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This paper focuses on exploring the convergence properties of a generic player's trajectory and empirical measures in an N-player Linear-Quadratic-Gaussian Nash game, where Brownian motion serves as the common noise. The study establishes…

Probability · Mathematics 2023-07-04 Jiamin Jian , Qingshuo Song , Jiaxuan Ye

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…

Analysis of PDEs · Mathematics 2020-03-10 Y Achdou , Z Kobeissi

We consider stochastic differential games with $N$ nearly identical players, linear-Gaussian dynamics, and infinite horizon discounted quadratic cost. Admissible controls are feedbacks for which the system is ergodic. We first study the…

Analysis of PDEs · Mathematics 2014-03-18 Fabio S. Priuli

We develop a variational approach to address risk-sensitive optimal control problems with an exponential-of-integral cost functional in a general linear-quadratic-Gaussian (LQG) single-agent setup, offering new insights into such problems.…

Optimization and Control · Mathematics 2025-03-28 Hanchao Liu , Dena Firoozi , Michèle Breton

A novel framework is presented that combines Mean Field Game (MFG) theory and Hybrid Optimal Control (HOC) theory to obtain a unique $\epsilon$-Nash equilibrium for a non-cooperative game with switching and stopping times. We consider the…

Systems and Control · Computer Science 2022-01-11 Dena Firoozi , Ali Pakniyat , Peter E. Caines

Mean field game (MFG) systems consisting of a major agent and a large number of minor agents were introduced in (Huang, 2010) in an LQG setup. The Nash certainty equivalence was used to obtain a Markovian closed-loop Nash equilibrium for…

Optimization and Control · Mathematics 2022-10-19 Dena Firoozi

Competitive games involving thousands or even millions of players are prevalent in real-world contexts, such as transportation, communications, and computer networks. However, learning in these large-scale multi-agent environments presents…

Optimization and Control · Mathematics 2025-02-04 Batuhan Yardim , Semih Cayci , Niao He

The paper is concerned with a zero-sum Stackelberg stochastic linear-quadratic (LQ, for short) differential game over finite horizons. Under a fairly weak condition, the Stackelberg equilibrium is explicitly obtained by first solving a…

Optimization and Control · Mathematics 2021-10-05 Jingrui Sun , Hanxiao Wang , Jiaqiang Wen

We analyze a simple variant of the Goldfarb-Idnani (GI) dual active-set method for computing variational generalized Nash equilibria of strongly monotone N-player games with convex quadratic costs and shared affine inequality and equality…

Optimization and Control · Mathematics 2026-05-21 Alberto Bemporad

This paper focuses on linear-quadratic (LQ for short) mean-field games described by forward-backward stochastic differential equations (FBSDEs for short), in which the individual control region is postulated to be convex. The decentralized…

Optimization and Control · Mathematics 2021-04-09 Liangquan Zhang , Xun Li

In this paper, we study large population multi-agent reinforcement learning (RL) in the context of discrete-time linear-quadratic mean-field games (LQ-MFGs). Our setting differs from most existing work on RL for MFGs, in that we consider a…

Systems and Control · Electrical Eng. & Systems 2020-10-02 Muhammad Aneeq uz Zaman , Kaiqing Zhang , Erik Miehling , Tamer Başar

This paper investigates the so-called asymptotic solvability problem in linear quadratic (LQ) mean field games. The model has asymptotic solvability if for all sufficiently large population sizes, the corresponding game has a set of…

Optimization and Control · Mathematics 2018-11-02 Minyi Huang , Mengjie Zhou

We develop the theory of linear-quadratic (LQ) mean field games (MFGs) in Hilbert spaces with common noise modeled by an infinite-dimensional Wiener process that affects the dynamics of all agents. In the presence of common noise, the…

Optimization and Control · Mathematics 2026-05-28 Hanchao Liu , Dena Firoozi

In this paper, we investigate a class of nonzero-sum dynamic stochastic games, where players have linear dynamics and quadratic cost functions. The players are coupled in both dynamics and cost through a linear regression (weighted average)…

Optimization and Control · Mathematics 2020-10-20 Jalal Arabneydi , Amir G. Aghdam , Roland P. Malhamé

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.…

Optimization and Control · Mathematics 2020-08-18 Weichen Wang , Jiequn Han , Zhuoran Yang , Zhaoran Wang

This paper presents a method for solving the Inverse Stochastic Differential Game (ISDG) problem in finite-horizon linear-quadratic Gaussian (LQG) differential games. The objective is to recover cost function parameters of all players, as…

Systems and Control · Electrical Eng. & Systems 2026-04-29 Lucas Günther , Felix Thömmes , Karl Handwerker , Balint Varga , Sören Hohmann

Mean Field Games (MFG) have been introduced to tackle games with a large number of competing players. Considering the limit when the number of players is infinite, Nash equilibria are studied by considering the interaction of a typical…

Optimization and Control · Mathematics 2021-06-14 Mathieu Lauriere

This paper concerns a Mean Field Game (MFG) system related to a Nash type equilibrium for dynamical games associated to large populations. One shows that the MFG system may be viewed as the Euler-Lagrange system for an optimal control…

Optimization and Control · Mathematics 2025-03-21 Stefana-Lucia Anita

Learning the behavior of large agent populations is an important task for numerous research areas. Although the field of multi-agent reinforcement learning (MARL) has made significant progress towards solving these systems, solutions for…

Multiagent Systems · Computer Science 2024-02-26 Christian Fabian , Kai Cui , Heinz Koeppl

In this paper, we address linear-quadratic-Gaussian (LQG) risk-sensitive mean field games (MFGs) with common noise. In this framework agents are exposed to a common noise and aim to minimize an exponential cost functional that reflects…

Optimization and Control · Mathematics 2024-03-07 Xin Yue Ren , Dena Firoozi