Search Results (572)

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

As global copper demand continues to grow, China, being the largest copper consumer, faces increasingly complex challenges in ensuring the security of its supply chain. However, a substantive gap remains: prevailing assessments rely on static index systems and discrete scenario analyses that seldom model uncertainty-driven, continuous-time strategic interactions, leaving the conditions for self-enforcing cooperation and the attendant policy trade-offs insufficiently identified. This study models the interaction between Chinese copper importers and foreign suppliers as a continuous-time stochastic differential game, with feedback Nash equilibria derived from a Hamilton–Jacobi–Bellman system. The supply security utility is specified as a diffusion process perturbed by Brownian shocks, while regulatory intensity and profit-sharing are treated as structural parameters shaping its drift and volatility—thereby delineating the parameter region for self-enforcing cooperation and clarifying how sudden disturbances reconfigure equilibrium security. The research findings reveal the following: (i) the mean and variance of supply security utility progressively strengthen over time under the influence of both parties’ maintenance efforts, while stochastic disturbances causing actual fluctuations remain controllable within the contract period; (ii) spontaneous cooperation can be achieved under scenarios featuring strong regulation of domestic importers, weak regulation of foreign suppliers, and a profit distribution ratio slightly favoring foreign suppliers, thereby reducing regulatory costs; this asymmetry is beneficial because stricter oversight of domestic importers curbs the primary deviation risk, lighter oversight of foreign suppliers avoids cross-border enforcement frictions, and a modest supplier-favored profit-sharing ratio sustains participation—together expanding the self-enforcing cooperation set; (iii) sudden events exert only short-term impacts on supply security with controllable long-term effects; however, an excessively stringent regulatory environment can paradoxically reduce long-term supply security. Security effort levels demonstrate positive correlation with supply security, while regulatory intensity must be maintained within a moderate range to balance incentives and constraints. Full article

Based on the perspective of multi-stage dynamic competition, this study constructs a discrete dynamic model of price competition between the “direct sales” and “resale” channels in cross-border e-commerce (CBEC) under three blockchain deployment modes. Drawing on nonlinear dynamics theory, the Nash equilibrium of the system and its stability conditions are examined. Using numerical simulations, the effects of factors such as the channel price adjustment speed, tariff rate, and commission ratio on the dynamic evolution, entropy, and stability of the system under the empowerment of blockchain technology are investigated. Furthermore, the impact of noise factors on system stability and the corresponding chaos control strategies are further analyzed. This study finds that a single-channel deployment tends to induce asymmetric system responses, whereas dual-channel collaborative deployment helps enhance strategic coordination. An increase in price adjustment speed, tariffs, and commission rates can drive the system’s pricing dynamics from a stable state into chaos, thereby raising its entropy, while the adoption of blockchain technology tends to weaken dynamic stability. Therefore, after deploying blockchain technology, each channel should make its pricing decisions more cautiously. Moderate noise can exert a stabilizing effect, whereas excessive disturbances may cause the system to diverge. Hence, enterprises should carefully assess the magnitude of disturbances and capitalize on the positive effects brought about by moderate fluctuations. In addition, the delayed feedback control method can effectively suppress chaotic fluctuations and enhance system stability, demonstrating strong adaptability across different blockchain deployment modes. Full article

The wind–solar–storage–thermal combined power generation system is one of the key measures for China’s energy structure transition, and rational capacity planning of each generation entity within the system is of critical importance. First, this paper addresses the uncertainty of wind and photovoltaic (PV) power outputs through scenario-based analysis. Considering the diversity of generation entities and their complex interest demands, a bi-level capacity optimization framework based on game theory is proposed. In the upper-level framework, a game-theoretic method is designed to analyze the multi-agent decision-making process, and the objective function of capacity allocation for multiple entities is established. In the lower-level framework, multi-objective optimization is performed on utility functions and node voltage deviations. The Nash equilibrium of the non-cooperative game and the Shapley value of the cooperative game are solved to study the differences in the capacity allocation, economic benefits, and power supply stability of the combined power generation system under different game modes. The case study results indicate that under the cooperative game mode, when the four generation entities form a coalition, the overall system achieves the highest supply stability, the lowest carbon emissions at 30,195.29 tons, and the highest renewable energy consumption rate at 53.93%. Moreover, both overall and individual economic and environmental performance are superior to those under the non-cooperative game mode. By investigating the capacity configuration and joint operation strategies of the combined generation system, this study effectively enhances the enthusiasm of each generation entity to participate in the energy market; reduces carbon emissions; and promotes the development of a more efficient, environmentally friendly, and economical power generation model. Full article

This paper delves into a multi-player non-renewable resource extraction differential game model, where the duration of the game is a random variable with a composite distribution function. We first explore the conditions under which the cooperative solution also constitutes a Nash equilibrium, thereby extending the theoretical framework from a fixed duration to the more complex and realistic setting of random duration. Assuming that players are unaware of the switching moment of the distribution function, we derive optimal estimates in both time-dependent and state-dependent cases. The findings contribute to a deeper understanding of strategic decision-making in resource extraction under uncertainty and have implications for various fields where random durations and cooperative strategies are relevant. Full article

In recent years, with the development of micro-satellite clusters and large-scale satellite constellations, the likelihood of multiple spacecraft engaging in orbital pursuit–evasion games has increased. This paper establishes a novel interception domain theory for planar orbital multi-player “encirclement-capture” differential games, and it proves the partitioned structure and classification properties of Nash equilibrium solutions. The main contributions of our study are the following: (1) Proposing the first rigorous definition of interception domains in orbital pursuit–evasion games, proving their convexity, developing computational methods for domain intersections, and establishing a complete classification of equilibrium for planar multi-pursuer interception games, which establishes a theoretical foundation for analyzing multi-spacecraft orbital pursuit–evasion games. (2) Analyzing Nash equilibrium properties for “encirclement-capture” differential games with two, three, or more pursuers, classifying degenerate/non-degenerate scenarios via spatial inclusion relationships. The equilibrium results indicate that as the number of pursuers increases, the game tends toward a degenerate scenario where the likelihood of redundant pursuers (whose actions do not affect the game outcome) rises. Full article

Contemporary multi-UAV formations face dual challenges of obstacle avoidance and rapid formation recovery. To enable UAV swarms to efficiently restore their predefined configurations post-obstacle navigation, a formation recovery strategy grounded in Nash equilibrium game theory is proposed in this paper. By integrating the IVY optimization algorithm, a collaborative control model that systematically balances individual UAV interests with swarm-level objectives through carefully designed optimization criteria is established. Comparative experimental results demonstrate that, compared to traditional formation obstacle-avoidance algorithms, Improved Particle Swarm Optimization (IPSO), Ant Colony Optimization (ACO), and Genetic Algorithm (GA), our method exhibits superior performance across multiple key metrics, including average path length, formation accuracy rate, recovery time, and total time consumption. Real-flight tests on a multi-UAV platform confirm IVYA-Nash surpasses improved APF in formation accuracy and aerodynamic disturbance resistance, proving robustness in dynamic multi-agent scenarios. The work provides an efficient and reliable solution for coordinated control of UAV formations in complex environments. Full article

Maximal Extractable Value (MEV) presents a significant challenge to the fairness and efficiency of decentralized finance (DeFi). This paper provides a game-theoretic analysis of the strategic interactions within the MEV supply chain, involving searchers, builders, and validators. A three-stage game of incomplete information is developed to model these interactions. The analysis derives the Perfect Bayesian Nash Equilibria for primary MEV attack vectors, such as sandwich attacks, and formally characterizes attacker behavior. The research demonstrates that the competitive dynamics of the current MEV market are best described as Bertrand-style competition, which compels rational actors to engage in aggressive extraction that reduces overall system welfare in a prisoner’s dilemma-like outcome. To address these issues, the paper proposes and evaluates mechanism design solutions, including commit–reveal schemes and threshold encryption. The potential of these solutions to mitigate harmful MEV is quantified. Theoretical models are validated against on-chain data from the Ethereum blockchain, showing a close alignment between theoretical predictions and empirically observed market behavior. Full article

This paper investigates a swarming strength allocation Bayesian game approach under incomplete information to address the high-value targets protection problem of swarming unmanned systems. The swarming strength allocation Bayesian game model is established by analyzing the non-zero sum incomplete information game mechanism during the protection process, considering high-tech and low-tech interception players. The model incorporates a game benefit quantification method based on an improved Lanchester equation. The method regards massive swarm individuals as a collective unit for overall cost calculation, thus avoiding the curse of dimensionality from increasing numbers of individuals. Based on it, a Bayesian Nash equilibrium solving approach is presented to determine the optimal swarming strength allocation for the protection player. Finally, compared with random allocation, greedy heuristic, rule-based assignment, and Colonel Blotto game, the simulations demonstrate the proposed method’s robustness in large-scale strength allocation. Full article

Distribution System Operators (DSOs) increasingly need planning tools that coordinate utility-influenced assets—such as electric-vehicle charging stations (EVCS) and voltage-support resources—with customer-sited distributed generation (DG). We present a Nash-equilibrium-based Iterative Best Response Algorithm (IBRA-NE) for joint planning of DG and EVCS in radial distribution networks. The framework supports two applicability modes: (i) a DSO-plannable mode that co-optimizes EVCS siting/sizing and utility-controlled reactive support (DG operated as VAR resources or functionally equivalent devices), and (ii) a customer-sited mode that treats DG locations as fixed while optimizing DG reactive set-points/sizes and EVCS siting. The objective minimizes network losses and voltage deviation while incorporating deployment costs and EV charging service penalties, subject to standard operating limits. A backward/forward sweep (BFS) load flow with Monte Carlo simulation (MCS) captures load and generation uncertainty; a Bus Voltage Deviation Index (BVDI) helps identify weak buses. On the EEU 114-bus system, the method reduces base-case losses by up to 57.9% and improves minimum bus voltage from 0.757 p.u. to 0.931 p.u.; performance remains robust under a 20% load increase. The framework explicitly accommodates regulatory contexts where DG siting is customer-driven by treating DG locations as fixed in such cases while optimizing EVCS siting and sizing under DSO planning authority. A mixed scenario with 5 DGs and 3 EVCS demonstrates coordinated benefits and convergence properties relative to PSO, GWO, RFO, and ARFO. Additionally, the proposed algorithm is also tested on the IEEE 69-bus system and results in acceptable performance. The results indicate that game-theoretic coordination, applied in a manner consistent with regulatory roles, provides a practical pathway for DSOs to plan EV infrastructure and reactive support in networks with uncertain DER behavior. Full article

To improve the traffic efficiency of connected and automated vehicles (CAVs) in on-ramp merging areas, this study proposes a novel region-level multi-agent reinforcement learning framework, Regionally Coordinated Nash-Advantage Decomposition Deep Q-Network with Conflict-Aware Q Fusion (RC-NashAD-DQN). Unlike existing vehicle-level control methods, which suffer from high computational overhead and poor scalability, our approach abstracts on-ramp and main road areas as region-level control agents, achieving coordinated yet independent decision-making while maintaining control precision and merging efficiency comparable to fine-grained vehicle-level approaches. Each agent adopts a value–advantage decomposition architecture to enhance policy stability and distinguish action values, while sharing state–action information to improve inter-agent awareness. A Nash equilibrium solver is applied to derive joint strategies, and a conflict-aware Q-fusion mechanism is introduced as a regularization term rather than a direct action-selection tool, enabling the system to resolve local conflicts—particularly at region boundaries—without compromising global coordination. This design reduces training complexity, accelerates convergence, and improves robustness against communication imperfections. The framework is evaluated using the SUMO simulator at the Taishan Road interchange on the S1 Yongtaiwen Expressway under heterogeneous traffic conditions involving both passenger cars and container trucks, and is compared with baseline models including C-DRL-VSL and MADDPG. Extensive simulations demonstrate that RC-NashAD-DQN significantly improves average traffic speed by 17.07% and reduces average delay by 12.68 s, outperforming all baselines in efficiency metrics while maintaining robust convergence performance. These improvements enhance cooperation and merging efficiency among vehicles, contributing to sustainable urban mobility and the advancement of intelligent transportation systems. Full article

Hirshleifer’s difference-form contest technology is a useful tool in the study of a class of conflict, especially military combats. We aim to highlight an important feature that the Hirshleifer contest model distinctively has, namely passivity (bidding zero effort) may stand as an effective choice in conflict even when the contest is highly deterministic (i.e., with small noise). For that purpose, we establish two propositions on the contest with $n\ge 2$ risk-neutral contestants under small noise. The first proposition states that every contestant bids arbitrarily close to zero (if not bidding zero with positive probability at all) under sufficiently small noise. The second proposition, more strikingly, states that every contestant either bids arbitrarily close to the second-highest valuation (among all the contestants’ valuations), or simply remains passive with certainty under any sufficiently small noise. We further show that the first proposition holds for the contest between risk-averse individuals endowed with constant absolute risk aversion as well, and illustrate by an example how quickly polarization in bidding among contestants, as is predicted by the propositions, may emerge as the noise of the contest abates. These results help pave the way toward a complete characterization of the difference-form contest. Full article