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Mean field games is a recent area of study introduced by Lions and Lasry in a series of seminal papers in 2006. Mean field games model situations of competition between large number of rational agents that play non-cooperative dynamic games…

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…

The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…

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…

Mean-Field Games are games with a continuum of players that incorporate the time-dimension through a control-theoretic approach. Recently, simpler approaches relying on the Best Reply Strategy have been proposed. They assume that the agents…

Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…

In [14], Gueant, Lasry and Lions considered the model problem ``What time does meeting start?'' as a prototype for a general class of optimization problems with a continuum of players, called Mean Field Games problems. In this paper we…

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…

Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout…

In this paper, we consider mean-field games where the interaction of each player with the mean-field takes into account not only the states of the players but also their collective behavior, To do so, we develop a random variable framework…

In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary…

Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean…

We consider a mean field game describing the limit of a stochastic differential game of $N$-players whose state dynamics are subject to idiosyncratic and common noise and that can be absorbed when they hit a prescribed region of the state…

Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, while minimizing a cost. The optimal transition rates are…

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…

Mean field games formalize dynamic games with a continuum of players and explicit interaction where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of…

Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been…

We study a family of mean field games arising in modeling the behavior of strategic economic agents which move across space maximizing their utility from consumption and have the possibility to accumulate resources for production (such as…

We introduce a mean field game with rank-based reward: competing agents optimize their effort to achieve a goal, are ranked according to their completion time, and paid a reward based on their relative rank. First, we propose a tractable…

The dynamics of minority games with agents trading on different time scales is studied via dynamical mean-field theory. We analyze the case where the agents' decision-making process is deterministic and its stochastic generalization with…