Related papers: Mean field games: convergence of a finite differen…
In this paper we study the long time behaviour of mean field games systems with fractional diffusion, modeling the case that the individual dynamics of the players is driven by independent jump processes and controlled through the drift…
In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…
We consider a class of continuous-time dynamic games involving a large number of players. Each player selects actions from a finite set and evolves through a finite set of states. State transitions occur stochastically and depend on the…
In this paper, we study the portfolio optimization problem formulated by Lacker and Soret. They formulate a finite time horizon model that allows agents to be competitive, measuring their utility not only by their absolute wealth but also…
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…
Log-linear learning has been extensively studied in both the game theoretic and distributed control literature. It is appealing for many applications because it often guarantees that the agents' collective behavior will converge in…
In the framework of continuous time symmetric stochastic differential games in open loop strategies, we introduce a generalization of mean field game solution, called coarse correlated solution. This can be seen as the analogue of a coarse…
We analyze asymptotic convergence properties of Newton's method for a class of evolutive Mean Field Games systems with non-separable Hamiltonian arising in mean field type models with congestion. We prove the well posedness of the Mean…
Here, we consider one-dimensional forward-forward mean-field games (MFGs) with congestion, which were introduced to approximate stationary MFGs. We use methods from the theory of conservation laws to examine the qualitative properties of…
This paper studies relative arbitrage opportunities in a market with competitive investors through stochastic differential games in the limit as the number of players tends to infinity. With common noises introduced by the stock…
We investigate how the framework of mean-field games may be used to investigate strategic interactions in large heterogeneous populations. We consider strategic interactions in a population of players which may be partitioned into…
In this paper, we study a class of discrete-time mean-field games under the infinite-horizon risk-sensitive discounted-cost optimality criterion. Risk-sensitivity is introduced for each agent (player) via an exponential utility function. In…
We study dynamic finite-player and mean-field stochastic games within the framework of Markov perfect equilibria (MPE). Our focus is on discrete time and space structures without monotonicity. Unlike their continuous-time analogues,…
We consider variational Mean Field Games endowed with a constraint on the maximal density of the distribution of players. Minimizers of the variational formulation are equilibria for a game where both the running cost and the final cost of…
We consider the basic problem of approximating Nash equilibria in noncooperative games. For monotone games, we design continuous time flows which converge in an averaged sense to Nash equilibria. We also study mean field equilibria, which…
In this paper, we consider a first-order deterministic mean field game model inspired by crowd motion in which agents moving in a given domain aim to reach a given target set in minimal time. To model interaction between agents, we assume…
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…
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…
Mean field games have traditionally been defined~[1,2] as a model of large scale interaction of players where each player has a private type that is independent across the players. In this paper, we introduce a new model of mean field teams…
First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit as the number of agents tends to infinity. The known results…