Related papers: Entropic Fictitious Play for Mean Field Optimizati…

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…

We propose a deep neural network-based algorithm to identify the Markovian Nash equilibrium of general large $N$-player stochastic differential games. Following the idea of fictitious play, we recast the $N$-player game into $N$ decoupled…

We are interested in the study of stochastic games for which each player faces an optimal stopping problem. In our setting, the players may interact through the criterion to optimise as well as through their dynamics. After briefly…

We study the long-term behavior of the fictitious play process in repeated extensive-form games of imperfect information with perfect recall. Each player maintains incorrect beliefs that the moves at all information sets, except the one at…

This paper considers the problem of designing optimal algorithms for reinforcement learning in two-player zero-sum games. We focus on self-play algorithms which learn the optimal policy by playing against itself without any direct…

We introduce two min-max problems: the first problem is to minimize the supremum of finitely many rational functions over a compact basic semi-algebraic set whereas the second problem is a 2-player zero-sum polynomial game in randomized…

Reinforcement learning is a powerful tool to learn the optimal policy of possibly multiple agents by interacting with the environment. As the number of agents grow to be very large, the system can be approximated by a mean-field problem.…

We address scaling up equilibrium computation in Mean Field Games (MFGs) using Online Mirror Descent (OMD). We show that continuous-time OMD provably converges to a Nash equilibrium under a natural and well-motivated set of monotonicity…

This paper considers the problem of inverse reinforcement learning in zero-sum stochastic games when expert demonstrations are known to be not optimal. Compared to previous works that decouple agents in the game by assuming optimality in…

Estimating the unknown reward functions driving agents' behaviors is of central interest in inverse reinforcement learning and game theory. To tackle this problem, we develop a unified framework for reward function recovery in two-player…

Existing deep learning methods for solving mean-field games (MFGs) with common noise fix the sampling common noise paths and then solve the corresponding MFGs. This leads to a nested-loop structure with millions of simulations of common…

Natural actor-critic (NAC) and its variants, equipped with the representation power of neural networks, have demonstrated impressive empirical success in solving Markov decision problems with large state spaces. In this paper, we present a…

Mean-field games have been used as a theoretical tool to obtain an approximate Nash equilibrium for symmetric and anonymous $N$-player games. However, limiting applicability, existing theoretical results assume variations of a "population…

Computing approximate Nash equilibria in multi-player general-sum Markov games is a computationally intractable task. However, multi-player Markov games with certain cooperative or competitive structures might circumvent this…

In this paper, we study finite-agent linear-quadratic games on graphs. Specifically, we propose a comprehensive framework that extends the existing literature by incorporating heterogeneous and interpretable player interactions. Compared to…

Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…

We study reinforcement learning for two-player zero-sum Markov games with simultaneous moves in the finite-horizon setting, where the transition kernel of the underlying Markov games can be parameterized by a linear function over the…

Mean field games (MFGs) model equilibria in games with a continuum of weakly interacting players as limiting systems of symmetric $n$-player games. We consider the finite-state, infinite-horizon problem with ergodic cost. Assuming Markovian…

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 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…