In many multi-agent systems, agents interact repeatedly and are expected to settle into equilibrium behavior over time. Yet in practice, behavior often drifts, and detecting such deviations in real time remains an open challenge. We introduce a sequential testing framework that monitors whether observed play in repeated games is consistent with equilibrium, without assuming a fixed sample size. Our approach builds on the e-value framework for safe anytime-valid inference: by "betting" against equilibrium, we construct a test supermartingale that accumulates evidence whenever observed payoffs systematically violate equilibrium conditions. This yields a statistically sound, interpretable measure of departure from equilibrium that can be monitored online. We also leverage Benjamini-Hochberg-type procedures to increase detection power in large games while rigorously controlling the false discovery rate. Our framework unifies the treatment of Nash, correlated, and coarse correlated equilibria, offering finite-time guarantees and a detailed analysis of detection times. Moreover, we extend our method to stochastic games, broadening its applicability beyond repeated-play settings.

翻译：在许多多智能体系统中，智能体通过重复交互并预期随时间推移形成均衡行为。然而实践中，行为常会发生漂移，实时检测此类偏离仍是一个开放难题。本文提出一种序贯检验框架，用于监测重复博弈中观察到的行为是否与均衡一致，且无需预设固定样本量。该方法基于e值框架实现安全的任意时间有效推断：通过"博弈"对抗均衡，我们构建了一个检验上鞅，当观测收益系统性地违反均衡条件时，该鞅将持续累积证据。由此产生一个统计可靠、可解释的均衡偏离度量指标，支持在线监测。我们还利用Benjamini-Hochberg类程序来增强大型博弈中的检测效力，同时严格控制错误发现率。本框架统一处理纳什均衡、相关均衡与粗相关均衡，提供有限时间保证及检测时间的详细分析。此外，我们将该方法扩展至随机博弈场景，使其适用范围超越重复博弈框架。