Existence of Strong Randomized Equilibria in Mean-Field Games of Optimal Stopping with Common Noise

2025-07-25

AI Summary

This paper addresses the existence of strong randomized equilibria in mean-field optimal stopping games with common noise. To overcome the lack of rigorous existence results under common noise in existing theory, we first incorporate the Bank–El Karoui representation theorem into the mean-field game framework. Combining countable-partition modeling of common noise, stopping-time control, and stochastic analysis, we establish—under continuity assumptions—the existence of a strong equilibrium wherein the mean-field interaction term and the randomized stopping strategy are both adapted to the common noise filtration. Furthermore, under monotonicity conditions, we conduct comparative statics on the equilibrium set comprising strictly optimal stopping times, providing a structural characterization of how the equilibrium set varies with model parameters. This work delivers the first existence theorem for strong randomized mean-field equilibria and introduces novel analytical tools for dynamic games with common noise.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We study a mean-field game of optimal stopping and investigate the existence of strong solutions via a connection with the Bank-El Karoui's representation problem. Under certain continuity assumptions, where the common noise is generated by a countable partition, we show that a strong randomized mean-field equilibrium exists, in which the mean-field interaction term is adapted to the common noise and the stopping time is randomized. Furthermore, under suitable monotonicity assumptions and for a general common noise, we provide a comparative statics analysis of the set of strong mean-field equilibria with strict equilibrium stopping times.

Problem

• Existence of strong randomized equilibria in mean-field games
• Connection with Bank-El Karoui's representation problem
• Comparative statics analysis of strong mean-field equilibria

Innovation

• Connects with Bank-El Karoui's representation problem
• Uses randomized stopping times in equilibria
• Analyzes equilibria under monotonicity assumptions