相关论文: Variational mean field games for market competitio…

This paper studies relative arbitrage opportunities in a market with competitive investors through stochastic differential games in the limit as the number of players tends to infinity. With common noises introduced by the stock…

This paper presents a general existence and uniqueness result for mean field games equations on graphs ($\mathcal{G}$-MFG). In particular, our setting allows to take into account congestion effects of almost any form. These general…

This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action. By active control, a player can bring its state to a resetting point. All players are…

We introduce a notion of weak solution of the master equation without idiosyncratic noise in Mean Field Game theory and establish its existence, uniqueness up to a constant and consistency with classical solutions when it is smooth. We work…

We show the convergence of finite state symmetric N-player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled…

We introduce a mean field game for a family of filtering problems related to the classic sequential testing of the drift of a Brownian motion. To the best of our knowledge this work presents the first treatment of mean field filtering games…

In this paper we provide the existence of classical solutions to stationary mean field game systems in the whole space $\mathbb{R}^N$, with coercive potential and aggregating local coupling, under general conditions on the Hamiltonian. The…

We study mean field portfolio games with consumption. For general market parameters, we establish a one-to-one correspondence between Nash equilibria of the game and solutions to some FBSDE, which is proved to be equivalent to some BSDE.…

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…

In this paper, we study the portfolio optimization problem formulated by Lacker and Soret. They formulate a finite time horizon model that allows agents to be competitive, measuring their utility not only by their absolute wealth but also…

We force uniqueness in finite state mean field games by adding a Wright-Fisher common noise. We achieve this by analyzing the master equation of this game, which is a degenerate parabolic second-order partial differential equation set on…

In this paper, we propose and study an inverse boundary problem for the mean field games (MFGs) governed by the first-order master equation in a bounded domain. We establish the unique identifiability result by showing that the running cost…

Here, we consider one-dimensional forward-forward mean-field games (MFGs) with congestion, which were introduced to approximate stationary MFGs. We use methods from the theory of conservation laws to examine the qualitative properties of…

We establish an existence of equilibrium result for a class of non-Markovian mean-field games with unbounded control space in weak formulation. Our result is based on new existence and stability results for quadratic-growth generalized…

In this paper we study a type of games regularized by the relative entropy, where the players' strategies are coupled through a random environment variable. Besides the existence and the uniqueness of equilibria of such games, we prove that…

The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of…

We discuss a natural game of competition and solve the corresponding mean field game with \emph{common noise} when agents' rewards are \emph{rank dependent}. We use this solution to provide an approximate Nash equilibrium for the finite…

We address the numerical solution of second-order Mean Field Game problems through Newton iterations in infinite dimensions, introduced in [14], where quadratic convergence of the method was rigorously established. Building upon this…

For a number of important mean field games models, the Hamiltonian is non-local and not additively separable. This means that the distribution of agents appears in the Hamiltonian only in an integral over the whole spatial domain. For mean…

We consider a single buyer with a combinatorial preference that would like to purchase related products and services from different vendors, where each vendor supplies exactly one product. We study the general case where subsets of products…