AI 中文总结
研究全局博弈中极限唯一性问题，核心方法是证明收益的一阶因子结构可消除风险主导的最优反应循环，主要贡献是得出相关结论并表明一阶结构可构建，确定了边界情况及噪声特性。
AI 中文摘要
在两人超模博弈中，当风险主导的最优反应循环存在时，极限唯一性失效（Veiel，2025）。我们证明收益上的一阶因子结构完全消除了此类循环，因此每个一阶超模博弈都有广义序数势，且对于任意数量的行动都有极限唯一性。边界是明确的：一个明确的三行动二阶博弈有长度为六的循环，没有超模博弈有长度为四的循环，并且在非退化一阶博弈的量化上确界范数范围内的每个博弈都是无循环的。一阶结构也可以构建：当玩家在许多具有共同潜在收益的独立市场中竞争时，堆叠观测矩阵是一阶加稀疏的，并且一个稳健主成分分析估计器会留下残余噪声，该噪声随信号规模消失但在任何有限样本下都保持为正，即使在部分观测情况下。
英文摘要
When does the global game information structure select a unique equilibrium? Limit uniqueness in two-player supermodular games fails exactly when a risk-dominant better response cycle exists (Veiel, 2025). We show that rank-one factor structure on payoffs eliminates such cycles entirely, so every rank-one supermodular game admits a generalized ordinal potential and limit uniqueness follows for any number of actions. The boundary is sharp: an explicit three-action rank-two game carries a length-six cycle, no supermodular game carries a cycle of length four, and every game within a quantified sup-norm margin of a nondegenerate rank-one game is cycle-free. Rank-one structure can also be manufactured: when players compete across many independent markets with common latent payoffs, the stacked observation matrix is rank one plus sparse, and a Robust PCA estimator leaves residual noise that vanishes with the signal scale yet stays positive at any finite sample, even under partial observation.
