Related papers: Approximation of deterministic mean field games un…

We discuss and compare two methods of investigations for the asymptotic regime of stochastic differential games with a finite number of players as the number of players tends to the infinity. These two methods differ in the order in which…

We use the recently developed probabilistic analysis of mean field games with finitely many states in the weak formulation, to set-up a principal / agent contract theory model where the principal faces a large population of agents…

This paper studies the mean field game (MFG) problem arising from a large population competition in fund management, featuring a new type of relative performance via the benchmark tracking. In the $n$-player model, each agent aims to…

In the context of simple finite-state discrete time systems, we introduce a generalization of mean field game solution, called correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium. Our notion of…

We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this…

Independent learners are agents that employ single-agent algorithms in multi-agent systems, intentionally ignoring the effect of other strategic agents. This paper studies mean-field games from a decentralized learning perspective, with two…

Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics…

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…

Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…

The paper is concerned with the dependence of the solution of the deterministic mean field game on the initial distribution of players. The main object of study is the mapping which assigns to the initial time and the initial distribution…

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…

We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a 2-player game. We exhibit a class of 2-player games having payoffs in the range [0,1] that show that Fictitious Play…

We study a multi-agent mean field type control problem in discrete time where the agents aim to find a socially optimal strategy and where the state and action spaces for the agents are assumed to be continuous. The agents are only weakly…

We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian behaves like a power of its arguments as they tend to infinity,…

This paper proposes a multiscale method for solving the numerical solution of mean field games which accelerates the convergence and addresses the problem of determining the initial guess. Starting from an approximate solution at the…

This study addresses primal-dual dynamics for a stochastic programming problem for capacity network design. It is proven that consensus can be achieved on the \textit{here and now} variables which represent the capacity of the network. The…

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…

The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…

This work tackles the problem of energy-efficient distributed power control in wireless networks with a large number of transmitters. The problem is modeled by a dynamic game. Each transmitter-receiver communication is characterized by a…

A multi-agent system operates in an uncertain environment about which agents have different and time varying beliefs that, as time progresses, converge to a common belief. A global utility function that depends on the realized state of the…