发表机构
City St George’s University of London（伦敦城市圣乔治大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出SSMA算法，将斯塔克尔伯格均衡计算转化为流形稳定问题，在500次非凸蒙特卡洛试验中实现100%成功率，迭代效率远优于基线，可快速高精度求解非线性双层博弈的局部斯塔克尔伯格均衡。
AI 中文摘要
求解非线性序列博弈中的局部斯塔克尔伯格均衡颇具挑战性，因为基于梯度的最优响应方法可能发散、循环，或收敛至不满足所需均衡条件的驻点。这些失效可能源于曲率不对称、不稳定的响应映射，以及对追随者最优响应流形缺乏不变性。本文提出斯塔克尔伯格滑模算法（Stackelberg Sliding-Mode Algorithm, SSMA），这一控制论框架将斯塔克尔伯格均衡计算重构为流形稳定问题。追随者和领导者的一阶最优性条件定义了斯塔克尔伯格滑模流形，滑模动力学驱动迭代点在有限时间内到达这些流形。追随者曲率和领导者约化曲率条件决定流形的吸引性，使有效的局部斯塔克尔伯格均衡具有吸引力，同时拒绝不满足二阶均衡条件的驻点。该方法在统一框架内整合了有限时间流形稳定、斯塔克尔伯格一致动力学和基于曲率的均衡选择。在500次非凸蒙特卡洛试验中，SSMA实现了100%的成功率，达到规定容差的迭代中位数为26次，而最近的完全成功基线为456次，且终端残差接近10^-16，同时收敛至有效的局部斯塔克尔伯格均衡。
英文摘要
Computing local Stackelberg equilibria in nonlinear sequential games is challenging because gradient-based best-response methods may diverge, cycle, or converge to stationary points that do not satisfy the required equilibrium conditions. These failures can result from curvature asymmetry, unstable response mappings, and lack of invariance with respect to the follower's best-response manifold. This paper introduces the Stackelberg Sliding-Mode Algorithm (SSMA), a control-theoretic framework that recasts Stackelberg equilibrium computation as a manifold-stabilization problem. The follower and leader first-order optimality conditions define Stackelberg sliding manifolds, and sliding-mode dynamics drive the iterates to these manifolds in finite time. The follower curvature and leader reduced-curvature conditions determine manifold attractivity, making valid local Stackelberg equilibria attractive while rejecting stationary points that fail the second-order equilibrium conditions. The resulting approach integrates finite-time manifold stabilization, Stackelberg-consistent dynamics, and curvature-based equilibrium selection within a unified framework. Across 500 nonconvex Monte Carlo trials, SSMA achieved 100\% success, reached the prescribed tolerance in a median of 26 iterations, compared with 456 for the nearest fully successful baselines, and attained terminal residuals near \(10^{-16}\), while converging to a valid local Stackelberg equilibrium.
