Search Results (1,408)

This study develops a game-theoretic framework to analyze collaborative advertising decisions between manufacturers and retailers in seasonal product supply chains characterized by competitive–cooperative channel relationships. We formulate a mathematical programming model to jointly optimize advertising efforts, the manufacturer’s advertising cost-sharing rate, order quantities, and inventory decisions across distinct channel configurations—including a single manufacturer–retailer dyad and a competitive multi-channel market. Numerical experiments and sensitivity analyses are conducted to investigate how key structural parameters—particularly demand elasticity and channel power asymmetry—influence overall system performance and equilibrium decision outcomes. Results indicate that well-designed collaborative advertising mechanisms enhance total channel profitability and, under specific conditions, yield Pareto-improving outcomes for both parties. This study makes three primary contributions: (i) it integrates inter-firm competition with intra-channel cooperation within a unified strategic framework; (ii) it jointly coordinates advertising and inventory decisions—two critical operational levers—rather than treating them in isolation; and (iii) it embeds financial arrangements (e.g., cost sharing) endogenously into the analytical model, thereby offering a novel, theoretically grounded, and practically implementable decision-support framework for distribution systems operating in complex, dynamic market environments. Full article

This study evaluates the demand dynamics of the 20 leading strategic destinations in the global tourism market by modeling the interactions between traditional macroeconomic determinants and climate-linked environmental sustainability indicators. The primary objective is to assess the predictive capacity of physical and structural environmental factors—including water stress, air pollution, renewable energy adoption, and sanitation infrastructure—relative to established economic metrics like GDP per capita. Employing non-parametric predictive frameworks on a panel dataset of 400 observations (2000–2019), the empirical analysis suggests that tree-based ensemble models, notably Extra Trees (90.54%) and CatBoost (84.75%), yield higher predictive accuracy than conventional multiple linear regression (73.97%). Interpretations derived from cooperative game theory via SHAP analysis suggest that environmental determinants may serve as important predictive drivers of tourism demand. Specifically, variables such as water stress (28.20%), renewable energy share (27.12%), and sanitation infrastructure carry substantial predictive weight, whereas the benchmark macroeconomic indicator (2.30%) exerts a relatively marginal influence within the model architecture. These findings imply that environmental sustainability metrics may capture international tourism demand variations more effectively than traditional economic variables. The results suggest that acute environmental vulnerabilities may be associated with reduced tourism inflows, potentially reflecting limitations in destination sustainability thresholds. Broadly, the evidence is consistent with the notion that contemporary global tourism demand may be increasingly interdependent with ecological resilience and low-carbon transition policies. It is important to note that the findings reported here reflect predictive associations derived from machine learning models and should not be interpreted as evidence of causal relationships. Full article

Background/Objectives: Free riding in healthcare occurs when actors benefit from health-related public goods, risk-pooling arrangements, common resources, or cooperative institutions while contributing less than is socially optimal. This review clarifies how free-rider dynamics differ across vaccination, health insurance and universal health coverage, antimicrobial resistance, organ donation and transplant allocation, and global health cooperation. Methods: A narrative review with conceptual synthesis was conducted. Searches of PubMed and Scopus were complemented by citation tracking and targeted inclusion of foundational economics, game theory, public-health ethics, and market-design sources. Sources were mapped by domain, actors, strategies, payoff structure, information conditions, time horizon, enforcement mechanism and policy relevance. Results: Across domains, free riding arises when private payoffs diverge from collective welfare, but the underlying game differs: threshold public-good and coordination games in vaccination, adverse-selection and participation games in insurance, common-pool-resource dilemmas in antimicrobial use, donor-registration and matching-market problems in transplantation, and repeated public-goods games in global health. The review identifies three policy functions: altering payoffs, altering information and beliefs, and changing the structure, repetition, or enforceability of the game. Conclusions: Game theory is most useful as a mechanism-based framework rather than a stand-alone policy prescription. Its policy value depends on empirical calibration, institutional context, ethical legitimacy, and attention to equity, incomplete information, behavioral responses, and enforcement capacity. The synthesis also emphasizes boundary conditions: game-theoretic prescriptions can fail when political economy, asymmetric power, implementation capacity, access barriers, or trust-related drivers are ignored. Full article

This paper studies the balancedness and core properties of stochastic cooperative games under proportional distribution mechanisms. Different from decomposed payoff structures in the existing literature, where individual payoffs are separated into deterministic and stochastic components, we consider a restricted allocation environment in which each player’s payoff is a fixed proportional share of the realized stochastic coalition payoff. This proportional allocation rule is relevant for institutional settings where exposure shares are determined ex ante and cannot be adjusted after uncertainty is realized. Under homogeneous preference structures, we employ expectation–variance and quantile-based evaluation criteria to transform random coalition outcomes into comparable deterministic indices. We show that, under the proportional distribution mechanism, the equivalence between balancedness and core non-emptiness is not unconditional. Rather, it can be recovered only under additional structural assumptions, especially homogeneous preferences and positivity of evaluated coalition values. These results clarify the boundary under which fixed proportional sharing can support stable cooperation in stochastic cooperative games. Full article

This paper presents a cooperative trajectory planning method for multiple aircraft avoiding thunderstorms, formulated within a game-theoretic optimal control framework. We model the multi-aircraft system as a non-cooperative game and employ an Iterative Best Response (IBR) algorithm to decompose the coupled planning problem into a series of single-agent, nonlinear optimal control subproblems. Each subproblem is solved using the CasADi framework, enabling the continuous and simultaneous optimization of both aircraft velocity and heading. This approach directly generates smooth, dynamically feasible 4D trajectories that satisfy strict on-time arrival constraints at each waypoint, addressing a key limitation of many existing methods. Our simulations show that the framework not only ensures safe separation from thunderstorms and other aircraft but also effectively manages arrival times, with errors on the order of seconds. These results demonstrate the method’s capability to produce safe, efficient, and punctual trajectories for complex multi-aircraft encounters in dynamic weather. Full article

We present a review on the application of the mathematical models for research on social processes, social structures, and actors in social systems. The scope of the review is not restricted to the classical applications of mathematics such as theory of probability, statistics, stochastic processes, differential equations, and game theory. We also discuss applications of the theory of networks for social network analysis and the numerical research on dynamics of social systems. The number of these applications has increased very fast in recent years. Special attention is given to the results from the area of sociophysics, where mathematical methodology is used to analyze social systems in cooperation with the models and concepts of physics. Another special topic in his review is connected to the results from econophysics, where the mathematical methodology and theories and methods of physics are used in the studies on the dynamics of economic systems. In addition, we give several examples for the application of mathematical methods to social systems: (a) application of difference equations to model the flow of substances in channels of networks; (b) analytical solution of nonlinear equations connected to the model of waves of popularity; (c) numerical results of the waves of popularity in a model that accounts for the change in the opinion of the supporters of the ideas for positive or negative popularity of a person, material item, or a piece of information (idea, theory, ideology, etc.) In the last case, we illustrate the effectiveness of the numerical analysis to discover new effects on the studied social system. The review ends with a large list of references. These references can be used as a guide of the way of new researchers to the large field of mathematical social dynamics. Full article

The aim of the study was to assess changes in athletes’ opinions on medical care in Polish Paralympic sport in 2004–2024 in the context of the evolution of the national legal framework. Against this background, to identify potential discrepancies between formal guarantees and functional access, the study analysed: (i) the evolution of Polish legal and organisational solutions governing medical care for Polish Paralympic athletes, and (ii) the longitudinal change in the opinions of Polish Paralympic athletes concerning the availability and quality of care in 2004–2024. The scope of the national legal framework was limited to statutory acts and regulations adopted by Polish institutions, understood as primary legal sources; the exegesis of normative material was supplemented with relevant documents from the legislative process. A total of n = 522 athletes with visual and locomotor impairments were examined, representing 97.4% of all Polish representatives who participated in the Summer Paralympic Games between 2004 and 2024. The study used a diagnostic survey protocol employing a questionnaire, as well as descriptive statistics, chi-square tests, and Student’s t-tests. The results indicate a clear increase in the percentage of athletes declaring participation in regular preventive examinations, as well as a significant improvement in evaluations of cooperation with physicians and physiotherapists when comparing 2004 with the period 2012–2024. At the same time, empirical data demonstrate that the introduction of legal solutions does not ensure full access to specialised medical care, and that the formal establishment of obligations and procedures does not automatically translate into the immediate adaptation of organisational practices. Full article

Uncertain dynamic games have recently emerged as a rigorous and versatile framework for the analysis and synthesis of multi-agent decision-making processes in complex, stochastic, and dynamically evolving environments. By integrating foundational concepts from dynamic game theory with neural network-based function approximation techniques, these methodologies facilitate the development of adaptive, data-driven strategies for agents whose interactions unfold over time and are subject to both state and control constraints. Notwithstanding these advances, practical implementations are invariably influenced by model inaccuracies, exogenous disturbances, and parametric uncertainties, all of which may substantially impair system performance and jeopardize stability if left unmitigated. In this context, the present study examines dynamic game formulations defined on perturbed and uncertain system models, explicitly incorporating state and control constraints, with the objective of ensuring robustness and reliability in both competitive and cooperative settings. We consider a broad class of nonlinear dynamic games characterized by system dynamics affected by unknown disturbances and uncertain parameters. Within this framework, Dynamic Neural Networks (DNNs) are employed to approximate feasible solutions to the associated robust control problem, thereby enabling the characterization of $\epsilon$-Nash equilibria through learning mechanisms driven by worst-case trajectory realizations. A comprehensive theoretical analysis is developed to elucidate the effects of perturbations and uncertainties on equilibrium existence, convergence behavior, and closed-loop stability properties. Furthermore, sufficient conditions are established under which the neural learning dynamics ensure boundedness and convergence to approximate Nash or saddle-point equilibria, despite the presence of modeling imperfections. The proposed framework effectively synthesizes principles from robust control theory and learning-based game-theoretic approaches, yielding formal guarantees that are often absent in purely data-driven methodologies. Finally, numerical simulations conducted on representative dynamic game scenarios substantiate the efficacy of the proposed approach, demonstrating enhanced robustness relative to nominal neural game formulations. These findings contribute to the advancement of dependable dynamic game architectures, with potential applications spanning autonomous systems, robotics, and networked control systems operating under uncertainty. Full article

This study systematically explores the underlying mechanisms of collaborative innovation driving the green transformation of traditional energy enterprises. Existing research primarily focuses on enterprise scale and overall competitiveness, rarely delving into these specific collaborative pathways. Furthermore, studies employing evolutionary game theory to analyze the tripartite relationship among the government, traditional energy, and emerging technology enterprises remain fragmented, failing to fully capture the dynamic mechanisms of multi-stakeholder strategic choices. To bridge these gaps, this paper constructs a tripartite evolutionary game model incorporating coordination costs and the benefit distribution ratio to explore their influence mechanisms. Replicator dynamics equations are employed to identify stable cooperation conditions, overcoming traditional two-party framework constraints. Additionally, MATLAB R2024b numerical simulations validate the theoretical findings. The results reveal two evolutionarily stable equilibrium points. First, higher initial willingness among participants accelerates the system’s evolution toward a stable cooperative state. Second, coordination costs induced by information asymmetry act as a core bottleneck that deters participation and risks collaborative collapse. Third, targeted government incentives and a rational benefit distribution ratio directly determine cooperation willingness; notably, enterprises adopt collaborative strategies only when this ratio falls between 0.27 and 0.69. Fourth, fair and transparent supervision is crucial for mitigating trust deficits and distribution disputes. Ultimately, scientifically designing incentives, optimizing benefit structures, promoting information sharing, and establishing robust supervision effectively facilitate a sustainable tripartite collaborative innovation pattern. Full article

Many engineering problems must account for the non-cooperative decisions and actions of multiple players. These problems can be modeled within a game-theoretic framework. The approach herein is to model such problems as mathematical games, convert them to semi-infinite programs, and utilize a semi-infinite program solver whose output is provably an $ϵ$-optimal Nash equilibrium. The approach is successfully benchmarked on two low-dimensional problems. Two types of higher-dimensional linear quadratic dynamic games are then investigated: ones where each player’s problem is convex and ones where at least one player’s problem is nonconvex. Within each type, variations based on information structure, control constraints, number of players, and semi-infinite objective are considered. The algorithm is tested with different internal solvers, and it successfully solves all test problems using MATLAB’s fmincon. The numerical solutions approximate analytical solutions (when they are known) within approximately one percent. For a three-player game with input saturation constraints, hundreds of variables, and no analytical solution, the computational time is approximately five minutes. Full article

A clean and efficient rural energy system is essential for building a modern energy system and for accelerating the transition to renewable energy in rural areas. Therefore, a robust collaborative optimal scheduling method for rural integrated energy systems is proposed, incorporating multi-agent gaming. First, a three-layer cooperative structure is developed based on current rural energy consumption patterns. Second, a scheduling model is formulated using potential game theory, with the objective of maximizing the overall benefits of all parties. The model also accounts for multi-energy complementarity, demand response, and multiple uncertainties, leading to a robust optimal scheduling framework based on information gap decision theory. The resulting problem is solved using a chicken swarm optimization algorithm improved by Lévy flight. Finally, a case study of the three-layer cooperative optimization model is presented. The results show that multi-energy complementarity can increase local renewable energy consumption and improve the economic efficiency of diverse energy use for rural consumers. Information gap decision theory helps balance economic and uncertain factors and supports decision-making for agents with different risk preferences. Full article

Environmental co-governance depends not only on the local stability of collaboration but also on whether ENGO-based collaborative participation is attainable from a broad range of initial conditions. This study develops a tripartite evolutionary game model involving local governments, environmental NGOs (ENGOs), and the public, and uses basin-of-attraction analysis to examine the global attainability of high-participation environmental co-governance. The model combines replicator dynamics, Jacobian-based local stability analysis, threshold conditions, numerical simulation, and basin-of-attraction estimation. The results show that collaborative stability is conditional: high-participation co-governance emerges only when institutional support, ENGO participation incentives, and public cooperation conditions jointly exceed critical thresholds. Institutional support is more effective when it improves coordination capacity and reduces implementation friction, whereas unconditional subsidies have ambiguous effects because they increase ENGO incentives while also reducing the government’s relative payoff from strong support. Public cooperation is especially sensitive to participation burden and targeted incentives, while higher passive payoffs for ENGOs enlarge low-participation traps. The analysis is theoretical and simulation-based, informed by China’s institutionally bounded ENGO context, and is not intended as an empirically calibrated prediction for a specific locality. The findings suggest that durable environmental co-governance requires coordinated institutional arrangements that jointly strengthen governmental support, ENGO participation incentives, and public cooperation conditions. Full article

Collaborative 3D path planning for multiple unmanned aerial vehicles (UAVs) in dense urban airspace is difficult, which does not come from one factor alone. Buildings, flight restrictions, moving obstacles, and inter-UAV coupling all act together, and the search space grows quickly as the scene becomes more crowded. In such cases, a standard swarm optimizer may still find a path, but it often struggles with early feasibility, later-stage refinement, and local replanning after the environment changes. To deal with these issues, this paper develops a spatio-temporal collaborative improved multi-strategy dung beetle optimization algorithm, called STC-IMSDBO, for urban multi-UAV path planning. The framework combines five linked components: feasible-airspace population initialization, spatio-temporal variable-step search, multi-factor adaptive weighting, local game-based conflict handling, and rolling-horizon replanning. A normalized multi-objective cost is used to balance flight efficiency, smoothness, obstacle avoidance, airspace compliance, and cooperative safety. The method is tested in four simulated urban scenarios and compared with six representative methods. In the tested cases, the STC-IMSDBO generates shorter feasible routes, uses less energy, converges in fewer iterations, and maintains better cooperative safety than the comparison methods. These results suggest that the method is a useful planning option for dense urban missions such as logistics, inspection, and emergency response. That said, larger-swarm runtime tests and field validation are still needed. Full article

We study a continuous-time cooperative differential game of pollution control in which the pollution stock accumulates emissions and affects long-run welfare. The key feature is a one-time random increase in the public damage weight, interpreted as a regime shift in environmental policy, social damage assessment, or regulatory pressure. Using dynamic programming, we characterize the grand-coalition feedback solution from the Hamilton–Jacobi–Bellman equations and derive closed-form expressions for cooperative emissions, pollution dynamics, regime-specific steady states, and transition paths. Under emission caps, we construct the coalition characteristic function using a conservative worst-case benchmark for outsider behavior rather than an unlimited-pollution assumption. For payoff allocation, we derive a dynamic payment schedule that implements the Shapley allocation along the stochastic pollution path and keeps the remaining payoff consistent with the corresponding continuation game. Finally, we extend the framework to a threshold-triggered shifted-exponential switching mechanism. This extension gives a computable objective for the optimal threshold-hitting time and clarifies how the pollution threshold and switching hazard can be interpreted as policy-relevant indicators of regulatory or ecological regime change. Full article

The interception of saturation incursions by Unmanned Aerial Vehicle (UAV) swarms presents critical challenges in multi-agent coordination, including the curse of dimensionality, heterogeneous interaction effects, and multi-scale decision-making requirements. This paper proposes a Hierarchical Multi-scale Mean-Field DDPG (HM-MF-DDPG) framework augmented by graph sampling and aggregation networks to address these challenges. The framework introduces three key innovations: (1) a graph-enhanced weighted mean-field approximation that employs attention mechanisms to dynamically assess the contextual importance of neighboring agents, overcoming the homogeneity limitation of conventional mean-field methods; (2) a hierarchical decision architecture that separates strategic coordination (via graph attention networks) from low-level flight control (via improved gated recurrent units with situational awareness modulation); and (3) a distributed target assignment mechanism formulated as a potential game and solved via parallel auction algorithms, enabling collision-free allocation without central coordination. Extensive simulations in a constructed UAV swarm interception environment demonstrate that the proposed framework achieves a 93% interception success rate with 50 interceptors against 25 intruders, outperforming Deep Deterministic Policy Gradient (DDPG) and Mean-Field DDPG (MF-DDPG) baselines in both convergence speed and task efficiency. The framework exhibits robust generalization across varying No-Fly Zone (NFZ) configurations and swarm scales, providing a scalable solution for cooperative interception under saturation incursions. Full article