English
Related papers

Related papers: Sharp semi-concavity in a non-autonomous control p…

200 papers

In this paper, we consider discrete-time partially observed mean-field games with the risk-sensitive optimality criterion. We introduce risk-sensitivity behaviour for each agent via an exponential utility function. In the game model, each…

Systems and Control · Electrical Eng. & Systems 2022-11-11 Naci Saldi , Tamer Basar , Maxim Raginsky

A mean-field selective optimal control problem of multipopulation dynamics via transient leadership is considered. The agents in the system are described by their spatial position and their probability of belonging to a certain population.…

Optimization and Control · Mathematics 2021-06-15 Giacomo Albi , Stefano Almi , Marco Morandotti , Francesco Solombrino

We consider variational Mean Field Games endowed with a constraint on the maximal density of the distribution of players. Minimizers of the variational formulation are equilibria for a game where both the running cost and the final cost of…

Analysis of PDEs · Mathematics 2019-06-19 Hugo Lavenant , Filippo Santambrogio

Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent…

Analysis of PDEs · Mathematics 2019-07-26 Diogo Gomes , Laurent Lafleche , Levon Nurbekyan

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

We consider deterministic Mean Field Games (MFG) in all Euclidean space with a cost functional continuous with respect to the distribution of the agents and attaining its minima in a compact set. We first show that the static MFG with such…

Analysis of PDEs · Mathematics 2024-03-18 Martino Bardi , Hicham Kouhkouh

Mean-field games (MFGs) are models of large populations of rational agents who seek to optimize an objective function that takes into account their location and the distribution of the remaining agents. Here, we consider stationary MFGs…

Analysis of PDEs · Mathematics 2016-11-28 David Evangelista , Diogo A. Gomes

Reinforcement learning is a powerful tool to learn the optimal policy of possibly multiple agents by interacting with the environment. As the number of agents grow to be very large, the system can be approximated by a mean-field problem.…

Optimization and Control · Mathematics 2020-08-18 Weichen Wang , Jiequn Han , Zhuoran Yang , Zhaoran Wang

Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players…

Systems and Control · Computer Science 2018-06-06 Naci Saldi , Tamer Basar , Maxim Raginsky

Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where…

Mathematical Finance · Quantitative Finance 2019-04-02 Philippe Casgrain , Sebastian Jaimungal

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

We study a class of deterministic mean field games and related optimal control problems, with a finite time horizon and in which the state space is a network. An agent controls her velocity, and, when she occupies a vertex, she can either…

Optimization and Control · Mathematics 2025-11-25 Yves Achdou , Claudio Marchi , Nicoletta Tchou

We study a general class of entropy-regularized multi-variate LQG mean field games (MFGs) in continuous time with $K$ distinct sub-population of agents. We extend the notion of actions to action distributions (exploratory actions), and…

Optimization and Control · Mathematics 2021-12-01 Dena Firoozi , Sebastian Jaimungal

We investigate a mean field optimal control problem obtained in the limit of the optimal control of large particle systems with forcing and terminal data which are not assumed to be convex. We prove that the value function, which is known…

Optimization and Control · Mathematics 2022-04-05 Pierre Cardaliaguet , Panagiotis Souganidis

In this paper we consider a mean field approach to modeling the agents flow over a transportation network. In particular, beside a standard framework of mean field games, with controlled dynamics by the agents and costs mass-distribution…

Optimization and Control · Mathematics 2020-06-18 Fabio Bagagiolo , Rosario Maggistro , Raffaele Pesenti

In this paper we study a mean field model for discrete time, finite number of states, dynamic games. These models arise in situations that involve a very large number of agents moving from state to state according to certain optimality…

Optimization and Control · Mathematics 2009-03-10 Diogo A. Gomes , Joana Mohr , Rafael R. Souza

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 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 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

The objective of this paper is to analyze the existence of equilibria for a class of deterministic mean field games of controls. The interaction between players is due to both a congestion term and a price function which depends on the…

Optimization and Control · Mathematics 2022-01-19 Joseph Frédéric Bonnans , Justina Gianatti , Laurent Pfeiffer