Search Results (615)

Uplink/downlink (UL/DL) decoupled access has emerged as a promising paradigm for heterogeneous cellular vehicle-to-everything (C-V2X) networks in beyond 5G (B5G) and 6G systems. In multi-operator scenarios, wireless service provider (WSP) selection becomes critical for vehicles to ensure communication quality while minimizing costs. This paper investigates the performance analysis and WSP selection problem in UL/DL decoupled access C-V2X networks. We derive tractable expressions for spectral efficiency of both UL and DL using stochastic geometry, considering three decoupled access cases where UL and DL independently associate with macro base stations (MBSs) or small base stations (SBSs). We formulate a hierarchical game framework combining evolutionary game for vehicle WSP selection and non-cooperative game for WSP bandwidth allocation. An evolutionary game algorithm is proposed to reach the equilibrium, and the uniqueness of Nash equilibrium in bandwidth allocation is proved. Extensive simulations validate the analytical results and demonstrate the convergence and stability of the proposed game framework. Full article

This paper presents an adaptive optimal consensus tracking control scheme for canonical nonlinear multi-agent systems (MASs) with unknown dynamics, employing an actor–critic reinforcement learning (RL) framework. The scheme integrates a sliding mode mechanism to suppress tracking errors and ensure consensus tracking between the followers and the leader. Additionally, optimal control is designed to find a Nash equilibrium in a graphical game. To address the intractability of obtaining an analytical solution for the coupled Hamilton–Jacobi–Bellman (HJB) equation, a policy iteration algorithm is utilized. Within this algorithm, a critic neural network (NN) approximates the gradient of the optimal value function, while an actor NN approximates the optimal control policy. Together, these networks form a compact actor–critic (AC) architecture that achieves optimal consensus tracking. Furthermore, the proposed method guarantees the boundedness of all closed-loop signals while ensuring consensus tracking. Finally, two simulations are conducted to verify the effectiveness and advantages of the proposed method. Full article

In the joint operation of multiple virtual power plants, after day-ahead optimal dispatch is completed, some participants may engage in speculative behaviors such as misreporting profit contribution data to obtain greater benefits during profit distribution, thereby undermining fairness. To address this issue, this paper constructs a profit distribution model designed to prevent speculation. An improved Nash bargaining equilibrium algorithm based on a third-party trading intermediary is proposed to curb speculative actions. Furthermore, a dual-layer monitoring mechanism centered on profit deviation is established, which can effectively identify both single-day speculative behaviors and long-term systematic speculative trends, thereby triggering verification procedures. This forms a closed-loop management mechanism for speculation prevention—“detection, monitoring, analysis, verification”—ensuring fair profit distribution among participants within virtual power plants. Case study results demonstrate that the proposed method achieves an average deviation of only 2.32% compared to the profit distribution outcome under non-speculative conditions. In contrast, commonly used methods such as the Shapley value method, nucleolus method, and Nash–Harsanyi bargaining solution exhibit an average deviation as high as 18.44%. The research presented in this paper enables the detection of speculative behaviors among participants and facilitates verification, significantly enhancing the fairness and rationality of profit distribution. Full article

Cloud-based intrusion detection systems (IDSs) increasingly rely on deep learning classifiers to identify malicious traffic; however, this reliance exposes them to adversarial evasion attacks in which adversaries craft near-imperceptible perturbations to bypass detection. Existing defenses based on conventional adversarial training often recover robustness against known perturbation patterns at the cost of degraded detection accuracy on canonical attack categories—a robustness–accuracy trade-off that remains an open challenge in the field. In this paper, we propose GT-CSAT (Game-Theoretic Cost-Sensitive Adversarial Training), a novel defense framework tailored for cloud security environments. GT-CSAT couples an improved Wasserstein GAN with Gradient Penalty (WGAN-GP) threat generator—conditioned on attack semantics to simulate functionally consistent and highly covert traffic variants—with a minimax adversarial training loop governed by a game-theoretic cost-sensitive loss function. The proposed loss function assigns asymmetric misclassification penalties derived from a two-player zero-sum payoff matrix, enabling the detector to maintain vigilance over both novel adversarial variants and well-characterized conventional threats simultaneously. Specifically, misclassifying an adversarially perturbed attack as benign incurs a strictly higher penalty than the symmetric cross-entropy baseline, while the cost weights are dynamically adapted via a Nash equilibrium-inspired update rule during training. We conduct comprehensive experiments on the Cloud Vulnerabilities Dataset (CVD), CICIDS-2017, and UNSW-NB15, which encompass diverse cloud-specific attack scenarios including denial-of-service, port scanning, brute-force, and SQL injection traffic. Under six representative evasion strategies—FGSM, PGD, C&W, BIM, DeepFool, and IDSGAN-style black-box perturbations—GT-CSAT achieves an average robust accuracy of 94.3%, surpassing standard adversarial training by 6.8 percentage points and the undefended baseline by 21.4 percentage points, while preserving clean-traffic detection at 97.1%. These results confirm that the game-theoretic cost structure effectively decouples robustness from accuracy, yielding a Pareto-superior detection profile relative to competing baselines across all evaluated threat models. The source code and experimental configurations have been publicly released to facilitate reproducibility. Full article

This paper investigates duopoly competition under both constant and decreasing returns to scale in a market characterized by an isoelastic demand function, where firms adjust their strategies using a gradient adjustment mechanism. To establish the stability conditions of the model, we adopt different analytical approaches depending on the type of returns to scale. Under constant returns to scale, we employ a traditional approach by deriving the closed-form solution of the Nash equilibrium and analyzing the Jacobian matrix to verify whether the moduli of all eigenvalues are less than one. In contrast, under decreasing returns to scale, we analyze the local stability of the Nash equilibrium using symbolic computation methods without deriving a closed-form solution. The results show that when firms have heterogeneous costs, the model can exhibit both period-doubling and Neimark–Sacker bifurcations under both types of returns to scale. However, when costs are homogeneous, only period-doubling bifurcations occur. Numerical simulations support these analytical results and further demonstrate the emergence of complex dynamics, including chaotic behavior. Full article

Recent advancements in satellite optical reconnaissance have elevated the sun angle to a critical factor in orbital pursuit-evasion games. The stringent imaging constraints imposed by sun angle and relative distance induce non-smoothness in the terminal region of such differential games, significantly complicating equilibrium-solution derivation. To address this challenge, we formulated a novel differential game model where the pursuer minimizes the time-to-entry into the evader’s effective imaging region. We first constructed a sequence of low-dimensional manifolds that collectively cover the terminal region, solving the differential game with this sequence to yield the Nash equilibrium. Subsequently, we approximated the terminal region using a smooth manifold of identical dimensions, enabling a computationally efficient approximate solution. Both methodologies demonstrate broad applicability to orbital differential games featuring non-smooth terminal regions. Simulation results confirm that the approximation error becomes pronounced only under extreme initial sun angles, though this error remains acceptable for practical space reconnaissance applications. Full article

Eigenvector-based centrality captures recursive notions of importance in networks. While the direct problem computes centrality from given edge weights, the inverse eigenvector centrality problem seeks edge weights that reproduce a prescribed centrality profile; for directed multigraphs, this inverse task is typically non-unique and depends on the admissible arc structure. We study the direct and inverse problems on directed multigraphs and derive an explicit linear characterization of the set of admissible edge-weight vectors that are compatible with a given centrality target. On this feasible set, we formulate a generalized Nash equilibrium problem with shared centrality constraints, in which multiple agents select edge weights to maximize economically interpretable payoffs that incorporate arc-level competition effects. We provide conditions under which the induced game admits a concave potential function, yielding equilibrium existence and, under standard strict concavity assumptions, uniqueness. Finally, we illustrate the model on an airport network where nodes represent airports and parallel arcs represent airline-specific routes, showing that equilibrium selection produces a feasible and interpretable weight configuration that preserves the prescribed centrality. Full article

With the rapid development of smart cities, coordinating diverse distributed energy resources through storage-centric shared management has become a critical challenge. This paper proposes a bi-level energy management framework to support peer-to-peer energy trading among multiple virtual power plants (VPPs) under multidimensional uncertainties. The interaction is modeled as a Stackelberg–Nash equilibrium framework, in which OK, we will make the necessary revisions as per the requirements.a public energy storage operator and a natural gas company act as leaders to maximize social welfare and design differentiated trading strategies for VPPs. The VPPs act as followers and participate in cooperative energy trading based on a generalized Nash equilibrium scheme, sharing surplus energy and allocating cooperative benefits according to their contributions. To address uncertainty, Conditional Value at Risk (CVaR) is adopted to quantify the expected loss of the upper-level decision makers. The lower-level VPP problem is formulated as a three-stage stochastic robust optimization model considering renewable generation uncertainty. To solve the resulting nonlinear bi-level problem, a two-stage solution approach combining particle swarm optimization and KKT-based reformulation is developed to transform it into a tractable mixed-integer linear programming model. Numerical case studies verify the effectiveness of the proposed framework. Full article

Coupling interference in densely integrated high-frequency communication architectures leads to significant degradation in transmission efficiency, particularly in modern 5G and GHz-range platforms. From a mathematical perspective, mitigating such interference can be formulated as a multi-criteria optimization problem involving competing design objectives and interacting control mechanisms. In this paper, we develop an equilibrium-based optimization framework by modeling coupling suppression as a finite non-cooperative game. Isolation mechanisms are represented as strategic players whose actions are defined over constrained design spaces, while utility functions incorporate coupling minimization, insertion-loss penalties, and fabrication complexity. Under this formulation, stable mitigation strategies are characterized through Nash equilibrium conditions. To address the inherent trade-offs among performance metrics, the equilibrium computation is integrated with a Pareto multi-objective optimization scheme, yielding Nash–Pareto optimal configurations that balance electromagnetic isolation performance with implementation feasibility. Numerical full-wave simulations in the 2–12 GHz frequency band demonstrate that the proposed equilibrium solutions achieve substantial interference suppression, with reductions exceeding 30 dB compared with conventional baseline designs. The proposed framework provides a mathematically structured approach for interference mitigation and offers a generalizable methodology for multi-objective optimization in high-frequency communication systems. Full article

Vehicular Edge Computing (VEC) can effectively guarantee the service experience of user vehicles, but resource-limited Roadside Units (RSUs) may face insufficient computing capacity during task peak periods. Utilizing Assisting Vehicles (AVs) with idle resources to share computing power can alleviate the pressure on RSUs. However, existing studies often fail to adequately incentivize selfish assisting vehicles to contribute resources and frequently lack a global optimization perspective from the overall system welfare. To address these challenges, this paper proposes an incentive-driven utility-balanced task offloading framework that aims to maximize social welfare while jointly optimizing resource allocation and profit pricing. Specifically, we first formulate the resource allocation as a Mixed-Integer Nonlinear Programming (MINLP) problem. To solve this problem, we introduce hybrid action representation learning to VEC for the first time and propose the HyAR-PPO algorithm to jointly optimize discrete offloading decisions and continuous resource allocation. This algorithm maps heterogeneous hybrid actions to a unified latent representation space through a Variational Autoencoder for the solution. Subsequently, equilibrium prices among user vehicles, Computation Service Providers (CSPs), and assisting vehicles are determined through Nash bargaining games, satisfying individual rationality constraints and achieving Pareto-optimal fair profit distribution. Experimental results demonstrate that the proposed framework can effectively coordinate multi-party interests. Compared with mainstream methods, the approach based on hybrid action representation learning achieves a significant improvement in social welfare, with its advantages being more pronounced in medium-to-large-scale scenarios. Full article

Between 1959 and 1962, Alvin Scodel, J. Sayer Minas, and colleagues conducted some of the earliest laboratory studies of strategic interaction using non-zero-sum games. Working at the margins of economics in the Journal of Conflict Resolution, they documented a striking pattern: subjects frequently chose options that reduced an opponent’s payoff by more than their own, even when mutual cooperation was both individually and collectively optimal. These results—especially the behavior observed in their so-called Game H4, a Harmony Game in which cooperation strictly dominated defection—anticipate a central insight of evolutionary game theory: what matters for adaptation is relative payoff, not absolute gain. This essay reinterprets the Scodel–Minas experiments through a Darwinian lens, arguing that they provide an early empirical challenge to Nash-equilibrium reasoning and to models that evaluate strategies solely in terms of absolute utility. By reconstructing the H4 payoff structure and embedding it within a simple evolutionary framework, I show how small levels of “competitive” behavior can destabilize cooperative equilibria that appear self-evident under standard assumptions. I then revisit three later “puzzles” in the evolution of cooperation—altruistic punishment, the fragility of “win–win” treaties, and rejections in ultimatum bargaining—to ask how differently they might have been framed had the Scodel–Minas findings been part of the canonical experimental literature. Rather than treating these phenomena as surprising anomalies, a historically informed, relative-payoff perspective suggests that they could have been recognized much earlier as natural expressions of an already documented pattern. Full article

Power control algorithms using the signal-to-interference-plus-noise ratio (SINR) metric in distributed radar systems (DRS) may suffer from performance degradation in infeasible conditions. In this paper, we present a Sigmoid-based Power Allocation Game (SigPAG) algorithm for target detection in DRS to minimize total power consumption while meeting predetermined target detection performance. Firstly, a physically interpretable Sigmoid function is designed to model radar detection probability as the utility function, overcoming the performance limitations and potential deviations of SINR-based utilities. Secondly, by integrating the proposed Sigmoid utility, SigPAG is established to describe the interaction among radar nodes in the DRS. The existence and uniqueness of the Nash equilibrium (NE) solution are proven by the closed-form expressions of the best response function. Furthermore, an iterative power allocation algorithm is proposed to adjust the transmit powers towards the NE point. Finally, simulation results obtained in a 4-node DRS with Radar Cross Section (RCS) values of [1, 0.3, 2, 5] m² demonstrate that the proposed algorithm achieves an energy efficiency improvement of 36.1% in target detection compared with the traditional SINR-based methods. Full article

Spacecraft pursuit–evasion in contested environments is complicated by strategic incompleteness: the evader can switch maneuvering modes and deploy multi-domain countermeasures that degrade the pursuer’s perception, leading to non-stationary information and distributionally ambiguous interference statistics. A dynamic time-window Nash equilibrium framework is developed for linearized Local Vertical Local Horizontal (LVLH) relative motion under interference-induced uncertainty. Perceptual degradation is modeled via an evidence–theoretic belief representation, and the Jensen–Shannon (JS) divergence is introduced to quantify discrepancies between nominal and interference-corrupted beliefs. The divergence metric drives an adaptive time-window partitioning policy and an uncertainty-aware running cost that balances nominal performance objectives with robustness regularization during high-degradation intervals. In each time window, sufficient conditions are provided for the existence of a local Nash equilibrium, and equilibrium strategies are characterized by the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation. A global consistency result is established: assuming state continuity, additive cost decomposition, and dynamic-programming compatibility at window boundaries, concatenating the window-wise equilibria yields a Nash equilibrium over the entire horizon. Unlike conventional receding-horizon differential games with a fixed replanning grid, the proposed policy partitions the horizon online in response to perceptual-degradation events and stitches adjacent windows through a continuation value. This boundary stitching enables the global consistency guarantee under additive costs and state continuity. To hedge against ambiguity in interference intensity, a variational distributionally robust optimization (DRO) problem with moment-constrained ambiguity sets is formulated, and the dual worst-case distribution is derived. The resulting Karush–Kuhn–Tucker (KKT) system is reformulated as a finite-dimensional variational inequality, for which an accelerated Alternating Direction Method of Multipliers (ADMM) operator-splitting solver is proposed for efficient real-time computation. Numerical simulations validate the framework and demonstrate improved robustness and computational scalability under time-varying interference compared with fixed-window baselines. Full article

We address the challenge of coordinating traffic at unsignalized intersections, particularly with an emergency vehicle, by proposing a game-theoretic decision model. In this non-cooperative game, each vehicle selects a Go or Yield strategy to maximize a utility function based on efficiency, collision risk, and driving style. We use the Iterated Best Response algorithm to find the pure strategy Nash equilibrium. A MATLAB–SUMO co-simulation validates that our model significantly enhances safety and efficiency while substantially reducing travel time. Full article

This paper investigates cooperative advertising decisions in production–retailing channels for seasonal products under demand seasonality. We develop analytical game-theoretic models to examine how advertising cooperation influences channel coordination and profit distribution between manufacturers and retailers. Two channel structures are considered: a single-manufacturer–single-retailer channel and a single-manufacturer channel with two competing retailers. For each structure, Stackelberg and Nash equilibrium settings are analyzed and compared. Our results show that cooperative advertising can serve as an effective coordination mechanism by increasing advertising intensity and improving channel efficiency. Retailers always benefit from manufacturer-supported advertising through cost sharing and higher profitability, whereas the manufacturer’s incentive to participate depends on whether demand expansion outweighs shared advertising costs. Importantly, we demonstrate that channel leadership plays a critical role: the Stackelberg equilibrium consistently dominates the Nash equilibrium in terms of total channel profit. This study contributes to the cooperative advertising literature by explicitly incorporating demand seasonality and competing retailers, and by clarifying when cooperative advertising leads to Pareto improvements in seasonal supply chains. Full article