Related papers: Existence and uniqueness for Mean Field Games with…

In this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study a class of deterministic mean field games and master equations, where the interaction of the agents happens…

We propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over…

We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become…

We provide a unified variational inequality framework for the study of fundamental properties of the Nash equilibrium in network games. We identify several conditions on the underlying network (in terms of spectral norm, infinity norm and…

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…

In this paper we study mean field games with possibly multiple mean field equilibria. Instead of focusing on the individual equilibria, we propose to study the set of values over all possible equilibria, which we call the set value of the…

We consider two classes of constrained finite state-action stochastic games. First, we consider a two player nonzero sum single controller constrained stochastic game with both average and discounted cost criterion. We consider the same…

We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical…

We consider a class of deterministic mean field games, where the state associated with each player evolves according to an ODE which is linear w.r.t. the control. Existence, uniqueness, and stability of solutions are studied from the point…

We investigate mean field games for players, who are weakly coupled via their empirical measure. To this end we investigate time-dependent pure jump type propagators over a finite space in the framework of non-linear Markov processes. We…

This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and affected by the aggregate behavior…

A general class of mean field games are considered where the governing dynamics are controlled diffusions in $\mathbb{R}^d$. The optimization criterion is the long time average of a running cost function. Under various sets of hypotheses,…

The mean field games system is a coupled pair of nonlinear partial differential equations arising in differential game theory, as a limit as the number of agents tends to infinity. We prove existence and uniqueness of classical solutions…

Since the seminal work by Meirowitz, there has been growing attention on the existence and uniqueness of continuous Bayesian Nash equilibria. In the existing literature, existence is typically established using Schauder's fixed-point…

In this article, we introduce a new class of entropy-penalized robust mean field game problems in which the representative agent is opposed to Nature. The agent's objective is formulated as a min-max stochastic control problem, in which…

We study the asymptotic organization among many optimizing individuals interacting in a suitable "moderate" way. We justify this limiting game by proving that its solution provides approximate Nash equilibria for large but finite player…

This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence…

Mean field game equilibria are predicated on the assumption of immediate pairwise interactions within a population of homogeneous agents with asymptotically vanishing influence as population size increases. However, in many real-world…

Mean-field games (MFG) were introduced to efficiently analyze approximate Nash equilibria in large population settings. In this work, we consider entropy-regularized mean-field games with a finite state-action space in a discrete time…

We study discrete-time mean-field Markov games with infinite numbers of agents where each agent aims to minimize its ergodic cost. We consider the setting where the agents have identical linear state transitions and quadratic cost…