Related papers: Scaling up Mean Field Games with Online Mirror Des…
The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…
To model complex real-world systems, such as traders in stock markets, or the dissemination of contagious diseases, graphon mean-field games (GMFG) have been proposed to model many agents. Despite the empirical success, our understanding of…
Mean-field games (MFGs) study the Nash equilibrium of systems with a continuum of interacting agents, which can be formulated as the fixed-point of optimal control problems. They provide a unified framework for a variety of applications,…
Fictitious play (FP) is one of the most fundamental game-theoretical learning frameworks for computing Nash equilibrium in $n$-player games, which builds the foundation for modern multi-agent learning algorithms. Although FP has provable…
In this work, we introduce the concept of non-negative weighted regret, an extension of non-negative regret \cite{anagnostides2022last} in games. Investigating games with non-negative weighted regret helps us to understand games with…
The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game…
In order to find Nash-equilibria for two-player zero-sum games where each player plays combinatorial objects like spanning trees, matchings etc, we consider two online learning algorithms: the online mirror descent (OMD) algorithm and the…
We provide several applications of Optimistic Mirror Descent, an online learning algorithm based on the idea of predictable sequences. First, we recover the Mirror Prox algorithm for offline optimization, prove an extension to Holder-smooth…
This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and…
In this paper, we consider a mean field game (MFG) model perturbed by small common noise. Our goal is to give an approximation of the Nash equilibrium strategy of this game using a solution from the original no common noise MFG whose…
The recent mean field game (MFG) formalism facilitates otherwise intractable computation of approximate Nash equilibria in many-agent settings. In this paper, we consider discrete-time finite MFGs subject to finite-horizon objectives. We…
Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and…
Self-play via online learning is one of the premier ways to solve large-scale two-player zero-sum games, both in theory and practice. Particularly popular algorithms include optimistic multiplicative weights update (OMWU) and optimistic…
In this paper we establish quantitative convergence results for both open and closed-loop Nash equilibria of N-player stochastic differential games in the setting of Mean Field Games of Controls (MFGC), a class of models where interactions…
Stochastic games generalize Markov decision processes (MDPs) to a multiagent setting by allowing the state transitions to depend jointly on all player actions, and having rewards determined by multiplayer matrix games at each state. We…
The approximation of mixed Nash equilibria (MNE) for zero-sum games with mean-field interacting players has recently raised much interest in machine learning. In this paper we propose a mean-field gradient descent dynamics for finding the…
Mean-field games (MFG) have become significant tools for solving large-scale multi-agent reinforcement learning problems under symmetry. However, the assumption of exact symmetry limits the applicability of MFGs, as real-world scenarios…
Stochastic differential games have been used extensively to model agents' competitions in Finance, for instance, in P2P lending platforms from the Fintech industry, the banking system for systemic risk, and insurance markets. The recently…
In the presence of a common noise, we study the convergence problems in mean field game (MFG) and mean field control (MFC) problem where the cost function and the state dynamics depend upon the joint conditional distribution of the…
We examine the long-run behavior of multi-agent online learning in games that evolve over time. Specifically, we focus on a wide class of policies based on mirror descent, and we show that the induced sequence of play (a) converges to Nash…