Related papers: A time-fractional mean field game
We consider a stationary Mean Field Games system defined on a network. In this framework, the transition conditions at the vertices play a crucial role: the ones here considered are based on the optimal control interpretation of the…
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…
In the present article, an approach to find the exact solution of the fractional Fokker-Planck equation is presented. It is based on transforming it to a system of first-order partial differential equation via Hopf transformation, together…
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…
This work is devoted to finding the closed-loop equilibria for a class of mean-field games (MFGs) with infinitely many symmetric players in a common switching environment when the cost functional is under general discount in time. There are…
Mean-field games (MFG) provide a statistical physics inspired modeling framework for decision making in large-populations of strategic, non-cooperative agents. Mathematically, these systems consist of a forward-backward in time system of…
In this paper we formulate and solve a mean-field game described by a linear stochastic dynamics and a quadratic or exponential-quadratic cost functional for each generic player. The optimal strategies for the players are given explicitly…
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…
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…
This paper is devoted to finite horizon deterministic mean field games in which the state space is a network. The agents control their velocity, and when they occupy a vertex, they can enter into any incident edge. The running and terminal…
We introduce a nonconvex Mean Field Games system by studying a model with a large number of identical pairs of players who are all rational, and each pair plays an identical zero-sum differential game. We study existence and uniqueness of…
We investigate time dependent, first order Mean Field Games on the torus comparing, in a broad and general framework, the classical differential formulation , given by a Hamilton Jacobi equation coupled with a continuity equation, with a…
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…
The classical stochastic control problem under partial information can be formulated as a control problem for Zakai equation, whose solution is the unnormalized conditional probability distribution of the state of the system. Zakai equation…
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…
Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where…
A mean field type differential game is a mathematical model of a large system of identical agents under mean-field interaction controlled by two players with opposite purposes. We study the case when the dynamics of each agent is given by…
Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…
The goal of this paper is to show existence of short-time classical solutions to the so called Master Equation of \emph{first order} Mean Field Games, which can be thought of as the limit of the corresponding master equation of a stochastic…
In this paper, we consider a class of infinitely degenerate partial differential systems to obtain the Nash equilibria in the mean field games. The degeneracy in the diffusion and the Hamiltonian may be different. This feature brings…