Related papers: A note on first order quasi-stationary Mean Field …
We study the short-time existence and uniqueness of solutions to a coupled system of partial differential equations arising in mean field game theory. It has the generic form $$ \left\{ \begin{array}{c} -\partial_t u - \Delta u +…
We critically revisit the evidence for the existence of quasistationary states in the globally coupled XY (or Hamiltonian mean-field) model. A slow-relaxation regime at long times is clearly revealed by numerical realizations of the model,…
We analyze a fractional mean field game of controls system, showing existence of solutions when the order of the fractional Laplacian is $s\in(\frac{1}{2},1)$. Here the running cost depends on the distribution $\mu$ of not only the states…
In this paper we study second order stationary Mean Field Game systems under density constraints on a bounded domain $\Omega \subset \mathbb{R}^d$. We show the existence of weak solutions for power-like Hamiltonians with arbitrary order of…
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…
Mean Field Game systems describe equilibrium configurations in differential games with infinitely many infinitesimal interacting agents. We introduce a learning procedure (similar to the Fictitious Play) for these games and show its…
We investigate time-dependent mean-field games with superquadratic Hamiltonians and a power dependence on the measure. Such problems pose substantial mathematical challenges as the key techniques used in the subquadratic case do not extend…
This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…
In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the…
Mean field type models describing the limiting behavior, as the number of players tends to $+\infty$, of stochastic differential game problems, have been recently introduced by J-M. Lasry and P-L. Lions. Numerical methods for the…
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 discuss the non-Boltzmannian nature of quasi-stationary states in the Hamiltonian Mean Field (HMF) model, a paradigmatic model for long-range interacting classical many-body systems. We present a theorem excluding the Boltzmann-Gibbs…
In this paper, we prove the existence of classical solutions for time dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses…
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…
The goal of the paper is to introduce a set of problems which we call mean field games of timing. We motivate the formulation by a dynamic model of bank run in a continuous-time setting. We briefly review the economic and game theoretic…
Mean-payoff games are important quantitative models for open reactive systems. They have been widely studied as games of full observation. In this paper we investigate the algorithmic properties of several sub-classes of mean-payoff games…
We propose a new viewpoint on variational mean-field games with diffusion and quadratic Hamiltonian. We show the equivalence of such mean-field games with a relative entropy minimization at the level of probabilities on curves. We also…
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…
Entry-exit dynamics are crucial in modeling crowd movement. Here, we present a novel first-order, stationary mean-field game model on a bounded domain that accurately captures these dynamics. The interior dynamics of the system are governed…
We consider continuous-time heterogeneous agent models with recursive utility (Epstein-Zin utility) cast as mean field games, in which agents prefer late resolution of uncertainty. The model leads to a system coupling a pair of…