Related papers: Monotone solutions for mean field games master equ…
We present a new notion of solution for mean field games master equations. This notion allows us to work with solutions which are merely continuous. We prove first results of uniqueness and stability for such solutions. It turns out that…
This paper is concerned with the study of mean field games master equations involving an additional variable modelling common noise. We address cases in which the dynamics of this variable can depend on the state of the game, which requires…
We present results of existence, regularity and uniqueness of solutions of the master equation associated with the mean field planning problem in the finite state space case, in the presence of a common noise. The results hold under…
This paper studies the convergence of mean field games with finite state space to mean field games with a continuous state space. We examine a space discretization of a diffusive dynamics, which is reminiscent of the Markov chain…
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…
We consider Mean Field Games without idiosyncratic but with Brownian type common noise. We introduce a notion of solutions of the associated backward-forward system of stochastic partial differential equations. We show that the solution…
We present a novel framework for mean field games with finite state space and common noise, where the common noise is given through shocks that occur at random times. We first analyze the game for up to $n$ shocks, in which case we are able…
This paper is concerned with extending the notion of monotone solution to the mean field game (MFG) master equation to situations in which the coefficients are displacement monotone, instead of the previously introduced notion in the flat…
We introduce a notion of weak solution of the master equation without idiosyncratic noise in Mean Field Game theory and establish its existence, uniqueness up to a constant and consistency with classical solutions when it is smooth. We work…
This paper provides a mathematical study of the well-posedness of master equation on finite state space involving terms modelling common noise. In this setting, the solution of the master equation depends on an additional variable modelling…
In this paper we unveil novel monotonicity conditions applicable for Mean Field Games through the exploration of finite dimensional $canonical\ transformations$. Our findings contribute to establishing new global well-posedness results for…
A theory of existence and uniqueness is developed for general stochastic differential mean field games with common noise. The concepts of strong and weak solutions are introduced in analogy with the theory of stochastic differential…
The objective of this work is to study the existence, uniqueness, and stability of equilibria in mean field games involving a major player and a continuum of minor players over finite intervals of arbitrary length. Following earlier…
In this paper, we consider a class of linear quadratic extended mean field games (MFGs) with common noises where the state coefficients and the cost functional vary with the mean field term in a nonlinear way. Based on stochastic maximum…
In this note we prove the uniqueness of solutions to a class of Mean Field Games systems subject to possibly degenerate individual noise. Our results hold true for arbitrary long time horizons and for general non-separable Hamiltonians that…
We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become…
We introduce the notion of stable solution in mean field game theory: they are locally isolated solutions of the mean field game system. We prove that such solutions exist in potential mean field games and are local attractors for learning…
We develop a theory of existence and uniqueness of solutions of MFG master equations when the initial condition is Lipschitz continuous. Namely, we show that as long as the solution of the master equation is Lipschitz continuous in space,…
In this paper, we consider Mean Field Games in the presence of common noise relaxing the usual independence assumption of individual random noise. We assume a simple linear model with terminal cost satisfying a convexity and a weak…
We study a mean-field game of optimal stopping and investigate the existence of strong solutions via a connection with the Bank-El Karoui's representation problem. Under certain continuity assumptions, where the common noise is generated by…