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Mean Field Game is a rather new field initially developed in applied mathematics and engineering in order to deal with the dynamics of a large number of controlled agents or objects in interaction. For a large class of these models, there…

Physics and Society · Physics 2021-08-25 Thibault Bonnemain , Thierry Gobron , Denis Ullmo

In this paper, we consider the mean field game with a common noise and allow the state coefficients to vary with the conditional distribution in a nonlinear way. We assume that the cost function satisfies a convexity and a weak monotonicity…

Optimization and Control · Mathematics 2021-05-26 Ziyu Huang , Shanjian Tang

Motivated by recent developments in mean-field games in ecology, in this paper we introduce a connection between the best response dynamics in evolutionary game theory, the minimization of the highest income of a game, and minimizing…

Optimization and Control · Mathematics 2024-11-13 Dante Kalise , Alessio Oliviero , Domènec Ruiz-Balet

Mean Field Games (MFG) theory describes strategic interactions in differential games with a large number of small and indistinguishable players. Traditionally, the players' control impacts only the drift term in the system's dynamics,…

Analysis of PDEs · Mathematics 2024-07-31 Vincenzo Ignazio , Michele Ricciardi

We propose a new viewpoint on variational mean-field games with diffusion and quadratic Hamiltonian. We show the equivalence of such mean-field games with a relative entropy minimization at the level of probabilities on curves. We also…

Optimization and Control · Mathematics 2019-04-01 Jean-David Benamou , Guillaume Carlier , Simone Di Marino , Luca Nenna

We investigate mean field game systems under invariance conditions for the state space, otherwise called {\it viability conditions} for the controlled dynamics. First we analyze separately the Hamilton-Jacobi and the Fokker-Planck…

Analysis of PDEs · Mathematics 2019-03-18 Alessio Porretta , Michele Ricciardi

This paper is devoted to finite horizon deterministic mean field games in which the state space is a network. The agents control their velocity, and when they occupy a vertex, they can enter into any incident edge. The running and terminal…

Optimization and Control · Mathematics 2023-11-21 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou

This work introduces a new general approach for the numerical analysis of stable equilibria to second order mean field games systems in cases where the uniqueness of solutions may fail. For the sake of simplicity, we focus on a simple…

Analysis of PDEs · Mathematics 2024-10-30 Jules Berry , Olivier Ley , Francisco J Silva

While the general theory for the terminal-initial value problem in mean-field games is widely used in many models of applied mathematics, the modeling potential of the corresponding forward-forward version is still under-considered. In this…

Analysis of PDEs · Mathematics 2024-02-01 Adriano Festa , Simone Gottlich , Michele Ricciardi

In this paper we study a class of matrix-valued linear-quadratic mean-field-type games for both the risk-neutral, risk-sensitive and robust cases. Non-cooperation, full cooperation and adversarial between teams are treated. We provide a…

Optimization and Control · Mathematics 2019-06-06 Julian Barreiro-Gomez , Tyrone E. Duncan , Hamidou Tembine

In this paper we study iterative procedures for stationary equilibria in games with large number of players. Most of learning algorithms for games with continuous action spaces are limited to strict contraction best reply maps in which the…

Machine Learning · Computer Science 2012-10-18 Hamidou Tembine , Raul Tempone , Pedro Vilanova

The purpose of this article is to show that an intrinsic noise with values in the space ${\mathcal P}({\mathbb R})$ of $1d$ probability measures may force uniqueness to first order mean field games. The structure of the noise is inspired…

Probability · Mathematics 2024-01-26 François Delarue , Youssef Ouknine

In this paper, we investigate the robustness of stationary mean-field equilibria in the presence of model uncertainties, specifically focusing on infinite-horizon discounted cost functions. To achieve this, we initially establish…

Systems and Control · Electrical Eng. & Systems 2026-04-10 Uğur Aydın , Naci Saldi

We develop a probabilistic approach to continuous-time finite state mean field games. Based on an alternative description of continuous-time Markov chain by means of semimartingale and the weak formulation of stochastic optimal control, our…

Probability · Mathematics 2018-08-24 Rene Carmona , Peiqi Wang

This paper studies the mean field game (MFG) and N-player game on relative performance portfolio management with two heterogeneous populations. In addition to the Brownian idiosyncratic and common noise, the first population invests in…

Optimization and Control · Mathematics 2025-11-20 Yuchen Li , Zongxia Liang , Xiang Yu

In this paper, the existence of non-trivial time periodic solutions of first order mean field games is proved. It is assumed that there is a non-trivial periodic orbit contained in the Mather set. The whole system is autonomous with a…

Analysis of PDEs · Mathematics 2024-01-17 Panrui Ni

Recent advances at the intersection of dense large graph limits and mean field games have begun to enable the scalable analysis of a broad class of dynamical sequential games with large numbers of agents. So far, results have been largely…

Computer Science and Game Theory · Computer Science 2022-02-21 Kai Cui , Heinz Koeppl

We develop a splitting method to prove the well-posedness, in short time, of solutions for two master equations in mean field game (MFG) theory: the second order master equation, describing MFGs with a common noise, and the system of master…

Analysis of PDEs · Mathematics 2020-01-29 Pierre Cardaliaguet , Marco Cirant , Alessio Porretta

Mean Field Games provide a powerful framework to analyze the dynamics of a large number of controlled objects in interaction. Though these models are much simpler than the underlying differential games they describe in some limit, their…

Physics and Society · Physics 2020-07-15 Thibault Bonnemain , Thierry Gobron , Denis Ullmo

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