Related papers: Decoding a mean field game by the Cauchy data arou…
This work investigates the ambient potential identification problem in inverse Mean-Field Games (MFGs), where the goal is to recover the unknown potential from the value function at equilibrium. We propose a simple yet effective iterative…
In this paper, we propose an initial value fomulation of the discrete mean field games on finite graphs (Graph MFG), and design a neural network based approach to solve it. Graph MFG describes infinite, non-cooperative and interactive…
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…
In this paper, we study the long-time behavior of mean field game (MFG) systems influenced by a common noise. While classical results establish the convergence of deterministic MFG towards stationary solutions under suitable monotonicity…
A retrospective analysis process for the mean field games system (MFGS) is considered. For the first time, Carleman estimates are applied to the analysis of the MFGS. Two new Carleman estimates are derived. They allow to obtain the…
In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems,…
The pairwise comparison dynamic is a forward ordinary differential equation in a Banach space whose solution is a time-dependent probability measure to maximize utility based on a nonlinear and nonlocal protocol. It contains a wide class of…
This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and…
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…
We investigate inverse backward-in-time problems for a class of second-order degenerate Mean-Field Game (MFG) systems. More precisely, given the final datum $(u(\cdot, T),m(\cdot, T))$ of a solution to the one-dimensional mean-field game…
The framework of Mean-field Games (MFGs) is used for modelling the collective dynamics of large populations of non-cooperative decision-making agents. We formulate and analyze a kinetic MFG model for an interacting system of non-cooperative…
The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…
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…
The recent mean field game (MFG) formalism has enabled the application of inverse reinforcement learning (IRL) methods in large-scale multi-agent systems, with the goal of inferring reward signals that can explain demonstrated behaviours of…
The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…
Learning the behavior of large agent populations is an important task for numerous research areas. Although the field of multi-agent reinforcement learning (MARL) has made significant progress towards solving these systems, solutions for…
This paper considers a class of mean field linear-quadratic-Gaussian (LQG) games with model uncertainty. The drift term in the dynamics of the agents contains a common unknown function. We take a robust optimization approach where a…
While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward-forward problem is still poorly understood - even in the one-dimensional setting.…
Mean-field games with absorption is a class of games, that have been introduced in Campi and Fischer (2018) and that can be viewed as natural limits of symmetric stochastic differential games with a large number of players who, interacting…
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…