilibrium strategies among the three parties regarding the regional green logistics, and they are affected by different factors. The government's subsidy, subsidy intensity and the platform's cost-sharing proportion can generate positive effects, but the latter two can also impact negatively beyond the effective ranges. The findings provide a theoretical basis for local governments, platforms and logistics enterprises to formulate justifiable subsidy intensity and determine reasonable sharing proportion.

Firstly, considering the significant relevance of local government, it is included in the evolution model, and the tripartite game (among government, platform and enterprises) is explored; Secondly, by comparing the equilibrium results under different game conditions, this paper analyzes the evolution of each party's game strategy to achieve the optimal return under bounded rationality and the important factors determining the strategic selection; Finally, the key factor of platform cost sharing is involved, and to what extent the change of platform cost sharing ratio will influence the systematic stability is explored.

The authors characterize the conditions under which a country may eventually split and when it splits within an infinite horizon multi-stage differential game.

In contrast to the existing literature, the authors do not assume that after splitting, players will adopt Markovian strategies. Instead, the authors assume that while the splitting country plays Markovian, the remaining coalition remains committed to the collective control of pollution and plays open-loop.

Within a full linear-quadratic model, the authors characterize the optimal strategies. The authors later compare with the outcomes of the case where the splitting country and the remaining coalition play both Markovian. The authors highlight several interesting results in terms of the implications for long-term pollution levels and the duration of coalitions under heterogenous strategies as compared to Markovian behavior.

In this paper, the authors have illustrated the richness of the simplications of enlarging the set of strategies in terms of the emergence of coalitions, their duration and the implied welfare levels per player. Varying only three parameters (the technological gap, pollution damage and coalition payoff share distribution across players), the authors have been able to generate, among other findings, quite different rankings of welfare per player depending on whether the remaining coalitions after split play Markovian or stay precommited to the pre-splitting period decisions.

In the context of constructing an integrated national strategic system, collaborative innovation among enterprises is the current social focus. Therefore, in order to find the interest relationship between multiple game subjects, to explore the influencing factors of collaborative innovation of civil-military integration enterprises. This paper constructs a collaborative innovation mechanism for military–civilian integration involving four game subjects (military enterprises, private enterprises, local governments, and science and technology intermediaries). It aims to solve and reveal the evolutionary game relationship among the four parties.

To explore the mechanism of military–civilian collaborative innovation involving four players, this study employs game theory and constructs an evolutionary game model for collaborative innovation with the participation of military enterprises, civilian enterprises, local governments, and technology intermediaries. The model reveals the evolutionary game patterns among these four entities, analyzes the impact of various parameters on the evolutionary process of the game system, and numerical simulation is used to show these changes more specifically.

The research findings demonstrate that active government subsidies promote cooperation throughout the system. Moreover, increasing the input-output ratio of research and development (R&D), the rate of technological spillovers, and the R&D investment of civilian enterprises all facilitate the tendency toward cooperation within the system. However, when the government chooses to actively provide subsidies, increasing R&D investment in military enterprises may hinder the tendency toward cooperation. Furthermore, central transfer payments, government punishment from the central government, and an increase in the information conversion rate of technology intermediaries may suppress the rate of cooperation within the system.

Most of the previous studies on the collaborative innovation of military–civilian integration have been tripartite game models between military enterprises, private enterprises, and local governments. In contrast, this study adds science and technology intermediaries on this basis, reveals the evolution mechanism of collaborative innovation of civil-military integration enterprises from the perspective of four-party participation, and analyzes the factors influencing the cooperation of the whole system. The conclusion of this study not only enriches the collaborative innovation evolution mechanism of military–civilian integration enterprises from the perspective of multiple agents but also provides practical guidance for the innovation-driven development of military–civilian integration enterprises.

The managerial questions of this paper are as follows, and the authors are trying to solve them: How revenue sharing contract (CSR) degree and government subsidy affect the agri-food quality? What kind of model (WPC, revenue-sharing contract [RSC] and cooperative) would be more effective in motivating manufacturers and retailer to increase effort and improve agri-food quality? What kind of model (WPC, RSC and cooperative) would make manufacturer and retailer better off?

Considering the jointing quality effort and contract decision in green agri-food supply chain, this paper proposes six models that consider CSR of manufacturer and retailer, and then the obtained optimal solutions are compared and analyzed. At the same time, the impact of government subsidies is analyzed, and corresponding conclusions are drawn.

The results show that, first of all, whether the increasing CSR of the manufacturer or the retailer can motivate both parties to improve the agri-food quality effort investment. Second, the WPC and RSC contract may play different role in different cases. Finally, under the model with government subsidies, regarding positive influence of government subsidies on efforts of manufacturer and retailer, quality and profits of members is investigated. Based on these conclusions, this study puts forward the following policy suggestions. Firstly, governments should formulate reasonable subsidy policies to support manufacturer and retailer to improve the agri-food quality, thereby promoting green industries' development. Secondly, manufacturer and retailer should actively improve CSR and strengthen the effort of agri-food so as to advance quality. Finally, manufacturer and retailer can choose cooperative model or WPC contract.

In this paper, one manufacturer and one retailer are considered. Since the agri-food supply chain structure in reality is more complicated, the future research direction can consider the supply chain structure with one manufacturer and multiple retailers. In addition, this paper only considers the subsidy, and future research can classify the subsidy into different types.

The study makes two substantive contributions to the body of knowledge in the field of sustainable operations:(1) incorporating quality-based demand function in supply chain and dynamic process of agri-food quality; (2) exploring the impact of CSR awareness of members and subsidy of government on agri-food quality, and comparing the influence in different models.

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as in the traction of transportation systems (such as electric vehicles and electric trains or ships with electric propulsion). The dynamic model of VSI-PMSMs is multivariable and exhibits complicated nonlinear dynamics. The inverters’ currents, which are generated through a pulsewidth modulation process, are used to control the stator currents of the PMSM, which in turn control the rotational speed of this electric machine. So far, several nonlinear control schemes for VSI-PMSMs have been developed, having as primary objectives the precise tracking of setpoints by the system’s state variables and robustness to parametric changes or external perturbations. However, little has been done for the solution of the associated nonlinear optimal control problem. The purpose of this study/paper is to provide a novel nonlinear optimal control method for VSI-fed three-phase PMSMs.

The present article proposes a nonlinear optimal control approach for VSI-PMSMs. The nonlinear dynamic model of VSI-PMSMs undergoes approximate linearization around a temporary operating point, which is recomputed at each iteration of the control method. This temporary operating point is defined by the present value of the voltage source inverter-fed PMSM state vector and by the last sampled value of the motor’s control input vector. The linearization relies on Taylor series expansion and the calculation of the system’s Jacobian matrices. For the approximately linearized model of the voltage source inverter-fed PMSM, an H-infinity feedback controller is designed. For the computation of the controller’s feedback gains, an algebraic Riccati equation is iteratively solved at each time-step of the control method. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control for this system, the H-infinity Kalman filter is proposed as a state observer. The proposed control method achieves fast and accurate tracking of the reference setpoints of the VSI-fed PMSM under moderate variations of the control inputs.

The proposed H-infinity controller provides the solution to the optimal control problem for the VSI-PMSM system under model uncertainty and external perturbations. Actually, this controller represents a min–max differential game taking place between the control inputs, which try to minimize a cost function that contains a quadratic term of the state vector’s tracking error, the model uncertainty, and exogenous disturbance terms, which try to maximize this cost function. To select the feedback gains of the stabilizing feedback controller, an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. To analyze the stability properties of the control scheme, the Lyapunov method is used. It is proven that the VSI-PMSM loop has the H-infinity tracking performance property, which signifies robustness against model uncertainty and disturbances. Moreover, under moderate conditions, the global asymptotic stability properties of this control scheme are proven. The proposed control method achieves fast tracking of reference setpoints by the VSI-PMSM state variables, while keeping also moderate the variations of the control inputs. The latter property indicates that energy consumption by the VSI-PMSM control loop can be minimized.

The proposed nonlinear optimal control method for the VSI-PMSM system exhibits several advantages: Comparing to global linearization-based control methods, such as Lie algebra-based control or differential flatness theory-based control, the nonlinear optimal control scheme avoids complicated state variable transformations (diffeomorphisms). Besides, its control inputs are applied directly to the initial nonlinear model of the VSI-PMSM system, and thus inverse transformations and the related singularity problems are also avoided. Compared with backstepping control, the nonlinear optimal control scheme does not require the state-space description of the controlled system to be found in the triangular (backstepping integral) form. Compared with sliding-mode control, there is no need to define in an often intuitive manner the sliding surfaces of the controlled system. Finally, compared with local model-based control, the article’s nonlinear optimal control method avoids linearization around multiple operating points and does not need the solution of multiple Riccati equations or LMIs. As a result of this, the nonlinear optimal control method requires less computational effort.

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as in the traction of transportation systems (such as electric vehicles and electric trains or ships with electric propulsion), The solution of the associated nonlinear control problem enables reliable and precise functioning of VSI-fd PMSMs. This in turn has a positive impact in all related industrial applications and in tasks of electric traction and propulsion where VSI-fed PMSMs are used. It is particularly important for electric transportation systems and for the wide use of electric vehicles as expected by green policies which aim at deploying electromotion and at achieving the Net Zero objective.

Unlike past approaches, in the new nonlinear optimal control method, linearization is performed around a temporary operating point, which is defined by the present value of the system’s state vector and by the last sampled value of the control input vector and not at points that belong to the desirable trajectory (setpoints). Besides, the Riccati equation, which is used for computing the feedback gains of the controller, is new, as is the global stability proof for this control method. Comparing with nonlinear model predictive control, which is a popular approach for treating the optimal control problem in industry, the new nonlinear optimal (H-infinity) control scheme is of proven global stability, and the convergence of its iterative search for the optimum does not depend on initial conditions and trials with multiple sets of controller parameters. It is also noteworthy that the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state-dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems that can be transformed to the linear parameter varying form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions.

The existence of the advertising delay effect and its impact on supply chain operations have been demonstrated in the current study. Therefore, this study develops a timely inventory control strategy for the fresh produce supply chain to address the advertising delay effect in the fresh produce supply chain.

This study proposes a game model based on the Nerlove-Arrow time delay differential equation and Pontryagin's maximum principle. Through comparative analyses of the optimal equilibrium strategies, the authors compare the optimal equilibrium strategies, product goodwill and optimal inventory trajectories for suppliers and retailers under secondary replenishment decisions and decentralized decisions.

The authors find that (1) Only when the sales cycle meets certain conditions can the overall profit of the supply chain under the secondary replenishment decision be greater than that under the decentralized decision. As the price markup coefficient increases, the total profit of the supply chain first increases and then decreases. (2) With the increase in the delay time, the replenishment quantity during the initial period gradually decreases. After the delay time elapses, the inventory depletion rate under secondary replenishment decisions is faster than that under decentralized decision-making. (3) Although there is a continuously increasing maximum value of product goodwill with the increase in delay time, it becomes difficult to achieve this value for longer delays.

The authors’ findings provide a theoretical basis for supply chain members of fresh agricultural products to select replenishment and inventory control strategies when adopting different levels of delay in advertising marketing.

Firstly, this paper explains the impact of advertising delay effect on fresh produce supply chain from a dynamic perspective, and secondly, it provides guidance on advertising formulation and inventory replenishment for fresh produce retailers under the influence of advertising delay effect.

This study aims to propose a risk-induced game theoretic forecasting model to predict average daily rate (ADR) under COVID-19, using an advanced recurrent neural network.

Using three data sets from upper-midscale hotels in three locations (i.e. urban, interstate and suburb), from January 1, 2018, to August 31, 2020, three long-term, short-term memory (LSTM) models were evaluated against five traditional forecasting models.

The models proposed in this study outperform traditional methods, such that the simplest LSTM model is more accurate than most of the benchmark models in two of the three tested hotels. In particular, the results show that traditional methods are inefficient in hotels with rapid fluctuations of demand and ADR, as observed during the pandemic. In contrast, LSTM models perform more accurately for these hotels.

This study is limited by its use of American data and data from midscale hotels as well as only predicting ADR.

This study produced a reliable, accurate forecasting model considering risk and competitor behavior.

This paper extends the application of game theory principles to ADR forecasting and combines it with the concept of risk for forecasting during uncertain times.

This study is the first study, to the best of the authors’ knowledge, to use actual hotel data from the COVID-19 pandemic to determine an appropriate neural network forecasting method for times of uncertainty. The application of Shapley value and operational risk obtained a game-theoretic property-level model, which fits best.