Related papers: Graphon Mean Field Games with a Representative Pla…
The theory of first-order mean field type differential games examines the systems of infinitely many identical agents interacting via some external media under assumption that each agent is controlled by two players. We study the…
Mean Field Games (MFG) are the class of games with a very large number of agents and the standard equilibrium concept is a Mean Field Equilibrium (MFE). Algorithms for learning MFE in dynamic MFGs are unknown in general. Our focus is on an…
We motivate and propose a new model for non-cooperative Markov game which considers the interactions of risk-aware players. This model characterizes the time-consistent dynamic "risk" from both stochastic state transitions (inherent to the…
We consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank…
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…
We present a graphon mean-field logit dynamic, a stationary mean-field game based on logit interactions. This dynamic emerges from a stochastic control problem involving a continuum of nonexchangeable and interacting agents and reduces to…
We present a new tool for the study of multiplayer stochastic games, namely the modified game, which is a normal-form game that depends on the discount factor, the initial state, and for every player a partition of the set of states and a…
The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…
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…
We propose a novel mean field games (MFGs) based GAN(generative adversarial network) framework. To be specific, we utilize the Hopf formula in density space to rewrite MFGs as a primal-dual problem so that we are able to train the model via…
Motivated by the recent applications of game-theoretical learning techniques to the design of distributed control systems, we study a class of control problems that can be formulated as potential games with continuous action sets, and we…
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…
We consider a general class of finite-player stochastic games with mean-field interaction, in which the linear-quadratic cost functional includes linear operators acting on controls in $L^2$. We propose a novel approach for deriving the…
We develop a general game-theoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional game-theoretic results (such as the existence of a Nash equilibrium) no longer…
This paper studies mean field game (MFG) of controls by featuring the joint distribution of the state and the control with the reflected state process along an exogenous stochastic reflection boundary. We contribute to the literature with a…
We study dynamic finite-player and mean-field stochastic games within the framework of Markov perfect equilibria (MPE). Our focus is on discrete time and space structures without monotonicity. Unlike their continuous-time analogues,…
Constrained Markov games offer a formal mathematical framework for modeling multi-agent reinforcement learning problems where the behavior of the agents is subject to constraints. In this work, we focus on the recently introduced class of…
In this paper we study mean field games with possibly multiple mean field equilibria. Instead of focusing on the individual equilibria, we propose to study the set of values over all possible equilibria, which we call the set value of the…
Multi-agent reinforcement learning methods have shown remarkable potential in solving complex multi-agent problems but mostly lack theoretical guarantees. Recently, mean field control and mean field games have been established as a…
Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and…