Related papers: Probabilistic Analysis of Mean-Field Games
We study mean field portfolio games with random market parameters, where each player is concerned with not only her own wealth but also relative performance to her competitors. We use the martingale optimality principle approach to…
We consider a general class of nonzero-sum $N$-player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a verification approach and provide sufficient conditions for…
We study in this paper three aspects of Mean Field Games. The first one is the case when the dynamics of each player depend on the strategies of the other players. The second one concerns the modeling of '' noise '' in discrete space models…
We study the traffic routing game among a large number of selfish drivers over a traffic network. We consider a specific scenario where the strategic drivers can be classified into teams, where drivers in the same team have identical payoff…
In two-player zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have…
We consider a class of dynamic collective choice models with social interactions, whereby a large number of non-uniform agents have to individually settle on one of multiple discrete alternative choices, with the relevance of their would-be…
Mean field games (MFGs) describe the limit, as $n$ tends to infinity, of stochastic differential games with $n$ players interacting with one another through their common empirical distribution. Under suitable smoothness assumptions that…
In this work, we study a class of stationary mean-field games of singular stochastic control under model uncertainty. The representative agent adjusts the dynamics of an It\^o diffusion via one-sided singular stochastic control, aiming to…
We introduce a simple stochastic dynamics for game theory. It assumes ``local'' rationality in the sense that any player climbs the gradient of his utility function in the presence of a stochastic force which represents deviation from…
We present a Mean Field Game approach to obtain the rate function for the empirical measure of interacting particles under McKean-Vlasov dynamics. Although the result is well known, our approach relies on PDE methods and provides another…
We construct numerical approximations for Mean Field Games with fractional or nonlocal diffusions. The schemes are based on semi-Lagrangian approximations of the underlying control problems/games along with dual approximations of the…
This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…
We consider two classes of constrained finite state-action stochastic games. First, we consider a two player nonzero sum single controller constrained stochastic game with both average and discounted cost criterion. We consider the same…
In this paper, we analyze mean-field game modulated by finite states markov chains. We first develop a sufficient stochastic maximum principle for the optimal control of a Markov-modulated stochastic differential equation (SDE) of…
We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence…
We consider stochastic differential games with a large number of players, with the aim of quantifying the gap between closed-loop, open-loop and distributed equilibria. We show that, under two different semi-monotonicity conditions, the…
We introduce two Smoothed Policy Iteration algorithms (\textbf{SPI}s) as rules for learning policies and methods for computing Nash equilibria in second order potential Mean Field Games (MFGs). Global convergence is proved if the coupling…
This paper investigates a linear-quadratic mean field games problem with common noise, where the drift term and diffusion term of individual state equations are coupled with both the state, control, and mean field terms of the state, and we…
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…
Reinforcement learning for multi-agent games has attracted lots of attention recently. However, given the challenge of solving Nash equilibria for large population games, existing works with guaranteed polynomial complexities either focus…