相关论文: Finite State Mean Field Games with Common Shocks
We study the forward-backward system of stochastic partial differential equations describing a mean field game for a large population of small players subject to both idiosyncratic and common noise. The unique feature of the problem is that…
We investigate mean field game systems under invariance conditions for the state space, otherwise called {\it viability conditions} for the controlled dynamics. First we analyze separately the Hamilton-Jacobi and the Fokker-Planck…
We propose a new mean-field game model with two states to study synchronization phenomena, and we provide a comprehensive characterization of stationary and dynamic equilibria along with their stability properties. The game undergoes a…
This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action, and benefits from the improvement of the condition of the overall population. Based on an…
The goal of this paper is to demonstrate that common noise may serve as an exploration noise for learning the solution of a mean field game. This concept is here exemplified through a toy linear-quadratic model, for which a suitable form of…
This paper studies mean field games for multi-agent systems with control-dependent multiplicative noises. For the general systems with nonuniform agents, we obtain a set of decentralized strategies by solving an auxiliary limiting optimal…
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 here address the question of restoration of uniqueness in mean-field games deriving from deterministic differential games with a large number of players. The general strategy for restoring uniqueness is inspired from earlier similar…
In this paper we unveil novel monotonicity conditions applicable for Mean Field Games through the exploration of finite dimensional $canonical\ transformations$. Our findings contribute to establishing new global well-posedness results for…
This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations…
Mean field games are limit models for symmetric $N$-player games with interaction of mean field type as $N\to\infty$. The limit relation is often understood in the sense that a solution of a mean field game allows to construct approximate…
A theory of existence and uniqueness is developed for general stochastic differential mean field games with common noise. The concepts of strong and weak solutions are introduced in analogy with the theory of stochastic differential…
We develop the theory of linear-quadratic (LQ) mean field games (MFGs) in Hilbert spaces with common noise modeled by an infinite-dimensional Wiener process that affects the dynamics of all agents. In the presence of common noise, the…
We introduce a simple class of mean field games with absorbing boundary over a finite time horizon. In the corresponding $N$-player games, the evolution of players' states is described by a system of weakly interacting It\^o equations with…
We study mean-field game (MFG) problems with rough common noise, in which the representative state dynamics are governed by a controlled rough stochastic differential equation driven by an idiosyncratic Brownian motion and a deterministic…
This paper provides a mathematical study of the well-posedness of master equation on finite state space involving terms modelling common noise. In this setting, the solution of the master equation depends on an additional variable modelling…
Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…
We study a class of linear-quadratic mean-field games with incomplete information. For each agent, the state is given by a linear forward stochastic differential equation with common noise. Moreover, both the state and control variables can…
We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider…
This paper establishes an equilibrium existence result for a class of Mean Field Games involving Reflected Stochastic Differential Equations. The proof relies on the framework of relaxed controls and martingale problems.