相关论文: Policy iteration method for time-dependent Mean Fi…

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…

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…

The purpose of this paper is to provide a complete probabilistic analysis of a large class of stochastic differential games for which the interaction between the players is of mean-field type. We implement the Mean-Field Games strategy…

In this paper we establish quantitative convergence results for both open and closed-loop Nash equilibria of N-player stochastic differential games in the setting of Mean Field Games of Controls (MFGC), a class of models where interactions…

We investigate time dependent, first order Mean Field Games on the torus comparing, in a broad and general framework, the classical differential formulation , given by a Hamilton Jacobi equation coupled with a continuity equation, with a…

H\"older stability estimate and uniqueness are proven for a retrospective problem of Mean Field Games with a non-quadratic Hamiltonian. The previous result was only for the quadratic Hamiltonian. The main tool is the apparatus of Carleman…

Subject to reasonable conditions, in large population stochastic dynamics games, where the agents are coupled by the system's mean field (i.e. the state distribution of the generic agent) through their nonlinear dynamics and their nonlinear…

First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit as the number of agents tends to infinity. The known results…

We introduce a novel framework to model and solve mean-field game systems with nonlocal interactions. Our approach relies on kernel-based representations of mean-field interactions and feature-space expansions in the spirit of kernel…

We study a particle approximation for one-dimensional first-order Mean-Field-Games (MFGs) with local interactions with planning conditions. Our problem comprises a system of a Hamilton-Jacobi equation coupled with a transport equation. As…

We prove existence and uniqueness of classical solutions of the master equation for mean field game (MFG) systems with fractional and nonlocal diffusions. We cover a large class of L\'evy diffusions of order greater than one, including…

Mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to +$\infty$, have been recently introduced by J-M. Lasry and P-L. Lions. Under suitable assumptions, they lead to a…

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…

Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…

We propose a mesh-free policy iteration framework that combines classical dynamic programming with physics-informed neural networks (PINNs) to solve high-dimensional, nonconvex Hamilton--Jacobi--Isaacs (HJI) equations arising in stochastic…

Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this…

In this paper we examine fully nonlinear mean-field games associated with a minimization problem. The variational setting is driven by a functional depending on its argument through its Hessian matrix. We work under fairly natural…

We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence…

In this paper, we consider Mean Field Games in the presence of common noise relaxing the usual independence assumption of individual random noise. We assume a simple linear model with terminal cost satisfying a convexity and a weak…

We develop the fictitious play algorithm in the context of the linear programming approach for mean field games of optimal stopping and mean field games with regular control and absorption. This algorithm allows to approximate the mean…