Related papers: Linear-quadratic extended mean field games with co…
This paper studies a class of linear quadratic mean field games where the coefficients of quadratic cost functions depend on both the mean and the variance of the population's state distribution through its quantile function. Such a…
In many stochastic games stemming from financial models, the environment evolves with latent factors and there may be common noise across agents' states. Two classic examples are: (i) multi-agent trading on electronic exchanges, and (ii)…
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…
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…
We provide a thorough study of a general class of linear-quadratic extended mean field games and control problems in any dimensions where the mean field terms are allowed to be unbounded and there are also presence of cross terms in the…
Mean-field games with common noise provide a powerful framework for modeling the collective behavior of large populations subject to shared randomness, such as systemic risk in finance or environmental shocks in economics. These problems…
We study the mean field games equations, consisting of the coupled Kolmogorov-Fokker-Planck and Hamilton-Jacobi-Bellman equations. The equations are complemented by initial and terminal conditions. It is shown that with some specific choice…
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…
This paper studies a new class of dynamic optimization problems of large-population (LP) system which consists of a large number of negligible and coupled agents. The most significant feature in our setup is the dynamics of individual…
This paper studies uniform stabilization and social optimality for linear quadratic (LQ) mean field control problems with multiplicative noise, where agents are coupled via dynamics and individual costs. The state and control weights in…
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…
In this article, we study the global-in-time well-posedness of second order mean field games (MFGs) with both nonlinear drift functions simultaneously depending on the state, distribution and control variables, and the diffusion term…
This paper focuses on exploring the convergence properties of a generic player's trajectory and empirical measures in an N-player Linear-Quadratic-Gaussian Nash game, where Brownian motion serves as the common noise. The study establishes…
We force uniqueness in finite state mean field games by adding a Wright-Fisher common noise. We achieve this by analyzing the master equation of this game, which is a degenerate parabolic second-order partial differential equation set on…
We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…
Mean field games model equilibria in games with a continuum of players as limiting systems of symmetric $n$-player games with weak interaction between the players. We consider a finite-state, infinite-horizon problem with two cost criteria:…
This paper studies approximate solutions to large-scale linear quadratic stochastic games with homogeneous nodal dynamics parameters and heterogeneous network couplings within the graphon mean field game framework in [2]-[4]. A graphon…
This paper considers a linear-quadratic (LQ) mean field control problem involving a major player and a large number of minor players, where the dynamics and costs depend on random parameters. The objective is to optimize a social cost as a…
In this paper we discuss a class of mean field linear-quadratic-Gaussian (LQG) games for large population system which has never been addressed by existing literature. The features of our works are sketched as follows. First of all, our…
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…