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Related papers: Mean field games systems of first order

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This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action. By active control, a player can bring its state to a resetting point. All players are…

Optimization and Control · Mathematics 2017-01-25 Minyi Huang , Yan Ma

We consider a class of extended mean field games with common noises, where there exists a strictly terminal constraint. We solve the problem by reducing it to an unconstrained control problem by adding a penalized term in the cost…

Optimization and Control · Mathematics 2025-06-10 Tianjiao Hua , Peng Luo

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

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 paper, we introduce a natural learning rule for mean field games with finite state and action space, the so-called myopic adjustment process. The main motivation for these considerations are the complex computations necessary to…

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

We argue that Hamilton-Jacobi equations provide a convenient and intuitive approach for studying the large-scale behavior of mean-field disordered systems. This point of view is illustrated on the problem of inference of a rank-one matrix.…

Probability · Mathematics 2018-11-13 Jean-Christophe Mourrat

Here, we consider stationary monotone mean-field games (MFGs) and study the existence of weak solutions. First, we introduce a regularized problem that preserves the monotonicity. Next, using variational inequalities techniques, we prove…

Analysis of PDEs · Mathematics 2016-01-13 Rita Ferreira , Diogo Gomes

We present the notion of monotone solution of mean field games master equations in the case of a continuous state space. We establish the existence, uniqueness and stability of such solutions under standard assumptions. This notion allows…

Analysis of PDEs · Mathematics 2023-10-27 Charles Bertucci

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

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

In this paper, we consider a first-order deterministic mean field game model inspired by crowd motion in which agents moving in a given domain aim to reach a given target set in minimal time. To model interaction between agents, we assume…

Optimization and Control · Mathematics 2022-02-21 Saeed Sadeghi Arjmand , Guilherme Mazanti

We discuss the system of Fokker-Planck and Hamilton-Jacobi-Bellman equations arising from the finite horizon control of McKean-Vlasov dynamics. We give examples of existence and uniqueness results. Finally, we propose some simple models for…

Analysis of PDEs · Mathematics 2015-03-18 Yves Achdou , Mathieu Lauriere

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

The goal of the paper is to develop the theory of finite state mean field games with major and minor players when the state space of the game is finite. We introduce the finite player games and derive a mean field game formulation in the…

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

In this paper, we investigate the existence and uniqueness of solutions to a stationary mean field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian with possibly singular congestion effects.…

Analysis of PDEs · Mathematics 2014-08-01 Diogo A. Gomes , Hiroyoshi Mitake

We consider Cournot mean field games of controls, a model originally developed for the production of an exhaustible resource by a continuum of producers. We prove uniqueness of the solution under general assumptions on the price function.…

Optimization and Control · Mathematics 2024-10-30 Fabio Camilli , Mathieu Laurière , Qing Tang

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

In this paper, we consider Mean Field Games in the presence of common noise relaxing the usual independence assumption of individual random noise. We assume a simple linear model with terminal cost satisfying a convexity and a weak…

Probability · Mathematics 2016-07-05 Saran Ahuja

In the framework of continuous time symmetric stochastic differential games in open loop strategies, we introduce a generalization of mean field game solution, called coarse correlated solution. This can be seen as the analogue of a coarse…

Probability · Mathematics 2024-12-20 Luciano Campi , Federico Cannerozzi , Markus Fischer

In this paper we unveil novel monotonicity conditions applicable for Mean Field Games through the exploration of finite dimensional $canonical\ transformations$. Our findings contribute to establishing new global well-posedness results for…

Analysis of PDEs · Mathematics 2026-01-14 Mohit Bansil , Alpár R. Mészáros