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We introduce a new mean-field game framework to analyze the impact of carbon pricing in a multi-sector economy with defaultable firms. Each sector produces a homogeneous good, with its price endogenously determined through market clearing.…

General Economics · Economics 2025-07-16 Zorana Grbac , Simone Pavarana , Thorsten Schmidt , Peter Tankov

We prove the global-in-time well-posedness for a broad class of mean field game problems, which is beyond the special linear-quadratic setting, as long as the mean field sensitivity is not too large. Through the stochastic maximum…

Optimization and Control · Mathematics 2025-01-23 Alain Bensoussan , Ho Man Tai , Tak Kwong Wong , Sheung Chi Phillip Yam

Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent…

Analysis of PDEs · Mathematics 2019-07-26 Diogo Gomes , Laurent Lafleche , Levon Nurbekyan

We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a lower threshold, and its default causes instantaneous losses…

Probability · Mathematics 2017-05-03 Sergey Nadtochiy , Mykhaylo Shkolnikov

We establish an existence of equilibrium result for a class of non-Markovian mean-field games with unbounded control space in weak formulation. Our result is based on new existence and stability results for quadratic-growth generalized…

Optimization and Control · Mathematics 2026-03-09 Ulrich Horst , Takashi Sato

We consider time-dependent viscous Mean-Field Games systems in the case of local, decreasing and unbounded coupling. These systems arise in mean-field game theory, and describe Nash equilibria of games with a large number of agents aiming…

Analysis of PDEs · Mathematics 2017-04-14 Marco Cirant , Daniela Tonon

We consider a system of $N$ interacting particles, governed by transport and diffusion, that converges in a mean-field limit to the solution of a McKean-Vlasov equation. From the observation of a trajectory of the system over a fixed time…

Statistics Theory · Mathematics 2021-03-16 Laetitia Della Maestra , Marc Hoffmann

This paper studies an optimal investment-consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as…

Optimization and Control · Mathematics 2024-05-06 Zongxia Liang , Keyu Zhang

We study the discrete Fokker-Planck equation associated with the mean-field dynamics of a particle system called the dispersion process. For different regimes of the average number of particles per site (denoted by $\mu > 0$), we establish…

Probability · Mathematics 2025-08-25 Fei Cao , Jincheng Yang

Neural network dynamics emerge from the interaction of spiking cells. One way to formulate the problem is through a theoretical framework inspired by ideas coming from statistical physics, the so-called mean-field theory. In this document,…

Analysis of PDEs · Mathematics 2020-11-11 Grégory Dumont , Pierre Gabriel

Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise.…

Neurons and Cognition · Quantitative Biology 2016-09-28 Diego Fasoli , Anna Cattani , Stefano Panzeri

We develop a model based on mean-field games of competitive firms producing similar goods according to a standard AK model with a depreciation rate of capital generating pollution as a byproduct. Our analysis focuses on the widely-used…

Mathematical Finance · Quantitative Finance 2024-07-18 Gianmarco Del Sarto , Marta Leocata , Giulia Livieri

We propose a new evolutionary dynamics for population games with a discrete strategy set, inspired by the theory of optimal transport and Mean field games. The dynamics can be described as a Fokker-Planck equation on a discrete strategy…

Optimization and Control · Mathematics 2018-11-14 Shui-Nee Chow , Wuchen Li , Jun Lu , Haomin Zhou

In this work we provide a simple setting that connects the structural modelling approach of Gai-Kapadia interbank networks with the mean-field approach to default contagion. To accomplish this we make two key contributions. First, we…

Mathematical Finance · Quantitative Finance 2021-07-08 Zachary Feinstein , Andreas Sojmark

We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…

Optimization and Control · Mathematics 2026-01-21 Zongxia Liang , Zhou Zhou , Yaqi Zhuang , Bin Zou

We consider the control of McKean-Vlasov dynamics (or mean-field control) with probabilistic state constraints. We rely on a level-set approach which provides a representation of the constrained problem in terms of an unconstrained one with…

Optimization and Control · Mathematics 2022-11-03 Maximilien Germain , Huyên Pham , Xavier Warin

Fokker-Planck equations represent a suitable description of the finite-time behavior for a large class of particle systems as the size of the population tends to infinity. Recently, the theory of graph limits has been introduced in the…

Probability · Mathematics 2022-03-24 Fabio Coppini

A simple banking network model is proposed which features multiple waves of bank defaults and is analytically solvable in the limiting case of an infinitely large homogeneous network. The model is a collection of nodes representing…

Risk Management · Quantitative Finance 2012-04-02 Igor Tsatskis

We study mean field games with unbounded coefficients. The existence of a solution is proved. We propose a new approach based on Fokker-Planck-Kolmogorov equations, the Ambrosio-Figalli-Trevisan superposition principle, the method of…

Analysis of PDEs · Mathematics 2026-03-02 Stanislav V. Shaposhnikov , Dmitry V. Shatilovich

We present a Mean Field Game approach to obtain the rate function for the empirical measure of interacting particles under McKean-Vlasov dynamics. Although the result is well known, our approach relies on PDE methods and provides another…

Analysis of PDEs · Mathematics 2023-10-13 Nikiforos Mimikos-Stamatopoulos