Paper: arXiv 2507.19123

Authors: Giorgio Ferrari, Anna Pajola

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical treatment of mean-field games of optimal stopping with common noise, leveraging advanced probabilistic techniques like Bank-El Karoui representations and Schauder/Tarski fixed-point theorems. However, it is entirely theoretical with zero empirical validation or computational implementation.

Research Flowchart

  flowchart TD
    A["Research Goal: Prove existence of strong randomized<br>MFG optimal stopping equilibria with common noise"] --> B["Inputs: Bank-El Karoui representation &<br>Common noise framework (Partition/General)"]
    B --> C["Method 1: Apply Bank-El Karoui problem under<br>continuity & countable partition noise"]
    B --> D["Method 2: Conduct comparative statics under<br>monotonicity for general common noise"]
    C --> E["Outcome 1: Existence of strong randomized equilibrium<br>(Mean-field interaction adapted to common noise)"]
    D --> F["Outcome 2: Structure & ordering of strong MFG<br>equilibria with strict stopping times"]

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0 of 36 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.