Technology Category
Game Theory and Economic Paradigms: EquilibriumReasoning under Uncertainty: Stochastic OptimizationMultiagent Systems: Mechanism Design
Existence of Strong Randomized Equilibria in Mean-Field Games of Optimal Stopping with Common Noise
🤖 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
Application Category
📝 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
Research questions and friction points this paper is trying to address.
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
Methods, ideas, or system contributions that make the work stand out.
Connects with Bank-El Karoui's representation problem
Uses randomized stopping times in equilibria
Analyzes equilibria under monotonicity assumptions
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