Betting on Equilibrium: Monitoring Strategic Behavior in Multi-Agent Systems

2026-01-08

arXiv.org

AI Summary

This work addresses the challenge of online detection of equilibrium drift in repeated multi-agent interactions, where deviations from equilibrium behavior are difficult to identify in real time. The authors propose a sequential testing method grounded in the e-value framework, constructing test supermartingales that “bet against” equilibrium hypotheses to accumulate evidence of deviation online. This approach unifies the monitoring of Nash, correlated, and coarse correlated equilibria. For the first time, anytime-valid statistical inference with finite-time guarantees is introduced to equilibrium testing, and the method is extended to stochastic games. By integrating Benjamini–Hochberg–type procedures to control the false discovery rate, the framework enhances detection power in large-scale settings. The resulting procedure enables online, interpretable, and theoretically robust detection of diverse equilibrium deviations.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• multi-agent systems
• equilibrium deviation
• real-time monitoring
• strategic behavior
• repeated games

Innovation

• e-value
• test supermartingale
• anytime-valid inference
• equilibrium monitoring
• false discovery rate