相关论文: Self-similar intermediate asymptotics for first-or…

We study the asymptotic behavior for singular solutions to a critical fourth order system generalizing the constant $Q$-curvature equation. Our main result extends to the case of strongly coupled systems, the celebrated asymptotic…

We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $n$-player equilibria converges to it as $n\to\infty$. However, both the finite and…

We study a level-set mean curvature flow equation with driving and source terms, and establish convergence results on the asymptotic behavior of solutions as time goes to infinity under some additional assumptions. We also study the…

Mean field approximation is a popular method to study the behaviour of stochastic models composed of a large number of interacting objects. When the objects are asynchronous, the mean field approximation of a population model can be…

This paper studies the relation between equilibria in single-period, discrete-time and continuous-time mean field game models. First, for single-period mean field games, we establish the existence of equilibria and then prove the…

An iterative finite difference scheme for mean field games (MFGs) is proposed. The target MFGs are derived from control problems for multidimensional systems with advection terms. For such MFGs, linearization using the Cole-Hopf…

We extend the weak-strong uniqueness principle for mean-field game (MFG) systems to a broad class of second-order stationary and time-dependent problems. Under standard monotonicity, growth, and coercivity assumptions on the Hamiltonian,…

We establish new asymptotic results for the solutions of the second-grade fluids equations and characterize their decay rate in terms of the behavior of the initial data. Moreover, assuming more regularity for the initial data, we study the…

We study a specific class of finite-horizon mean field optimal stopping problems by means of the dynamic programming approach. In particular, we consider problems where the state process is not affected by the stopping time. Such problems…

This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsive force. Our setting covers pile-ups of dislocations,…

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 +…

This paper considers discounted infinite horizon mean field games by extending the probabilistic weak formulation of the game as introduced by Carmona and Lacker (2015). Under similar assumptions as in the finite horizon game, we prove…

In this paper we study Mean Field Game systems under density constraints as optimality conditions of two optimization problems in duality. A weak solution of the system contains an extra term, an additional price imposed on the saturated…

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…

We employ a nonlocal method to study the asymptotic behavior at infinity ofsolutions to the two-dimensional supercritical Lagrangian mean curvature equation \[ \arctan \lambda_1(D^2u)+\arctan \lambda_2(D^2u) = \theta + f(x) \] on exterior…

We provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow to prove existence and approximation of strong mean field equilibria in models where data may not be continuous with…

Competitive games involving thousands or even millions of players are prevalent in real-world contexts, such as transportation, communications, and computer networks. However, learning in these large-scale multi-agent environments presents…

Recent advances at the intersection of dense large graph limits and mean field games have begun to enable the scalable analysis of a broad class of dynamical sequential games with large numbers of agents. So far, results have been largely…

We study the mean field game problem for a nervous system consisting of a large number of neurons with mean-field interaction. In this system, each neuron can modulate its spiking activity by controlling its membrane potential to…

We study a Mean Field Games (MFG) system in a real, separable infinite dimensional Hilbert space. The system consists of a second order parabolic type equation, called Hamilton-Jacobi-Bellman (HJB) equation in the paper, coupled with a…