Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

Large Banks and Systemic Risk: Insights from a Mean-Field Game Model

This paper presents a dynamic game framework to analyze the role of large banks in interbank markets. By extending existing models, we incorporate a large bank as a dynamic decision-maker interacting with multiple small banks. Using the mean-field game methodology and convex analysis, best-response

Lab Rats Math 8.5 Rigor 3.5 ·  May 28, 2023

Ranking Quantilized Mean-Field Games with an Application to Early-Stage Venture Investments

Quantilized mean-field game models involve quantiles of the population’s distribution. We study a class of such games with a capacity for ranking games, where the performance of each agent is evaluated based on its terminal state relative to the population’s $α$-quantile value, $α\in (0,1)$. This ev

Lab Rats Math 8 Rigor 3.5 ·  July 1, 2025

Risk-Sensitive Mean Field Games with Common Noise: A Theoretical Study with Applications to Interbank Markets

In this paper, we address linear-quadratic-Gaussian (LQG) risk-sensitive mean field games (MFGs) with common noise. In this framework agents are exposed to a common noise and aim to minimize an exponential cost functional that reflects their risk sensitivity. We leverage the convex analysis method t

Lab Rats Math 9 Rigor 2.5 ·  March 6, 2024

Simultaneously Solving Infinitely Many LQ Mean Field Games In Hilbert Spaces: The Power of Neural Operators

Traditional mean-field game (MFG) solvers operate on an instance-by-instance basis, which becomes infeasible when many related problems must be solved (e.g., for seeking a robust description of the solution under perturbations of the dynamics or utilities, or in settings involving continuum-paramete

Lab Rats Math 9.5 Rigor 2 ·  October 22, 2025

LQG Risk-Sensitive Single-Agent and Major-Minor Mean-Field Game Systems: A Variational Framework

We develop a variational approach to address risk-sensitive optimal control problems with an exponential-of-integral cost functional in a general linear-quadratic-Gaussian (LQG) single-agent setup, offering new insights into such problems. Our analysis leads to the derivation of a nonlinear necessar

Lab Rats Math 9.2 Rigor 1.5 ·  May 24, 2023

Infinite-Dimensional LQ Mean Field Games with Common Noise: Small and Arbitrary Finite Time Horizons

We extend the results of (Liu and Firoozi, 2025), which develops the theory of linear-quadratic (LQ) mean field games (MFGs) in Hilbert spaces, by incorporating a common noise. This common noise is modeled as an infinite-dimensional Wiener process affecting the dynamics of all agents. In the presenc

Lab Rats Math 9.5 Rigor 1 ·  January 20, 2026

Hilbert Space-Valued LQ Mean Field Games: An Infinite-Dimensional Analysis

This paper presents a comprehensive study of linear-quadratic (LQ) mean field games (MFGs) in Hilbert spaces, generalizing the classic LQ MFG theory to scenarios involving $N$ agents with dynamics governed by infinite-dimensional stochastic equations. In this framework, both state and control proces

Lab Rats Math 9.5 Rigor 1 ·  March 1, 2024

A Decomposition Method for LQ Conditional McKean-Vlasov Control Problems with Random Coefficients

We propose a decomposition method for solving a general class of linear-quadratic (LQ) McKean-Vlasov control problems involving conditional expectations and random coefficients, where the system dynamics are driven by two independent Wiener processes. Unlike existing approaches in the literature for

Lab Rats Math 9 Rigor 1 ·  April 13, 2026

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