AI 中文总结
本文针对具有重叠参与者影响的Friedkin-Johnsen网络，通过势博弈分析其竞争性一步超前控制的纳什均衡、收敛性与稳定性，刻画不同目标限制下的可实现均衡，推导竞争导致的福利损失闭式表达式并经数值验证。
AI 中文摘要
本文研究具有重叠参与者影响的Friedkin-Johnsen网络的竞争性一步超前控制问题。一步交互是一个精确势博弈，其唯一纳什均衡由对称正定系统求得；顺序最佳响应扫描对所有冻结网络状态均收敛，并行扫描服从精确雅可比条件（两名参与者时始终收敛），单扫描实现需增广状态-动作稳定性测试。对于边际网络，符号左右阻尼条件足以保证精确均衡稳定性，当符号反转时则成为尖锐的一阶不稳定性测试；预解恒等式阐明反馈几何，控制感知中心性识别最关键的目标冲突。本文刻画了无约束、凸和稀疏目标限制下可实现的均衡，给出竞争导致的同状态福利损失闭式表达式，数值示例验证了稳定性阈值、几何及福利预测。
英文摘要
This paper studies competitive one-step-ahead control of Friedkin-Johnsen networks with overlapping player influence. The one-step interaction is an exact potential game with a unique Nash equilibrium obtained from a symmetric positive-definite system. Sequential best-response sweeps converge for every frozen network state, parallel sweeps obey an exact Jacobi condition (and always converge with two players), and one-sweep implementations require an augmented state-action stability test. For marginal networks, a signed left-right damping condition is sufficient for exact-equilibrium stability and becomes a sharp first-order instability test when its sign is reversed. A resolvent identity clarifies the feedback geometry, while a control-aware centrality identifies the goal conflicts that matter most. We characterize attainable equilibria under unconstrained, convex, and sparse goal restrictions and give a closed form for the same-state welfare loss caused by competition. Numerical examples verify the stability thresholds, geometry, and welfare predictions.
Comments11 pages, 2 figures. Submitted to IEEE Transactions on Control of Network Systems
