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While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward-forward problem is still poorly understood - even in the one-dimensional setting.…

Analysis of PDEs · Mathematics 2016-06-30 Diogo Gomes , Levon Nurbekyan , Marc Sedjro

We investigate the resolution of second-order, potential, and monotone mean field games with the generalized conditional gradient algorithm, an extension of the Frank-Wolfe algorithm. We show that the method is equivalent to the fictitious…

Optimization and Control · Mathematics 2023-08-22 Pierre Lavigne , Laurent Pfeiffer

We consider a dynamic traffic routing game over an urban road network involving a large number of drivers in which each driver selecting a particular route is subject to a penalty that is affine in the logarithm of the number of drivers…

Optimization and Control · Mathematics 2020-01-22 Takashi Tanaka , Ehsan Nekouei , Ali Reza Pedram , Karl Henrik Johansson

We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. Particular instances of the problem considered here are mean…

Optimization and Control · Mathematics 2022-12-21 Justina Gianatti , Francisco J. Silva

This paper develops a linear programming approach for mean field games with reflected jump-diffusion dynamics. We first prove the equivalence between the mean field equilibria in the linear programming formulation and those in the weak…

Optimization and Control · Mathematics 2025-11-14 Zongxia Liang , Xiang Yu , Keyu Zhang

In this work, we study the convergence rate of the $N$-player LQG game with a Markov chain common noise towards its asymptotic Mean Field Game. By postulating a Markovian structure via two auxiliary processes for the first and second…

Optimization and Control · Mathematics 2023-08-30 Jiamin Jian , Peiyao Lai , Qingshuo Song , Jiaxuan Ye

The formulation of Mean Field Games (MFG) typically requires continuous differentiability of the Hamiltonian in order to determine the advective term in the Kolmogorov--Fokker--Planck equation for the density of players. However, in many…

Numerical Analysis · Mathematics 2024-04-03 Yohance A. P. Osborne , Iain Smears

This paper studies the n-player game and the mean field game under the CRRA relative performance on terminal wealth, in which the interaction occurs by peer competition. In the model with n agents, the price dynamics of underlying risky…

Mathematical Finance · Quantitative Finance 2023-02-10 Lijun Bo , Shihua Wang , Xiang Yu

We consider a mean field game describing the limit of a stochastic differential game of $N$-players whose state dynamics are subject to idiosyncratic and common noise and that can be absorbed when they hit a prescribed region of the state…

Probability · Mathematics 2022-05-25 Matteo Burzoni , Luciano Campi

In recent years, mean field games (MFGs) have garnered considerable attention and emerged as a dynamic and actively researched field across various domains, including economics, social sciences, finance, and transportation. The inverse…

Analysis of PDEs · Mathematics 2024-10-02 Hongyu Liu , Catharine W. K. Lo , Shen Zhang

This paper studies a type of rank-based mean field game in which competing agents strategically switch among multiple effort regimes. We propose an entropy regularized auxiliary problem where the switching decisions are randomized to the…

Optimization and Control · Mathematics 2026-05-29 Zongxia Liang , Shu Wang , Xiang Yu

We address the numerical solution of second-order Mean Field Game problems through Newton iterations in infinite dimensions, introduced in [14], where quadratic convergence of the method was rigorously established. Building upon this…

Numerical Analysis · Mathematics 2026-03-20 Elisabetta Carlini , Ahmad Zorkot

The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…

Optimization and Control · Mathematics 2019-03-19 Bruce Hajek , Michael Livesay

Mean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas.…

Analysis of PDEs · Mathematics 2017-10-05 David Evangelista , Rita Ferreira , Diogo A. Gomes , Levon Nurbekyan , Vardan Voskanyan

In this work, we consider a first order mean field games system with non-local couplings. A Lagrange-Galerkin scheme for the continuity equation, coupled with a semi-Lagrangian scheme for the Hamilton-Jacobi-Bellman equation, is proposed to…

Analysis of PDEs · Mathematics 2023-03-28 E Carlini , Francisco José Silva , Ahmad Zorkot

This paper presents a Gaussian Process (GP) framework, a non-parametric technique widely acknowledged for regression and classification tasks, to address inverse problems in mean field games (MFGs). By leveraging GPs, we aim to recover…

Computer Science and Game Theory · Computer Science 2023-12-27 Jinyan Guo , Chenchen Mou , Xianjin Yang , Chao Zhou

Diffusion approximations have been a popular tool for performance analysis in queueing theory, with the main reason being tractability and computational efficiency. This dissertation is concerned with establishing theoretical guarantees on…

Probability · Mathematics 2017-04-28 Anton Braverman

Markov Population Model is a commonly used framework to describe stochastic systems. Their exact analysis is unfeasible in most cases because of the state space explosion. Approximations are usually sought, often with the goal of reducing…

Systems and Control · Computer Science 2014-05-19 Luca Bortolussi , Rytis Paškauskas

This paper introduces a new approach of treating platoon systems using mean-variance control formulation. The underlying system is a controlled switching diffusion in which the random switching process is a continuous-time Markov chain.…

Optimization and Control · Mathematics 2014-01-22 Zhixin Yang , G. Yin , Le Yi Wang , Hongwei Zhang

This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and…

Optimization and Control · Mathematics 2021-10-12 Xin Guo , Anran Hu , Renyuan Xu , Junzi Zhang