Search Results (583)

Efficient resource allocation is a central challenge in multi-tenant cloud, fog, and edge environments, where heterogeneous tenants compete for shared resources under dynamic and uncertain workloads. Static or purely heuristic methods often fail to capture strategic tenant behavior, whereas many existing game-theoretic approaches overlook stochastic demand variability, fairness, or scalability. This paper proposes a Dynamic and Stochastic Game-Theoretic Allocation (DSGTA) model that jointly models non-cooperative tenant interactions, repeated strategy adaptation, and random workload fluctuations. The framework combines a Nash-like dynamic equilibrium, achieved via a lightweight best-response update rule, with an approximate Shapley-value-based fairness mechanism that remains tractable for large tenant populations. The model is evaluated on synthetic scenarios, with a trace-driven setup built from the Google 2019 Cluster dataset, and a scalability study is conducted with up to $K=500$ heterogeneous tenants. Using a consistent set of core metrics (tenant utility, resource cost, fairness index, and SLA satisfaction rate), DSGTA is compared against a static game-theoretic allocation (SGTA) and a dynamic pricing-based allocation (DPBA). The results, supported by statistical significance tests, show that DSGTA achieves higher utility, lower average cost, improved fairness and competitive utilization across diverse strategy profiles and stochastic conditions, thereby demonstrating its practical relevance for scalable, fair, and economically efficient resource allocation in realistic multi-tenant cloud environments. Full article

To address the challenges of renewable energy curtailment under normal conditions and severe power outages under extreme scenarios, this paper proposes a hydrogen-integrated comprehensive energy system (H-IES) configuration method aimed at enhancing the resilience of distribution networks. The proposed method improves energy utilization efficiency while achieving a balance between economic performance and resilience. First, an operational model of the H-IES is established considering the operating characteristics of distribution networks under extreme conditions. On this basis, a Nash bargaining-based equilibrium model is developed, where economic performance and resilience act as game participants negotiating toward equilibrium. By applying the particle swarm optimization algorithm, the Nash equilibrium solution is obtained, realizing a Pareto-optimal trade-off between the two objectives. Finally, case studies demonstrate that the proposed configuration improves the resilience index by 3.13% and reduces total cost by 10.86% compared with mobile battery energy storage. Under the Nash bargaining framework, the equilibrium configuration increases renewable energy utilization and provides up to 21.6% higher resilience compared with an economy-only optimization scheme. Full article

As data product transactions become increasingly standardized, the operational strategies of data product manufacturers and service providers play a pivotal role in shaping market outcomes. This study develops a game-theoretic framework that incorporates dynamic data updates under alternative power structures to examine the equilibrium performance of pricing, demand, technological investment, update rates, and promotional effort. The results indicate that optimal prices under Stackelberg leadership exceed those in the Nash game, whereas demand, technological investment, update frequency, and promotion are consistently higher in the Nash setting. The effects of these decisions are moderated by end-user preference heterogeneity: when users exhibit stronger promotion preferences, service-provider leadership generates superior outcomes, while stronger quality preferences favor manufacturer leadership. Demand preferences and cost coefficients significantly influence profitability—enhanced preferences improve the leader’s returns, whereas high technological and promotional costs suppress profits for both parties. Cost savings in dynamic updates and increases in perceived value exert strong positive effects on market competitiveness, while higher update investment and data acquisition costs exert negative effects. Overall, this study deepens the theoretical understanding of how power structures interact with dynamic updating and user preferences, providing analytical insights and decision support for optimizing operational strategies in data product markets. Full article

In China’s on-demand service platforms, daigou agents utilize locational differences through proxy purchasing. Daigou creates an informal supply chain that directly competes with official channels. This study incorporates daigou arbitrage into the channel competition framework via a multi-stage Stackelberg game-theoretic model. An analysis of the subgame perfect Nash equilibrium shows that daigou activity disrupts the manufacturer’s profits. We have thus developed a strategy based on mathematical optimization and compared its effectiveness and side effects with those of existing methods. We came to identify purchase restrictions as one of the most powerful strategies. Equilibrium analysis and numerical experiments confirm that proper purchase restriction choices reduce daigou arbitrage and minimize negative impacts on legitimate demand. This work provides the first game-theoretic model that integrates informal proxy-purchase supply chains into dual-channel competitions. Full article

Green co-creation plays a vital role in promoting sustainability by engaging both firms and consumers in value creation, yet most studies examine competition and cooperation separately without considering their interplay. This study investigates the dynamics of coopetition in green co-creation by developing a two-stage biform game that integrates competitive interaction and cooperative bargaining within a unified framework. The results show that (1) greater green co-creation efforts, representing deeper firm–customer interactions, improve both parties’ equilibrium outcomes; (2) cooperation leads to greater green effort investment than pure competition; and (3) when Nash bargaining conditions are satisfied, coopetition improves both individual profits and total welfare compared with sole competition. These findings highlight that coopetition not only strengthens mutual economic benefits, but also enhances sustainability performance by balancing competitive and cooperative forces. This study provides an analytical foundation for understanding firm–customer coopetition and offers actionable insights for advancing sustainable value creation in green supply chain management. Full article

This paper addresses the retail pricing problem for electricity retailers who also act as virtual power plant (VPP) operators, aggregating distributed energy resources (DERs). In future power markets where multiple such retailers compete for customers, a key challenge is to design pricing strategies that balance economic profitability with low-carbon objectives. Existing research often overlooks the impact of retailers’ heterogeneous resource portfolios, particularly the share of low-carbon resources like photovoltaics (PVs), on their competitive advantage and pricing decisions. To bridge this gap, we propose a novel retail pricing model that integrates a non-cooperative game framework with Markov Decision Processes (MDPs). The model enables each retailer to formulate optimal real-time pricing strategies by anticipating competitors’ actions and customer responses, ultimately reaching a Nash equilibrium. A distinctive feature of our approach is the incorporation of spatially differentiated carbon emission factors, which are adjusted based on each retailer’s share of PV generation. This creates a tangible low-carbon incentive, allowing retailers with greener resource mixes to leverage their environmental advantage. The proposed framework is validated on a modified IEEE 30-bus system with six competing retailers. Simulation results demonstrate that our method effectively incentivizes optimal load distribution, alleviates network congestion, and improves branch loading indices. Critically, retailers with a higher share of PV resources achieved significantly higher profits, directly translating their low-carbon advantage into economic value. Notably, the Branch Load Index (BLI) was reduced by 12% and node voltage deviations were improved by 1.32% at Bus 12, demonstrating the model’s effectiveness in integrating economic and low-carbon objectives. Full article

Small and Medium-sized Enterprises (SMEs) face disproportionately high risks from Advanced Persistent Threats (APTs), which often evade traditional cybersecurity measures. Existing frameworks catalogue adversary tactics and defensive solutions but provide limited quantitative guidance for allocating limited resources under uncertainty, a challenge amplified by the growing use of AI in both offensive operations and digital forensics. This paper proposes a game-theoretic model for improving digital forensic readiness (DFR) in SMEs. The approach integrates the MITRE ATT&CK and D3FEND frameworks to map APT behaviors to defensive countermeasures and defines 32 custom DFR metrics, weighted using the Analytic Hierarchy Process (AHP), to derive utility functions for both attackers and defenders. The main analysis considers a non-zero-sum attacker–defender bimatrix game and yields a single Nash equilibrium in which the attacker concentrates on Impact-oriented tactics and the defender on Detect-focused controls. In a synthetic calibration across ten organizational profiles, the framework achieves a median readiness improvement of 18.0% (95% confidence interval: 16.3% to 19.7%) relative to pre-framework baselines, with targeted improvements in logging and forensic preservation typically reducing key attacker utility components by around 15–30%. A zero-sum variant of the game is also analyzed as a robustness check and exhibits consistent tactical themes, but all policy conclusions are drawn from the empirical non-zero-sum model. Despite relying on expert-driven AHP weights and synthetic profiles, the framework offers SMEs actionable, equilibrium-informed guidance for strengthening forensic preparedness against advanced cyber threats. Full article

This paper pioneers the introduction of nabla fractional calculus into distributed Nash equilibrium (NE) seeking for non-cooperative games (NGs), proposing several novel discrete-time fractional-order algorithms. We first develop a gradient play-based algorithm under perfect information and subsequently extend it to partial-information settings. Two types of communication network topologies among agents, namely connected undirected graphs and strongly connected unbalanced directed graphs, are explicitly considered. When the pseudo-gradient mapping of the NG is Lipschitz continuous and strongly monotone, the proposed algorithms are proven to achieve asymptotic convergence to the NE with at least a Mittag–Leffler convergence rate. Both the step size and the fractional order act as tunable parameters that jointly influence the convergence performance. Numerical experiments on potential games and Nash–Cournot games demonstrate the effectiveness of the proposed algorithms. Full article

Understanding the success of romantic relationships remains a complex scientific challenge with significant implications for modern Western societies. In particular, the mechanisms underlying successful relationships—those that are both long-term and emotionally fulfilling—are still not fully understood, especially regarding the role of psychological and environmental factors in shaping their evolution. This gap is partly due to the limited availability of long-term data on marital quality. In this paper, we use a differential game model to replicate the long-term dynamics of successful relationships. We analytically characterize how variations in each partner’s subjective evaluation of emotional rewards and costs influence key relational outcomes, such as equilibrium effort levels, overall happiness, and relationship quality. Through numerical simulations, we further explore how asymmetries in emotional processing between partners affect optimal effort policies and individual happiness. Notably, our results suggest that one’s own emotional traits exert a stronger influence on relationship satisfaction than those of one’s partner, aligning with findings from relationship science. Full article

We investigate a susceptible–exposed–infected–recovered $\left(SEIR\right)$ epidemic model that distinguishes between two subpopulations: individuals favoring vaccination (pro-vaccination), represented by the compartments $(S_P,E_P,I_P,R_P)$, and those opposing vaccination (anti-vaccination), described by $(S_A,E_A,I_A,R_A)$. The two systems are interconnected through flows between the susceptible classes, capturing the possibility of individuals switching their vaccination strategy, as well as through transitions involving recovered individuals. This framework captures the behavioral interplay during an epidemic, where individuals may reconsider their strategies depending on infection prevalence and the perceived costs and benefits of vaccination versus infection. In the model, immunity may be acquired either through vaccination or after being infected, while waning immunity adds further complexity to individual decision-making. To study these dynamics, we embed the epidemiological system into an evolutionary game framework, where strategy adoption depends on infection levels and associated payoffs. Our analysis shows that, at Nash equilibrium, both pro- and anti-vaccination groups exhibit similar behavior. Numerical simulations further indicate that greater vaccination coverage mitigates the social dilemma, whereas higher rates of waning immunity intensify it. Full article

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. Full article

This paper investigates the leader–follower consensus problem for a class of second-order multi-agent systems. These systems are composed of both discrete-time and continuous-time subsystems and are governed by switching dynamics. Within the framework of a fixed directed topology involving multiple leaders, two control strategies are formulated. One applies separate control protocols to the continuous and discrete subsystems, while the other adopts an unified sampled-data control protocol. First, a multi-player game model is established based on the analysis and simulation of conflict behaviors among agents, and the existence of a unique Nash equilibrium(NE) for the system is proven. Then, based on the Nash equilibrium, a continuous–discrete-time game-based switching control system is formulated. Furthermore, the results confirm that the proposed system achieves consensus under both control strategies, even under arbitrary switching patterns. Finally, the performance of the approach is verified through numerical simulations. Full article

We propose a one-shot, non-cooperative mechanism that implements the core in a large class of public goods games. Players simultaneously choose conditional commitment functions, which are binding unilateral commitments that condition a player’s contribution on the contributions of others. We prove that the set of strong Nash equilibrium outcomes of this mechanism coincides exactly with the core of the underlying cooperative game. We further show that these core outcomes can be found via simple individual learning dynamics. Full article

Agricultural systems are complex social–ecological systems shaped by interactions among diverse stakeholders including governments, enterprises, farmers, consumers, and financial institutions. To examine policy-driven sustainability transitions, this study focuses on three principal actors—government regulatory agencies, agricultural enterprises, and farmers—whose strategic interactions critically determine transition outcomes. The aim is to drive agricultural systems toward sustainability in China. This study develops a three-party evolutionary game model involving the government, enterprises, and farmers to explore how policy-driven incentives influence sustainable development practices. The model incorporates both static and dynamic reward–punishment mechanisms, calibrated with empirical data, to examine behavioral dynamics across stakeholders. The results indicate that fluctuations in enterprise and government engagement contribute to instability in agricultural sustainability transitions. While static reward mechanisms mitigate peak fluctuations, they are insufficient to fully stabilize enterprise commitment, with actors oscillating between sustainable and conventional agricultural practices. Linear dynamic reward mechanisms offer partial stabilization but lack the capacity to maintain long-run Nash equilibrium. In contrast, nonlinear dynamic mechanisms effectively align stakeholder incentives, fostering a stable and enduring shift toward sustainable agricultural systems. This study underscores the importance of tailored dynamic strategies to build resilient agricultural systems with integrated sustainability objectives. Full article

The intelligent transformation of the wastewater treatment industry, as a core component of the modern environmental governance system, is of decisive significance for achieving sustainable development goals. This study focuses on the issue of multi-stakeholder collaborative governance in the intelligent transformation of the wastewater treatment industry, with differential game theory as the core framework. A tripartite game model involving the government, wastewater treatment enterprises, and digital twin platforms is developed to depict the dynamic interrelations and mutual influences of strategy choices, thereby capturing the coordination mechanisms among government regulation, enterprise technology adoption, and platform support in the transformation process. Based on the dynamic optimization properties of differential games, the Hamilton–Jacobi–Bellman (HJB) equation is employed to derive the long-term equilibrium strategies of the three parties, presenting the evolutionary paths under Nash non-cooperative games, Stackelberg games, and tripartite cooperative games. Furthermore, the Sobol global sensitivity analysis is applied to identify key parameters influencing system performance, while the response surface method (RSM) with central composite design (CCD) is used to quantify parameter interaction effects. The findings are as follows: (1) compared with Nash non-cooperative and Stackelberg games, the tripartite cooperative strategy based on the differential game model achieves global optimization of system performance, demonstrating the efficiency-enhancing effect of dynamic collaboration; (2) the most sensitive parameters are β, α, μ₃, and η₃, with β having the highest sensitivity index (ST_i = 0.459), indicating its dominant role in system performance; (3) significant synergistic enhancement effects are observed among α–β, α–μ₃, and β–μ₃, corresponding, respectively, to the “technology stability–benefit conversion” gain effect, the “technology decay–platform compensation” dynamic balance mechanism, and the “benefit conversion–platform empowerment” performance threshold rule. Full article