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Related papers: Minimal-time mean field games

200 papers

We study continuous-time heterogeneous agent models cast as Mean Field Games, in the Aiyagari-Bewley-Huggett framework. The model couples a Hamilton-Jacobi-Bellman equation for individual optimization with a Fokker-Planck-Kolmogorov…

Optimization and Control · Mathematics 2025-10-02 Fabio Camilli , Qing Tang , Yong-shen Zhou

In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on…

Optimization and Control · Mathematics 2020-11-06 Youness Mezzan , Moulay Hicham Tber

We introduce and study a mean-field model for a system of spatially distributed players interacting through an evolutionary game driven by a replicator dynamics. Strategies evolve by a replicator dynamics influenced by the position and the…

Optimization and Control · Mathematics 2018-05-11 Luigi Ambrosio , Massimo Fornasier , Marco Morandotti , Giuseppe Savaré

This study addresses primal-dual dynamics for a stochastic programming problem for capacity network design. It is proven that consensus can be achieved on the \textit{here and now} variables which represent the capacity of the network. The…

Optimization and Control · Mathematics 2020-09-11 Casper T. Röling , Dario Bauso , Hamidou Tembine

We study a family of mean field games arising in modeling the behavior of strategic economic agents which move across space maximizing their utility from consumption and have the possibility to accumulate resources for production (such as…

Analysis of PDEs · Mathematics 2026-01-22 Daria Ghilli , Fausto Gozzi , Giovanni Zanco

We explore a mechanism of decision-making in Mean Field Games with myopic players. At each instant, agents set a strategy which optimizes their expected future cost by assuming their environment as immutable. As the system evolves, the…

Optimization and Control · Mathematics 2018-02-05 Charafeddine Mouzouni

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

In this article, we introduce a new class of entropy-penalized robust mean field game problems in which the representative agent is opposed to Nature. The agent's objective is formulated as a min-max stochastic control problem, in which…

Optimization and Control · Mathematics 2026-03-27 François Delarue , Pierre Lavigne

In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a locally compact Polish…

Systems and Control · Computer Science 2017-01-17 Naci Saldi , Tamer Başar , Maxim Raginsky

We derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ODEs and a PDE of Vlasov-type. Such problems arise naturally as ${\Gamma}$-limits of optimal control problems subject to ODE…

Optimization and Control · Mathematics 2015-04-10 Mattia Bongini , Massimo Fornasier , Francesco Rossi , Francesco Solombrino

Mean field game equilibria are predicated on the assumption of immediate pairwise interactions within a population of homogeneous agents with asymptotically vanishing influence as population size increases. However, in many real-world…

Systems and Control · Electrical Eng. & Systems 2026-05-20 Farid Rajabali , Roland Malhame , Sadegh Bolouki

This paper examines mean field linear-quadratic-Gaussian (LQG) social optimum control with volatility-uncertain common noise. The diffusion terms in the dynamics of agents contain an unknown volatility process driven by a common noise. We…

Optimization and Control · Mathematics 2019-12-16 Jianhui Huang , Bing-Chang Wang , Jiongmin Yong

We consider an economy made of competing firms which are heterogeneous in their capital and use several inputs for producing goods. Their consumption policy is fixed rationally by maximizing a utility and their capital cannot fall below a…

Analysis of PDEs · Mathematics 2022-07-13 Yves Achdou , Guillaume Carlier , Quentin Petit , Daniela Tonon

We consider both $N$-player and mean-field games of optimal portfolio liquidation in which the players are not allowed to change the direction of trading. Players with an initially short position of stocks are only allowed to buy while…

Mathematical Finance · Quantitative Finance 2025-07-31 Guanxing Fu , Paul P. Hager , Ulrich Horst

This article introduces a novel mean-field game model for multi-sector economic growth in which a dynamically evolving externality, influenced by the collective actions of agents, plays a central role. Building on classical growth theories…

Optimization and Control · Mathematics 2026-05-05 Pierre Lavigne , Quentin Petit , Xavier Warin

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

In this paper, we propose a mean-field game model for the price formation of a commodity whose production is subjected to random fluctuations. The model generalizes existing deterministic price formation models. Agents seek to minimize…

Analysis of PDEs · Mathematics 2020-03-05 Diogo Gomes , Julian Gutierrez , Ricardo Ribeiro

This paper studies social optimal control of mean field LQG (linear-quadratic-Gaussian) models with uncertainty. Specially, the uncertainty is represented by a uncertain drift which is common for all agents. A robust optimization approach…

Optimization and Control · Mathematics 2019-08-06 Bing-Chang Wang , Jianhui Huang , Ji-Feng Zhang

We propose the concept of a Lagrangian game to solve constrained Markov games. Such games model scenarios where agents face cost constraints in addition to their individual rewards, that depend on both agent joint actions and the evolving…

Optimization and Control · Mathematics 2025-03-14 Soham Das , Santiago Paternain , Luiz F. O. Chamon , Ceyhun Eksin

Mean Field Games with state constraints are differential games with infinitely many agents, each agent facing a constraint on his state. The aim of this paper is to provide a meaning of the PDE system associated with these games, the…

Optimization and Control · Mathematics 2019-01-01 Piermarco Cannarsa , Rossana Capuani , Pierre Cardaliaguet