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In stochastic dynamic games, when the number of players is sufficiently large and the interactions between agents depend on empirical state distribution, one way to approximate the original game is to introduce infinite-population limit of…

Optimization and Control · Mathematics 2019-08-26 Naci Saldi

In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary…

Optimization and Control · Mathematics 2015-09-23 Diogo A. Gomes , Joana Mohr , Rafael R. Souza

We consider finite horizon stochastic mean field games in which the state space is a network. They are described by a system coupling a backward in time Hamilton-Jacobi-Bellman equation and a forward in time Fokker-Planck equation. The…

Analysis of PDEs · Mathematics 2019-03-08 Yves Achdou , Manh-Khang Dao , Olivier Ley , Nicoletta Tchou

We study a degenerate second order mean field game (MFG) system in a Hilbert space $H$ which couples a Fokker--Planck equation describing the evolution of probability measures on $H$ with a Hamilton--Jacobi--Bellman (HJB) equation for the…

Analysis of PDEs · Mathematics 2026-05-14 Andrzej Święch , Lukas Wessels

The paper is concerned with the dependence of the solution of the deterministic mean field game on the initial distribution of players. The main object of study is the mapping which assigns to the initial time and the initial distribution…

Optimization and Control · Mathematics 2019-02-27 Yurii Averboukh

Mean Field Game (MFG) models implicitly assume "rational expectations", meaning that the heterogeneous agents being modeled correctly know all relevant transition probabilities for the complex system they inhabit. When there is common…

Analysis of PDEs · Mathematics 2026-02-26 Benjamin Moll , Lenya Ryzhik

We formulate a mean field game where each player stops a privately observed Brownian motion with absorption. Players are ranked according to their level of stopping and rewarded as a function of their relative rank. There is a unique mean…

Optimization and Control · Mathematics 2021-03-09 Marcel Nutz , Yuchong Zhang

This paper revisits the well-studied \emph{optimal stopping} problem but within the \emph{large-population} framework. In particular, two classes of optimal stopping problems are formulated by taking into account the \emph{relative…

Optimization and Control · Mathematics 2022-06-08 Jianhui Huang , Tinghan Xie

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…

Probability · Mathematics 2020-11-03 Masaaki Fujii

In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of sales-and-purchase orders in the exchange market, where a large number of…

Mathematical Finance · Quantitative Finance 2021-09-28 Masaaki Fujii , Akihiko Takahashi

In this work we develop a numerical method for solving a type of convex graph-structured tensor optimization problems. This type of problems, which can be seen as a generalization of multi-marginal optimal transport problems with…

Optimization and Control · Mathematics 2024-03-25 Axel Ringh , Isabel Haasler , Yongxin Chen , Johan Karlsson

In this paper, we introduce a bilevel optimization framework for addressing inverse mean-field games, alongside an exploration of numerical methods tailored for this bilevel problem. The primary benefit of our bilevel formulation lies in…

Optimization and Control · Mathematics 2024-11-13 Jiajia Yu , Quan Xiao , Tianyi Chen , Rongjie Lai

In this letter, we study a class of linear-quadratic mean-field-type difference games with coupled affine inequality constraints. We show that the mean-field-type equilibrium can be characterized by the existence of a multiplier process…

Optimization and Control · Mathematics 2025-10-06 Partha Sarathi Mohapatra , Puduru Viswanadha Reddy

This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations…

Optimization and Control · Mathematics 2011-10-19 Olivier Guéant

This work is mainly concerned with the so-called limit theory for mean-field games. Adopting the weak formulation paradigm put forward by Carmona and Lacker, we consider a fully non-Markovian setting allowing for drift control and…

Probability · Mathematics 2023-12-25 Dylan Possamaï , Ludovic Tangpi

Mean field Game (MFG) Partial Differential Inclusions (PDI) are generalizations of the system of Partial Differential Equations (PDE) of Lasry and Lions to situations where players in the game may have possibly nonunique optimal controls,…

Optimization and Control · Mathematics 2025-09-15 Yohance A. P. Osborne , Iain Smears

We extend the weak-strong uniqueness principle for mean-field game (MFG) systems to a broad class of second-order stationary and time-dependent problems. Under standard monotonicity, growth, and coercivity assumptions on the Hamiltonian,…

Analysis of PDEs · Mathematics 2026-04-02 Rita Ferreira , Diogo Gomes , Bashayer Majrashi

We develop a convex analysis approach for solving LQG optimal control problems and apply it to major-minor (MM) LQG mean-field game (MFG) systems. The approach retrieves the best response strategies for the major agent and all minor agents…

Systems and Control · Computer Science 2020-06-15 Dena Firoozi , Sebastian Jaimungal , Peter E. Caines

We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…

Analysis of PDEs · Mathematics 2020-03-10 Y Achdou , Z Kobeissi

This paper studies an inverse problem for a multipopulation mean field game (MFG) system where the objective is to reconstruct the running and terminal cost functions of the system that couples the dynamics of different populations. We…

Analysis of PDEs · Mathematics 2025-02-17 Kui Ren , Nathan Soedjak , Kewei Wang