Background As destructive diseases, governments increasingly utilize emergency co-production to satisfy the keen need for medical products. Although governments have provided purchase commitment payments to promote co-production with manufacturers, research has mainly focused on regular medical production without purchase commitment payment, whereas research on emergency co-production with purchase commitments remains scarce. Method Our study fills the gap by analyzing the regular and emergency co-production models using differential game approaches to optimize purchase commitment. Results First, we find that even if the production and storage costs are relatively high, the emergency co-production mode sometimes has a higher production rate than the regular medical production mode. Next, the purchase commitment payment could increase the relative advantage of emergency co-production in the per-unit product value. Moreover, the emergency co-production model dominates when the demand exceeds a threshold. Furthermore, the regular medical production mode dominates the higher value and less-demanding emergency production. Conclusions Hence, both regular medical production and co-production modes can show superior performance depending on the level of demand and the degree of purchase commitment payment. Critical management insights offer takeaways for manufacturers and policy makers' decisions on emergency medical co-production to prepare for future onslaughts of destructive diseases.

Agent or merchant? Unpacking hotel-OTA selling formats with differential games

Integrating opinion dynamics and differential game modeling for sustainable groundwater management.

Correction to: The Impacts of Reward Frequency and Reward Conditionality on Sustainable Use of Common Resources: a Stochastic Common Property Differential Game Model

This article examines the coordination challenges within a supply chain comprising a manufacturer and a retailer, operating under the influence of environmental regulation instrument, namely green subsidy. A Stackelberg differential game model is developed to analyse equilibrium functions pertaining to environmental performance, retail pricing, and environmental perception levels in both integrated and decentralised channel settings. A two-part tariff contract is introduced for decentralised supply chain coordination, and a Nash bargaining model is subsequently employed to investigate the allocation of additional profits. Numerical simulations are conducted to assess the impact of the green subsidy coefficient and supply chain environmental standards on steady-state solutions and overall supply chain profit. The main findings underscore the flexible pricing strategies adopted by the supply chain in both integrated and decentralised settings. And the study indicates that the overall performance of the former surpasses that of latter. A two-part tariff contract emerges as a pivotal instrument for achieving effective supply chain coordination. Moreover, green subsidy coefficient exhibits a positive influence on enhancing coordination capability, whereas the supply chain environmental standard acts as a deactivator.

This paper presents a novel approach to address the problem of intercepting non-cooperative targets with multiple satellites in Earth orbit. The multi-satellite interception problem is formulated as a multi-player pursuit–evasion game that explicitly accounts for stochastic disturbances and control constraints. By combining differential game theory with stochastic optimization techniques, the paper derives optimal interception trajectories that ensure safety and performance under modeling uncertainties. A linear exponential quadratic cost functional is established, and corresponding Nash equilibrium strategies are obtained to determine the optimal control laws. Numerical simulations validate the effectiveness and robustness of the proposed approach in achieving reliable interception performance.

This paper investigates the non-zero-sum stochastic differential game problem of optimal asset-liability management (ALM) between insurers and reinsurers. Combining the investment- reinsurance problem with the ALM, this paper innovatively studies the investment-reinsurance ALM non-zero-sum game within the framework of the constant elasticity of variance (CEV) model under common shock dependence. We allow the insurance companies to purchase proportional reinsurance from reinsurance companies, and both companies can invest in a financial market composed of one risk-free asset and one risk asset whose price process follows the CEV model. By innovatively introducing a class of stochastic liability processes associated with the volatility of risky assets, we obtain the dynamic evolution of net wealth. Using stochastic control theory, we obtain an explicit expression of Nash equilibrium strategy for the problem and a closed-form expression for the corresponding equilibrium value function by maximizing the expected utility from the terminal net wealth. Finally, we illustrate the effect of relevant parameters on the optimal investment-reinsurance strategy by means of numerical examples.

In this paper, we present a numerical solution for an open-loop Nash differential game modeling competition between two firms. Using the fourth-order Runge-Kutta method, we computed the numerical solution and analyzed the stability of the open-loop Nash equilibrium. Additionally, we examined the uniform convergence of the solution. Finally, an illustrative example is presented to clarify the results, accompanied by figures to illustrate the findings.

Considering a low-carbon operating environment featured by consumer low-carbon preference (CLP) and hybrid carbon policies, we construct a green brand supply chain consisting of a dominant manufacturer and two retailers. Under the green brand (GB) strategy, the manufacturer achieves green production through green technology and recycling, and the two retailers conduct green marketing activities. We adopt the differential game approach to characterise the dynamics of the green brand (GB) image, and fully consider the possibility of alliance between competing retailers and the consequent power structure shift. By analysing the four models, the results show that only when the retailer alliance has equal bargaining power with the manufacturer, i.e. the Nash power structure, competing retailers always have incentives to form an alliance. Under other power structures, the market condition for retailers to ally depends on the marginal effect of green production on GB image. For the manufacturer, the emergence of the retailer alliance may lead to positive outcomes. Under certain conditions, each player has the highest profit under the Nash power structure. In addition, we examine the impacts of the dynamic operating environment on equilibrium solutions and retailers’ alliance behaviour.

A Stochastic Differential Oligopoly Game for Housing Characteristics in Investment Decisions

We investigate the interception problem in a differential game with non-inertial players (a pursuer and an evader) who move in dynamic flow fields with various influences. Throughout the paper, we solve the pursuit and ``life-line'' game problems. To solve the pursuit, the strategy of parallel pursuit ($\bf{\Pi}$-strategy for short) is defined and used. With the help of the $\bf{\Pi}$-strategy and applying the Gr\"{o}nwall-Bellman inequality, sufficient pursuit condition is determined. In order to solve the ``life-line'' game to the advantage of the pursuer, we build the set of meeting points of the players and prove that this set monotonically decreases with regard to inclusion relative to time. The ``life-line'' game to the advantage of the evader is solved by constructing evader's attainability domain where it reaches without being caught for an arbitrary control of the pursuer.

We analyze an evasion differential game involving one evader and multiple pursuers in $\R^n$. The control functions of the players are subject to exponential integral constraints to ensure bounded energy consumption. Evasion is considered possible if, for any time $t$, the position of the evader differs from the positions of all the pursuers. In this work, we establish a sufficient condition for the possibility of evasion. We construct an admissible evasion strategy and demonstrate that, for any number of pursuers $m$, evasion is possible. Additionally, we show that the number of maneuvers required for evasion does not exceed $m$.

Sustainable strategies for marine plastic waste remanufacturing systems under diverse carbon reduction policies.

Blockchain-enabled governance of greenwashing in the building material supply chain: A differential game approach

Optimal risk sharing with correlated insurance businesses in a Stackelberg-Nash differential game

Target defense differential game for autonomous surface vehicles

Non-zero-sum linear quadratic stochastic differential games with jump diffusion and input delay: an asymmetric information framework

Abstract The title of this semi-tutorial, expository paper might be applicable to the remarkable body of research by Professor Tamer Başar with his students Didinski and Pan in the 1990s on robustification of parameter identifiers and adaptive controllers through game-theoretic methods. The author’s inspiration indeed fuses their work with his results from that period on inverse optimal adaptive stabilization and inverse optimal disturbance attenuation in a differential game formulation. Inverse optimal adaptive and minimax techniques are merged in this paper’s first half to obtain solutions to adaptive differential games between the adaptive controller and a disturbance. The article’s second half introduces a recent advance in disturbance-robustification of adaptive control for persistent disturbances (merely bounded, rather than square-integrable), by Iasson Karafyllis and this article’s author. While not with a minimax capability, this robustification is first in forty years to attain regulation with a bias that is arbitrarily low and independent of both the unknown parameter and the persistent disturbance.

Parameter estimation for stochastic dynamic systems is crucial yet challenging due to inherent randomness and noise. Traditional deterministic methods often fail to cope with such uncertainties. Inspired by the deterministic tracking approach, we propose a new parameter estimation method—stochastic dynamic problem based parameter estimation method (SDPE), which firstly transforms the original stochastic optimal control problem into a stochastic differential game problem by introducing a perturbation term, and then realizes the simultaneous estimation of the system parameters and the optimal control function. We prove the consistency of the SDPE estimator. Numerical simulations demonstrate that this method exhibits superior performance in terms of accuracy and robustness compared to maximum likelihood estimation (MLE), likelihood-based methods (EM) and Bayesian inference methods (MCMC), particularly under varying noise levels and sample sizes. Furthermore, we apply SDPE to a stochastic optimal control SIRD model to analyze COVID-19 data from Florida, USA. Results demonstrate that SDPE effectively captures time-varying transmission, recovery, and mortality rates, providing a powerful tool for modeling and understanding complex epidemic dynamics.

Abstract This study proposes a geometric solution to the norm differential game design problem in target-attacker-defender (TAD) engagements, addressing key limitations of conventional zero-effort-miss approaches. By leveraging the geometric analogy between guidance-law-generated trajectories and Dubins paths, we reformulate the derivation of zero-effort-miss-based guidance laws as a Nash equilibrium optimisation problem, with optimal strategies determined through reachable set analysis of Dubins path frontier. The resulting model is a non-convex optimisation problem, which prevents the derivation of traditional state-feedback control laws. To overcome this limitation and enable real-time implementation, we develop a custom back propagation neural network, enhanced with a relaxation factor method for output filtering, a Holt linear trend model for outlier compensation and a saturation function for oscillation suppression. Extensive simulations demonstrate that the proposed framework significantly outperforms baseline methods. These results validate the effectiveness and robustness of our approach for high-performance TAD applications.