Related papers: Entropy Regularization in Mean-Field Games of Opti…

The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game…

This paper is devoted to finite horizon deterministic mean field games in which the state space is a network. The agents control their velocity, and when they occupy a vertex, they can enter into any incident edge. The running and terminal…

This paper is interested in the problem of optimal stopping in a mean field game context. The notion of mixed solution is introduced to solve the system of partial differential equations which models this kind of problem. This notion…

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 propose a reinforcement learning algorithm for stationary mean-field games, where the goal is to learn a pair of mean-field state and stationary policy that constitutes the Nash equilibrium. When viewing the mean-field state and the…

We propose a novel mean field games (MFGs) based GAN(generative adversarial network) framework. To be specific, we utilize the Hopf formula in density space to rewrite MFGs as a primal-dual problem so that we are able to train the model via…

This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and…

This paper concerns a Mean Field Game (MFG) system related to a Nash type equilibrium for dynamical games associated to large populations. One shows that the MFG system may be viewed as the Euler-Lagrange system for an optimal control…

We introduce Mean-Field Trust Region Policy Optimization (MF-TRPO), a novel algorithm designed to compute approximate Nash equilibria for ergodic Mean-Field Games (MFG) in finite state-action spaces. Building on the well-established…

Reinforcement Learning (RL) has emerged as a powerful framework for sequential decision-making in dynamic environments, particularly when system parameters are unknown. This paper investigates RL-based control for entropy-regularized…

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…

We present a simulation-based approach for solution of mean field games (MFGs), using the framework of empirical game-theoretical analysis (EGTA). Our primary method employs a version of the double oracle, iteratively adding strategies…

We consider stochastic differential games with a large number of players, with the aim of quantifying the gap between closed-loop, open-loop and distributed equilibria. We show that, under two different semi-monotonicity conditions, the…

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…

The objective of this work is to study the existence, uniqueness, and stability of equilibria in mean field games involving a major player and a continuum of minor players over finite intervals of arbitrary length. Following earlier…

A mean-field game (MFG) seeks the Nash Equilibrium of a game involving a continuum of players, where the Nash Equilibrium corresponds to a fixed point of the best-response mapping. However, simple fixed-point iterations do not always…

This paper aims to establish an entropy-regularized value-based reinforcement learning method that can ensure the monotonic improvement of policies at each policy update. Unlike previously proposed lower-bounds on policy improvement in…

Traditional mean-field game (MFG) solvers operate on an instance-by-instance basis, which becomes infeasible when many related problems must be solved (e.g., for seeking a robust description of the solution under perturbations of the…

Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players…

To model complex real-world systems, such as traders in stock markets, or the dissemination of contagious diseases, graphon mean-field games (GMFG) have been proposed to model many agents. Despite the empirical success, our understanding of…