Search Results (225)

The integration of renewable energy into the grid has led to problems such as low utilization rate of energy storage resources (“underutilization after construction”) and insufficient system stability. This paper studied the co-evolution mechanism of power market entities empowered by shared energy storage. Based on the interaction among power generation enterprises, power grid operators, and government regulatory agencies, this paper constructed a three-party evolutionary game model. The model introduced a dynamic reward and punishment mechanism as well as a random interference mechanism, which makes it more in line with the actual situation. The stability conditions of the game players were analyzed by using stochastic differential equations, and the influences of key parameters and incentive mechanisms on the stability of the game players were investigated through numerical simulation. The main research results showed the following: (1) The benefits of shared energy storage and opportunistic gains had a significant impact on the strategic choices of power generation companies and grid operators. (2) The regulatory efficiency had significantly promoted the long-term stable maintenance of the system. (3) Dynamic incentives were superior to static incentives in promoting cooperation, while the deterrent effect of static penalties is stronger than that of dynamic penalties. (4) The increase in the intensity of random disturbances led to strategy oscillation. This study suggested that the government implement gradient-based dynamic incentives, maintain strict static penalties to curb opportunism, and enhance regulatory robustness against uncertainty. This research provided theoretical and practical inspirations for optimizing energy storage incentive policies and promoting multi-subject coordination in the power market. Full article

As supply chains rapidly digitize, platform-driven models have become central to global commerce, requiring sophisticated mathematical modeling for optimization. This systematic review comprehensively analyzes research across six critical technological domains in platform supply chains (PSCs): blockchain integration, Internet of Things applications, Industry 4.0 systems, cloud computing, live streaming commerce, and generative artificial intelligence. Our analysis finds that operational coordination and strategic decision-making under information asymmetry represent primary research focuses, with pricing strategies receiving predominant attention. Methodologically, game theory, particularly Stackelberg models, emerges as the dominant optimization framework across all domains. However, significant gaps remain in dynamic modeling capabilities, empirical validation of theoretical frameworks, and cross-technology integration. This review provides foundational insights into mathematical optimization techniques and highlights the critical need for incorporating stochastic approaches and real-world data to advance PSC management in the digital era. Full article

This study investigates collaborative disaster response strategies involving the government and social organizations from a dynamic perspective, incorporating stochastic disturbances that influence emergency resource supply. To examine the strategic interactions among the participants, three stochastic differential game models are formulated under distinct scenarios: centralized decision making for collusive emergency response, decentralized emergency response without a cost-sharing contract, and decentralized emergency response with a cost-sharing contract. Under an infinite-horizon planning framework, the closed-form solutions for the optimal response efforts and the corresponding value functions are derived for all three scenarios and comparatively analyzed. The results indicate that compared with the purely decentralized scenario, introducing a cost-sharing mechanism achieves a Pareto improvement by optimizing both overall system efficiency and emergency supply availability. Although the centralized collusive model results in the highest expected level of emergency resource supply, it is also associated with the greatest uncertainty. Furthermore, a numerical simulation based on emergency resource allocation during the Wenchuan earthquake is conducted. The results show significant differences in resource availability and response performance under different response mechanisms. Centralized collaboration, together with a well-designed cost-sharing mechanism, can significantly enhance the robustness and efficiency of the overall system, offering important insights for optimizing real-world disaster response strategies. Full article

This paper examines stochastic cooperation in markets with two sellers who exhibit one-sided dependency. The independent seller’s pricing influences the dependent seller’s demand, but not vice versa. We study the one-dimensional hybrid game class whose parameter is the exogenously given probability of cooperation. In each game of this class, both sellers simultaneously choose prices that determine their endogenous threats, i.e., conflict profits. The sellers are aware of the cooperation probability but cannot condition prices on whether or not there is cooperation. We characterize the equilibrium prices and the sellers’ expected profits. Our main result shows that the independent seller earns higher expected profits when cooperation is more likely. In contrast, the dependent seller earns lower expected profits when the likelihood of cooperation is below a threshold that we characterize explicitly, and higher profits are earned thereafter. These findings suggest that, within our framework, antitrust concerns may be mitigated. Since dependent sellers can incur losses from cooperation, collusion attempts become less viable in markets with one-sided dependency. Full article

This paper investigates a repeated stochastic security game against a non-stationary attacker. Most of the work to date assumes that the defender has a repeated interaction with a fixed type of attacker. In fact, the defender is more likely to encounter changing attackers in multi-round games. A defender faces an attacker whose identity is unknown. The attacker type changes stochastically over time and the defender cannot detect when these changes occur. We adopt the BPR (Bayesian Policy Reuse) algorithm to detect the switches of the attacker, and the defender could play the accurate policy correspondingly. The experiment results show that BPR algorithm could accurately detect switches and help the defender gain more utilities than the EXP3-S algorithm. Full article

As the global carbon neutrality process accelerates, the proportion of distributed power sources such as wind power and photovoltaic power continues to increase. This transformation, while promoting the development of clean energy, also brings about the issue of new energy consumption. As wind and solar distributed generation rapidly expands into modern power grids, consumption issues become increasingly prominent. In this paper, a robust optimal scheduling method considering multiple uncertainties is proposed for community microgrids containing multiple renewable energy sources based on potential games. Firstly, the flexible loads of community microgrids are quantitatively classified into four categories, namely critical base loads, shiftable loads, power-adjustable loads, and dispersible loads, and a stochastic model is established for the wind power and load power; secondly, the user’s comprehensive electricity consumption satisfaction is included in the operator’s scheduling considerations, and the user’s demand is quantified by constructing a comprehensive satisfaction function that includes comfort indicators and economic indicators. Further, the flexible load-response expectation uncertainty and renewable generation uncertainty model are used to establish a robust optimization uncertainty set. This set portrays the worst-case scenario. Based on this, a two-stage robust optimization framework is designed: with the dual objectives of minimizing operator cost and maximizing user satisfaction, a potential game model is introduced to achieve a Nash equilibrium between the interests of the operator and the users, and solved by a column and constraint generation algorithm. Finally, the rationality and effectiveness of the proposed method are verified through examples, and the results show that after optimization, the cost dropped from CNY 2843.5 to CNY 1730.8, a reduction of 39.1%, but the user satisfaction with electricity usage increased to over 98%. Full article

This paper suggests a theoretical framework to summarise the empirical literature on the relationships between sports and both religious and secular ethics, and it suggests two interrelated theoretical models to empirically evaluate the extent to which religious and secular ethics, as well as sports policies, affect achievements in sports. I identified two national ethics (national pride/efficiency) and two social ethics (social cohesion/ethics) by measuring achievements in terms of alternative indexes based on Olympic medals. I referred to three empirical models and applied three estimation methods (panel Poisson, Data Envelopment, and Stochastic Frontier Analyses). I introduced two sports policies (a quantitative policy aimed at social cohesion and a qualitative policy aimed at national pride), by distinguishing sports in terms of four possibly different ethics to be used for the eight summer and eight winter Olympic Games from 1994 to 2024. I applied income level, health status, and income inequality, to depict alternative social contexts. I used five main religions and three educational levels to depict alternative ethical contexts. I applied country dummies to depict alternative institutional contexts. Empirical results support the absence of Olympic ethics, the potential substitution of sport and secular ethics in providing social cohesion, and the dependence of sports on politics, while alternative social contexts have different impacts on alternative sport achievements. Full article

With the increase in urban–rural disparities in China, rural public transportation systems in low-density areas face unique challenges, especially in the contexts of sparse population, complex topography, and uneven resource allocation; research on public transportation in low-density areas has had less attention compared to high-density urban areas. Therefore, how to solve the dilemma of public transportation service provision in low-density rural areas due to sparse population and long travel distances has become an urgent problem. In this paper, a dynamic optimization model based on a two-layer planning framework was constructed. The upper layer optimized the topology of multimodal transportation nodes through the Floyd shortest path algorithm to generate a composite network of trunk roads and feeder routes; the lower layer adopted an improved Logit discrete choice model, integrating the heterogeneous utility parameters, such as time cost, economic cost, and comfort, to simulate and realize the equilibrium allocation of stochastic users. It was found that the dynamic game mechanism based on the “path optimization–fairness measurement” can optimize the travel time, mode, route, and bus stop selection of rural residents. At the same time, the mechanism can realize the fair distribution of rural transportation network subjects (people–vehicles–roads). This provides a dynamic, multi-scenario macro policy reference basis for the optimization of a rural transportation network layout. Full article

This paper proposes a two-stage stochastic non-cooperative game model to solve relief supplies procurement and distribution optimization of multiple rescue organizations in crisis rescue. Rescue organizations with limited budgets minimize rescue costs through relief supply procurement, storage, and transportation in an uncertain environment. Under a mild assumption, we establish the existence and uniqueness of the equilibrium point and derive the optimality conditions by using the duality theory, characterizing the saddle point in the Lagrange framework. The problem is further reformulated as a constraint system governed by Lagrange multipliers, and its optimality is characterized by the Karush–Kuhn–Tucker condition. The economic interpretation of the multipliers as shadow prices is elucidated. Numerical experiments verify the effectiveness of the model in cost optimization in crisis rescue scenarios. Full article

Biological systems, ranging from ant colonies to neural ecosystems, exhibit remarkable self-organizing intelligence. Inspired by these phenomena, this study investigates how bio-inspired computing principles can bridge game-theoretic rationality and multi-agent adaptability. This study systematically reviews the convergence of multi-agent reinforcement learning (MARL) and game theory, elucidating the innovative potential of this integrated paradigm for collective intelligent decision-making in dynamic open environments. Building upon stochastic game and extensive-form game-theoretic frameworks, we establish a methodological taxonomy across three dimensions: value function optimization, policy gradient learning, and online search planning, thereby clarifying the evolutionary logic and innovation trajectories of algorithmic advancements. Focusing on complex smart city scenarios—including intelligent transportation coordination and UAV swarm scheduling—we identify technical breakthroughs in MARL applications for policy space modeling and distributed decision optimization. By incorporating bio-inspired optimization approaches, the investigation particularly highlights evolutionary computation mechanisms for dynamic strategy generation in search planning, alongside population-based learning paradigms for enhancing exploration efficiency in policy refinement. The findings reveal core principles governing how groups make optimal choices in complex environments while mapping the technological development pathways created by blending cross-disciplinary methods to enhance multi-agent systems. Full article

To facilitate power system decarbonization, optimizing clean energy integration has emerged as a critical pathway for establishing sustainable power infrastructure. This study addresses the multi-timescale operational challenges inherent in power networks with high renewable penetration, proposing a novel stochastic dynamic programming framework that synergizes intraday microgrid dispatch with a multi-phase carbon cost calculation mechanism. A probabilistic carbon flux quantification model is developed, incorporating source–load carbon flow tracing and nonconvex carbon pricing dynamics to enhance environmental–economic co-optimization constraints. The spatiotemporally coupled multi-microgrid (MMG) coordination paradigm is reformulated as a continuous state-action Markov game process governed by stochastic differential Stackelberg game principles. A communication mechanism-enabled multi-agent twin-delayed deep deterministic policy gradient (CMMA-TD3) algorithm is implemented to achieve Pareto-optimal solutions through cyber–physical collaboration. Results of the measurements in the MMG containing three microgrids show that the proposed approach reduces operation costs by 61.59% and carbon emissions by 27.95% compared to the least effective benchmark solution. Full article

Mobile edge computing was conceived to address the increasing computing demand generated by users at the communication network edge. It is expected to play a significant role in next-generation (5G, 6G, and beyond) communication systems as new applications such as augmented/extended reality, teleoperations, telemedicine, and gaming become prolific. As the networks become denser, more and more edge servers are expected to be deployed, and the question of task offloading becomes more complicated. In this study, we present a framework for task offloading in the presence of multiple edge servers that employ round-robin task scheduling. Most studies in the literature attempt to optimize the offloading process under the assumption that each user generates just a single task, or they generate one task every time slot in a discrete-time system where all the tasks are handled within a slot. Furthermore, first-come-first-served queueing models are typically used in studies where queueing is considered at all. The work presented is novel in that we assume continuous and stochastic task arrivals generated by multiple users and round-robin task scheduling at the edge servers. This setting is considerably more realistic with respect to the existing works, and we demonstrate through extensive simulations that round-robin task scheduling significantly reduces task delay. We also present a comparison of a number of server selection mechanisms. Full article

Marine oil spills significantly adversely affect the socio-economic environment and marine ecosystems. Establishing an efficient emergency cooperation mechanism that enables swift and coordinated responses from all stakeholders is crucial to mitigate the harmful consequences of such spills and protect regional security. This study uses stochastic evolutionary game theory to develop an emergency cooperation model, focusing on the strategic interactions and dynamic evolution between three main parties: the local government, port enterprises, and specialized oil spill cleanup units. The findings indicate the following: (1) The strategy choice of the local government plays a dominant role in the three-party game and has a significant guiding effect on the behavioral decisions of port enterprises and specialized oil spill cleanup units. (2) The strength of the government’s reward and punishment mechanism directly affects the cooperation tendency of the port enterprises and specialized oil spill cleanup units. (3) When the emergency response is more efficient and the cooperation effect is significant, the cleanup units may choose negative cooperation based on payoff maximization in order to prolong the cleaning time. (4) In the process of system evolution, the strategies of local governments and port enterprises are more stable and less affected by random perturbations, while the strategy fluctuations of cleanup units are more sensitive. The findings enrich the theoretical framework for handling marine oil spill emergencies and provide valuable insights for developing efficient collaborative mechanisms and formulating well-grounded regulatory incentive policies. Full article

The construction industry’s small and medium-sized enterprises (SMEs) face significant financial difficulties, exacerbated by disruptions such as COVID-19. Traditional supply chain finance models, relying on core enterprise credit, fail to address the dynamic nature of this sector. This study proposes a novel approach to value co-creation among stakeholders (core enterprises, suppliers, and financial institutions) through an evolutionary game theory framework. A stochastic model was developed to examine the strategic decisions of these parties, considering risk, penalty, and incentive coefficients. The results reveal that higher incentives encourage faster participation, while financial institutions are less sensitive to risk and penalty changes. This study provides new insights into promoting cooperative behavior and enhancing the sustainability of small and medium-sized enterprises (SMEs) in the construction industry through platform-based models. Full article

Stochastic vibration control of uncertain structures under random loading is an important problem and its minimax optimal control strategy remains to be developed. In this paper, a stochastic optimal control strategy for uncertain structural systems under random excitations is proposed, based on the minimax stochastic dynamical programming principle and the Bayes optimal estimation method with the combination of stochastic dynamics and Bayes inference. The general description of the stochastic optimal control problem is presented including optimal parameter estimation and optimal state control. For the estimation, the posterior probability density conditional on observation states is expressed using the likelihood function conditional on system parameters according to Bayes’ theorem. The likelihood is replaced by the geometrically averaged likelihood, and the posterior is converted into its logarithmic expression to avoid numerical singularity. The expressions of state statistics are derived based on stochastic dynamics. The statistics are further transformed into those conditional on observation states based on optimal state estimation. Then, the obtained posterior will be more reliable and accurate, and the optimal estimation will greatly reduce uncertain parameter domains. For the control, the minimax strategy is designed by minimizing the performance index for the worst-parameter system, which is obtained by maximizing the performance index based on game theory. The dynamical programming equation for the uncertain system is derived according to the minimax stochastic dynamical programming principle. The worst parameters are determined by the maximization of the equation, and the optimal control is determined by the minimization of the resulting equation. The minimax optimal control by combining the Bayes optimal estimation and minimax stochastic dynamical programming will be more effective and robust. Finally, numerical results for a five-story frame structure under random excitations show the control effectiveness of the proposed strategy. Full article