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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

We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian behaves like a power of its arguments as they tend to infinity,…

Analysis of PDEs · Mathematics 2020-06-24 Z Kobeissi

We analyze optimal transport problems with additional entropic cost evaluated along curves in the Wasserstein space which join two probability measures $m_0,m_1$. The effect of the additional entropy functional results into an elliptic…

Analysis of PDEs · Mathematics 2022-11-18 Alessio Porretta

In this paper, we are concerned with the inverse problem of determining anomalies in the state space associated with the stationary mean field game (MFG) system. We establish novel unique identifiability results for the intrinsic structure…

Analysis of PDEs · Mathematics 2025-05-14 Hongyu Liu , Catharine W. K. Lo

The paper considers a forward-backward system of parabolic PDEs arising in a Mean Field Game (MFG) model where every agent controls the drift of a trajectory subject to Brownian diffusion, trying to escape a given bounded domain $\Omega$ in…

Analysis of PDEs · Mathematics 2022-12-23 Romain Ducasse , Guilherme Mazanti , Filippo Santambrogio

The paper is concerned with the deterministic limit of mean field games with the nonlocal coupling. It is assumed that the dynamics of mean field games are given by nonlinear Markov processes. This type of games includes stochastic mean…

Optimization and Control · Mathematics 2018-01-08 Yurii Averboukh

The goal of the paper is to introduce a formulation of the mean field game with major and minor players as a fixed point on a space of controls. This approach emphasizes naturally the role played by McKean-Vlasov dynamics in some of the…

Probability · Mathematics 2016-10-19 Rene Carmona , Peiqi Wang

In this paper, we characterize the asymptotic behavior of a first-order stationary mean-field game (MFG) with a logarithm coupling, a quadratic Hamiltonian, and a periodically oscillating potential. This study falls into the realm of the…

Analysis of PDEs · Mathematics 2019-05-07 Rita Ferreira , Diogo Gomes , Xianjin Yang

Here, we observe that mean-field game (MFG) systems admit a two-player infinite-dimensional general-sum differential game formulation. We show that particular regimes of this game reduce to previously known variational principles.…

Analysis of PDEs · Mathematics 2018-04-25 Marco Cirant , Levon Nurbekyan

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

Mean field games models describing the limit of a large class of stochastic differential games, as the number of players goes to $+\infty$, have been introduced by J.-M. Lasry and P.-L. Lions. We use a change of variables to transform the…

Numerical Analysis · Mathematics 2011-06-17 Olivier Guéant

We consider both finite-state game graphs and recursive game graphs (or pushdown game graphs), that can model the control flow of sequential programs with recursion, with multi-dimensional mean-payoff objectives. In pushdown games two types…

Computer Science and Game Theory · Computer Science 2013-08-09 Krishnendu Chatterjee , Yaron Velner

We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled continuity equation featuring a nonlinear activation function on…

Optimization and Control · Mathematics 2023-10-10 Yuan Gao , Wuchen Li , Jian-Guo Liu

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

An overdetermination is introduced in an initial condition for the second order mean field games system (MFGS). This makes the resulting problem close to the classical ill-posed Cauchy problems for PDEs. Indeed, in such a problem and…

Analysis of PDEs · Mathematics 2023-03-09 Michael V. Klibanov

The aim of this paper is to study the long time behavior of solutions to deterministic mean field games systems on Euclidean space. This problem was addressed on the torus ${\mathbb T}^n$ in [P. Cardaliaguet, {\it Long time average of first…

Optimization and Control · Mathematics 2019-12-11 Piermarco Cannarsa , Wei Cheng , Cristian Mendico , Kaizhi Wang

Mean field games formalize dynamic games with a continuum of players and explicit interaction where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of…

Optimization and Control · Mathematics 2020-01-09 Berenice Anne Neumann

We study the behavior of solutions to the first-order mean field games system with a local coupling, when the initial density is a compactly supported function on the real line. Our results show that the solution is smooth in regions where…

Analysis of PDEs · Mathematics 2023-08-02 Pierre Cardaliaguet , Sebastian Munoz , Alessio Porretta

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

We consider the optimal control of solutions of first order Hamilton-Jacobi equations, where the Hamiltonian is convex with linear growth. This models the problem of steering the propagation of a front by constructing an obstacle. We prove…

Optimization and Control · Mathematics 2013-10-11 Philip Jameson Graber