Low-altitude Emergency Strategy Using Ad-hoc Radio Relay eVTOLs in Karst Topography and Game Analysis

This article investigates a trilateral stochastic differential reinsurance and investment game with heterogeneous reinsurance premiums. As the leader in the Stackelberg game, the reinsurer maximizes the expected utility of the combination of the three players’ terminal wealth other than its own utility. The degree to which a reinsurer pays attention to an insurer depends on the coefficient α i ( i = 1 , 2 ) . The insurers spread their risks and expand their underwriting capacity by purchasing reinsurance with strategies involving relative performance in a non-zero-sum stochastic differential game. We derive explicit expressions of the Nash equilibrium strategy and prove the verification theorem using dynamic programming and backward induction methods. We discuss the parameters comparative static analysis of the equilibrium strategies through numerical examples. The numerical results show that the coefficient α i ( i = 1 , 2 ) is proportional to the reinsurance premium price and is inversely proportional to the reinsurance ratio.

PurposeThe government plays an important role in the financing process of small and medium enterprises (SMEs), but the current government-enterprise cooperation (GEC) mechanism cannot well solve the financing problem of SMEs. In addition, since government-enterprise cooperation is a long-term dynamic process, this study aims to explore the cooperation strategy between the government and core enterprises in supply chain finance (SCF) under the dynamic structure.Design/methodology/approachConsidering both parties have the characteristics of disappointment aversion, our research constructs a game theory model of government subsidy and the effort of the enterprise to implement SCF based on differential game and studies different game strategies in the non-cooperative game, the Stackelberg game and the cooperative game.FindingsOur findings show that the government subsidy can significantly spur the enterprise in the supply chain to implement SCF. We also find that the limitation of the government subsidy exists. In addition, the optimal strategy, the optimal benefit and the total benefit of the financing system formed by the government and the enterprise in the cooperative game are better than those in the non-cooperative game. Pareto optimality is achieved.Research limitations/implicationsThe limitations of this paper are: (1) In theory, this paper only takes the government and enterprise as game subjects without considering other participants in the supply chain. In addition, only disappointment aversion is taken into consideration while in reality the participants often exhibit multiple behavior preferences. (2) In methodology, only the numerical solution is given through the solution algorithm and all parameters are assumed to be determined as time changes for the convenience of calculation.Practical implicationsThe government can motivate enterprises in the supply chain to implement SCF by providing subsidies. However, it should be noted that excessive subsidy will make the enterprise dependent on the government and as a result, decrease the effort level to implement SCF. Thus, it is necessary for the government to keep track of the business conditions of the enterprise to make a subsidy strategy. In addition, the government can reduce the impact of disappointing aversion by making more targeted policies and taking risk management measures.Social implicationsOn one hand, it is necessary for the government to keep track of the business conditions of the enterprise to make a subsidy strategy. In addition, the government can reduce the impact of their own disappointing aversion by making more targeted policies and adopting risk management measures. On the other, it is important for the enterprise to improve the regulatory mechanism and optimize the compensation structure of decision-makers to inhibit the impact of decision-makers' disappointing aversion.Originality/valueThis study is the first to investigate the mechanism of GEC in the setting of SCF based on a differential game. Furthermore, our study provides a theoretical basis for the government and enterprises to cooperate in SCF.

This paper investigates three-dimensional pursuit problems in noncooperative stochastic differential games. By introducing a novel polynomial value function capable of addressing high-dimensional dynamic systems, the forward–backward stochastic differential equations (FBSDEs) for optimal strategies are derived. The uniqueness of the value function under bounded control inputs is rigorously established as a theoretical foundation. The proposed methodology constructs optimal closed-loop feedback strategies for both pursuers and evaders, ensuring state convergence and solution uniqueness. Furthermore, the Lebesgue measure of the barrier surface is computed, enabling the design of strategies for scenarios involving multiple pursuers and evaders. To validate its applicability, the method is applied to missile interception games. Simulations confirm that the optimal strategies enable pursuers to consistently intercept evaders under stochastic dynamics, demonstrating the robustness and practical relevance of the approach in pursuit–evasion problems.

On the Existence of an Evasion Strategy in a Linear Differential Game with Integral Constraints

Against the backdrop of an aging population, community pension initiatives are gaining traction, permeating societal landscapes. This study delves into the equilibrium strategy within the context of a defined benefit pension plan, employing a differential game framework with a community pension model. Hence, the model entails the company’s controls over investment rates in funds, juxtaposed with employees’ inclination towards a greater proportion of community pension allocation in said funds. To tackle this issue, a stochastic differential game model for pensions under a community pension scheme is formulated. Leveraging the Hamilton-Jacobi-Bellman equation, we derive the Markov Perfect Nash Equilibrium solution and optimal portfolio. Through numerical simulations, we analyze the impact of varying risk aversion levels across different parameter values on equilibrium ratios, thereby offering insights into managerial risk tolerance.

This paper discusses the optimal synchronisation problem of multi-agent systems with unknown system dynamics, where each agent is subject to both input saturation and external disturbances. A novel data-driven control approach is developed in this paper based on low-gain technique, output regulation, differential game theory, and adaptive dynamic programming (ADP). Unlike existing approaches to the data-driven optimal synchronisation problem, our method eliminates the need for an initially admissible stabilising control policy, and the proposed distributed control law ensures asymptotic tracking even in the presence of both modelling disturbances and unmodeled disturbances.

This paper considers a stochastic non‐zero‐sum differential game between two competitive insurers. Both insurers are allowed to invest in one risk‐free asset and one risky asset, whose price dynamics follow the constant elasticity of variance (CEV) model, specifically the extended CEV (E‐CEV) model. At the same time, they are permitted to purchase proportional reinsurance to control the risks associated with individual claims. The goal of each insurer is to determine optimal strategies that maximize the expected utility of terminal wealth relative to that of their competitor. The Nash equilibrium reinsurance and investment strategies are explicitly derived using stochastic control theory techniques. Finally, we numerically examine the effect of model parameters on optimal investment and reinsurance strategies.

Analytical Scheduling for Selfishness Detection in OppNets Based on Differential Game

Wasted mine revitalization through Eco-environment-oriented Development: A dynamic analysis based on differential games

Publications on mathematical game theory with many (not less than 2) players can be conditionally distributed in four directions: non-cooperative, hierarchical, cooperative and coalition games. The last two, in turn, are divided into games with side and non-side payments and games with transferable and nontransferable payoffs, respectively. If the first ones are actively studied (St. Petersburg State Faculty of Applied Mathematics and Control Processes, St. Petersburg Institute of Economics and Mathematics, Institute of Applied Mathematical Research of Karelian Research Centre RAS), the games with non-transferable payoffs are not covered. The paper proposes the conception of objections and counter-objections. The initial investigations were published in two monographs of E.I. Vilkas, the Lithuanian mathematician (the student of N.N. Vorobjev, the professor of St. Petersburg University). For the differential games this conception was first applied by E.M. Waisbord in 1974, then it was continued by the first author of the present article together with E.M. Waisbord in the book Introduction to the theory of differential games of n-persons and its application (1980), and in the monograph Equilibrium of objections and counterobjections (2010) by V.I. Zhukovskiy. The paper proves that in еру mathematical model there is no Nash equilibrium but there are equilibria of objections and conterobjections and simultaneously Pareto maximality.

In this paper, the problems of green innovation investment and coordination are investigated for a three-echelon closed-loop supply chain with Big Data services, where the considered supply chain consists of a manufacturer, a retailer and Big Data service provider. Firstly, by considering the effects of product energy efficiency level (EEL) on demand and recycling quantity, the differential game models under centralized and decentralized decision modes are established. By applying optimal control theory, both the equilibrium strategies and channel profits are solved and compared under the two modes. Then, the joint contract including a revenue-sharing contract and a bilateral cost-sharing contract is proposed to coordinate the supply chain. Finally, the impacts of key system parameters on equilibrium strategies, product EEL, brand goodwill and channel profits are discussed by numerical examples. Meanwhile, the effectiveness of the joint contract in coordinating the decentralized channel is verified. The results show that the green innovation effort, the Dig Data marketing effort, the EEL of product, the brand goodwill and channel profits under centralized decision mode are higher than those values under decentralized decision mode, but the recycling quantity is relatively low. The joint contract can coordinate three-echelon closed-loop supply chain.

In a finite-dimensional Euclidean space, the problem of pursuing of a group of evaders by a group of pursuers is considered, described by a linear non-stationary system of differential equations with fractional Caputo derivatives. Sets of admissible players’ controls — compacts, terminal sets — origin of coordinates. Sufficient conditions have been obtained for the capture of at least one evader and all evaders under the condition that the evaders use the same control. In the study, the method of matrix and scalar resolving functions is used as a basic one. It is shown that differential games described by equations with fractional derivatives have properties that are different from those of differential games described by ordinary differential equations.

We study a pursuit differential game problem involving one pursuer and one evader in a Hilbert space. The motion of the pursuer is governed by first-order differential equations, while that of the evader is described by a second-order differential equation. The control functions of the pursuer and the evader are subject to integral constraints. The pursuit is considered completed if the equality y(θ)=x(θ) is achieved. We formulate and prove two theorems that provide sufficient conditions for the completion of pursuit at a given time.

The new media environment driven by digital intelligence technologies provides new opportunities for enterprise development, but also brings new challenges for enterprise crisis management and network public opinion information (referred as public opinion) guidance. Focusing on the contradictions between the complex diversity of crisis types and the limited governance resources, it is of great significance for enterprises to determine the best public opinion guidance strategy. Considering the dynamic complexity of public opinion derived from enterprise crisis, this paper innovatively proposed a decision-making model of enterprise public opinion under crisis differentiation based on differential game. Then, the balance strategy of each stakeholder and the guiding effect of public opinion were discussed under four decision scenarios. Finally, the optimal resources allocation ratio of different types of crises is determined under the constraints of governance resources, and the key parameters of public opinion guidance process are identified. The results show that, under four decision scenarios, the dual-guidance strategy achieves the best public opinion guidance effect and Pareto-optimal outcome for the game system. The overall benefit is maximized when the optimal investment ratio for the four types of crises (Values-type, Product-type, Marketing-type, and Internal management-type) is 60:28:8.4:3.6. The subsidy coefficients of enterprise to netizens and media both significantly the guidance effect of public opinion, but compared with the former, it is more sensitive to the changes of the letter. Based on the research results, this paper provides targeted suggestions for enterprises crisis response and their sustainable development under the new media environment.

Gradient-Based Algorithms With Intermediate Observations in Static and Differential Games

We study a pursuit differential game problem involving one pursuer and one evader in a Hilbert space. The motion of the pursuer is governed by first-order differential equations, while that of the evader is described by a second-order differential equation. The control functions of the pursuer and the evader are subject to integral constraints. The pursuit is considered completed if the equality y(θ)=x(θ) is achieved. We formulate and prove two theorems that provide sufficient conditions for the completion of pursuit at a given time.

Regional coalition of basin water pollution control based on differential game

Learning to Win: DDPG vs. Differential Games in Orbital Pursuit-Evasion

Multi-Quadrotor Differential Graphical Containment Game with Noncooperative Active Leaders Subject to External Disturbances