AI 中文总结
针对有限玩家最优停止博弈复杂度随玩家数快速增长的问题，引入独立随机化形式，构造α-位势函数，提出Potential-CT-DDPG学习算法，数值实验验证了方法的有效性。
AI 中文摘要
有限玩家非零和最优停止博弈通常会产生耦合均衡系统，其复杂度随玩家数量增长迅速提升。我们引入一种独立随机化形式，其中每个停止规则由适应的非递减累积停止过程表示。标准嵌入保留纯策略收益，且纯策略是原博弈的纳什均衡当且仅当其嵌入是随机博弈的纳什均衡。我们采用α-位势方法构造α_N-位势函数，在弱相互作用下误差α_N=O(N⁻¹)。我们还确定了具有闭式阈值均衡的精确位势子类。对于局部停止状态相互作用，随机化收益允许局部停止质量表示，位势最大化可表述为带有局部梯度约束和有限跳非局部条件的多维奇异控制问题。在适当正则性假设下，我们研究相关的哈密尔顿-雅可比-贝尔曼拟变分不等式及其正则性性质。对于未知模型系数，我们提出有界强度的Potential-CT-DDPG学习算法。数值实验与分析基准高度匹配，且产生的最佳响应改进与N⁻¹缩放一致。
英文摘要
Finite-player nonzero-sum optimal stopping games typically lead to coupled equilibrium systems whose complexity grows rapidly with the number of players. We introduce an independently randomized formulation in which each stopping rule is represented by an adapted, nondecreasing cumulative stopping process. The canonical embedding preserves pure-profile payoffs, and a pure profile is a Nash equilibrium of the original game if and only if its embedding is a Nash equilibrium of the randomized game. We adopt the $α$-potential approach to construct an $α_N$-potential function, with the error $α_N=O(N^{-1})$ under weak-interaction. We also identify an exact-potential subclass with a closed-form threshold equilibrium. For local stopped-status interactions, randomized payoffs admit a local stopped-mass representation, and potential maximization can be formulated as a multidimensional singular-control problem with local gradient constraints and a nonlocal condition for finite jumps. Under suitable regularity assumptions, we study the associated Hamilton-Jacobi-Bellman quasi-variational inequality and its regularity properties. For unknown model coefficients, we propose a bounded-intensity Potential-CT-DDPG learning algorithm. Numerical experiments closely match the analytical benchmark and yield estimated best-response improvements consistent with $N^{-1}$ scaling.
