Related papers: A rank based mean field game in the strong formula…
This paper revisits the well-studied \emph{optimal stopping} problem but within the \emph{large-population} framework. In particular, two classes of optimal stopping problems are formulated by taking into account the \emph{relative…
In this paper, we investigate a class of mean field games where the mean field interactions are achieved through the joint (conditional) distribution of the controlled state and the control process. The strategies are of $open\;loop$ type,…
The paper is devoted to the first-order mean field game system in the case when the distribution of players can contain atoms. The proposed definition of a generalized solution is based on the minimax approach to the Hamilton-Jacobi…
In a game theoretic framework, we study energy markets with a continuum of homogenous producers who produce energy from an exhaustible resource such as oil. Each producer simultaneously optimizes production rate that drives her revenues, as…
We formulate and solve a multi-player stochastic differential game between financial agents who seek to cost-efficiently liquidate their position in a risky asset in the presence of jointly aggregated transient price impact, along with…
This paper continues the study of the mean field game (MFG) convergence problem: In what sense do the Nash equilibria of $n$-player stochastic differential games converge to the mean field game as $n\rightarrow\infty$? Previous work on this…
This paper provides theoretical bounds for empirical game theoretical analysis of complex multi-agent interactions. We provide insights in the empirical meta game showing that a Nash equilibrium of the meta-game is an approximate Nash…
This paper analyzes a class of infinite-time-horizon stochastic games with singular controls motivated from the partially reversible problem. It provides an explicit solution for the mean-field game (MFG) and presents sensitivity analysis…
Multi-agent games are becoming an increasing prevalent formalism for the study of electronic commerce and auctions. The speed at which transactions can take place and the growing complexity of electronic marketplaces makes the study of…
We analyze the behavior of a large number of strategic drivers traveling over an urban traffic network using the mean-field game framework. We assume an incentive mechanism for congestion mitigation under which each driver selecting a…
We present a simpler proof of the existence of equilibria for a class of mean field games with common noise, where players interact through the conditional law given the current value of the common noise rather than its entire path. By…
Recent advances at the intersection of dense large graph limits and mean field games have begun to enable the scalable analysis of a broad class of dynamical sequential games with large numbers of agents. So far, results have been largely…
Computing an equilibrium in congestion games can be challenging when the number of players is large. Yet, it is a problem to be addressed in practice, for instance to forecast the state of the system and be able to control it. In this work,…
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 examine global non-asymptotic convergence properties of policy gradient methods for multi-agent reinforcement learning (RL) problems in Markov potential games (MPG). To learn a Nash equilibrium of an MPG in which the size of state space…
The goal of the paper is to develop the theory of finite state mean field games with major and minor players when the state space of the game is finite. We introduce the finite player games and derive a mean field game formulation in the…
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…
In this paper we study Mean Field Game systems under density constraints as optimality conditions of two optimization problems in duality. A weak solution of the system contains an extra term, an additional price imposed on the saturated…
In general, Nash equilibria in normal-form games may require players to play (probabilistically) mixed strategies. We define a measure of the complexity of finite probability distributions and study the complexity required to play Nash…
While it is known that shared quantum entanglement can offer improved solutions to a number of purely cooperative tasks for groups of remote agents, controversy remains regarding the legitimacy of quantum games in a competitive setting--in…