Related papers: Determining state space anomalies in mean field ga…
Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…
Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading…
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…
We use the Markov chain approximation method to construct approximations for the solution of the mean field game (MFG) with reflecting barriers studied in Bayraktar, Budhiraja, and Cohen (2017). The MFG is formulated in terms of a…
Mean Field Games (MFG) theory describes strategic interactions in differential games with a large number of small and indistinguishable players. Traditionally, the players' control impacts only the drift term in the system's dynamics,…
In this paper we provide the existence of classical solutions to stationary mean field game systems in the whole space $\mathbb{R}^N$, with coercive potential, aggregating local coupling, and under general conditions on the Hamiltonian,…
We prove existence and uniqueness of classical solutions of the master equation for mean field game (MFG) systems with fractional and nonlocal diffusions. We cover a large class of L\'evy diffusions of order greater than one, including…
In this paper, we prove the existence of classical solutions for second order stationary mean-field game systems. These arise in ergodic (mean-field) optimal control, convex degenerate problems in calculus of variations, and in the study of…
Here, we prove the existence of smooth solutions for mean-field games with a singular mean-field coupling; that is, a coupling in the Hamilton-Jacobi equation of the form $g(m)=-m^{-\alpha}$. We consider stationary and time-dependent…
A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action pairs. This article presents some…
We discuss in detail the derivation of stochastic differential equations for the continuum time limit of the Minority Game. We show that all properties of the Minority Game can be understood by a careful theoretical analysis of such…
Mean Field Games with state constraints are differential games with infinitely many agents, each agent facing a constraint on his state. The aim of this paper is to provide a meaning of the PDE system associated with these games, the…
We introduce a mean field game for a family of filtering problems related to the classic sequential testing of the drift of a Brownian motion. To the best of our knowledge this work presents the first treatment of mean field filtering games…
We use scaling results to identify the crossover to mean-field behavior of equilibrium statistical mechanics models on a variant of the small world network. The results are generalizable to a wide-range of equilibrium systems. Anomalous…
We consider a class of optimal control problems that arise in connection with optimal advertising under uncertainty. Two main features appear in the model: a delay in the control variable driving the state dynamics; a mean-field term both…
In a regular mean field game (MFG), the agents are assumed to be insignificant, they do not realize their effect on the population level and this may result in a phenomenon coined as the Tragedy of the Commons by the economists. However, in…
In this paper, we investigate the robustness of stationary mean-field equilibria in the presence of model uncertainties, specifically focusing on infinite-horizon discounted cost functions. To achieve this, we initially establish…
While the general theory for the terminal-initial value problem in mean-field games is widely used in many models of applied mathematics, the modeling potential of the corresponding forward-forward version is still under-considered. In this…
In the present work, we study deterministic mean field games (MFGs) with finite time horizon in which the dynamics of a generic agent is controlled by the acceleration. They are described by a system of PDEs coupling a continuity equation…
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…