Related papers: A Mean Field Games approach to Cluster Analysis
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…
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…
We study mean field games and corresponding $N$-player games in continuous time over a finite time horizon where the position of each agent belongs to a finite state space. As opposed to previous works on finite state mean field games, we…
In the paper, we use the equivalent formulation of a finite state mean field game as a control problem with mixed constraints to study the dependence of solutions to finite state mean field game on an initial distribution of players. We…
A mixture of multivariate contaminated normal (MCN) distributions is a useful model-based clustering technique to accommodate data sets with mild outliers. However, this model only works when fitted to complete data sets, which is often not…
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…
The theory of Mean-Field Games is interested in the behaviour of interacting particle systems in which the individual interaction between particles (players) decreases as the size of the population increases. In recent years, it was…
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…
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…
This work studies the behaviors of two large-population teams competing in a discrete environment. The team-level interactions are modeled as a zero-sum game while the agent dynamics within each team is formulated as a collaborative…
Mean field type models describing the limiting behavior, as the number of players tends to $+\infty$, of stochastic differential game problems, have been recently introduced by J-M. Lasry and P-L. Lions. Numerical methods for the…
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…
Mean Field Game systems describe equilibrium configurations in differential games with infinitely many infinitesimal interacting agents. We introduce a learning procedure (similar to the Fictitious Play) for these games and show its…
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…
This paper studies a linear-quadratic mean-field game of stochastic large-population system, where the large-population system satisfies a class of $N$ weakly coupled linear backward stochastic differential equation. Different from the…
Clustering is one of the most common unsupervised learning tasks in machine learning and data mining. Clustering algorithms have been used in a plethora of applications across several scientific fields. However, there has been limited…
Understanding and modeling pedestrian dynamics in dense crowds is a complex yet essential aspect of crowd management and urban planning. In this work, we investigate the dynamics of a dense crowd crossed by a cylindrical intruder using a…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
We develop the fictitious play algorithm in the context of the linear programming approach for mean field games of optimal stopping and mean field games with regular control and absorption. This algorithm allows to approximate the mean…
We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled continuity equation featuring a nonlinear activation function on…