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Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout…

Optimization and Control · Mathematics 2019-12-30 Julien Claisse , Zhenjie Ren , Xiaolu Tan

Fictitious play (FP) is a well-studied algorithm that enables agents to learn Nash equilibrium in games with certain reward structures. However, when agents have no prior knowledge of the reward functions, FP faces a major challenge: the…

Computer Science and Game Theory · Computer Science 2025-08-28 Semih Kara , Tamer Başar

When controlling multi-agent systems, the trade-off between performance and scalability is a major challenge. Here, we address this difficulty by using mean field games (MFGs), which is a framework that deduces the macroscopic dynamics…

Optimization and Control · Mathematics 2021-08-06 Daisuke Inoue , Yuji Ito , Takahito Kashiwabara , Norikazu Saito , Hiroaki Yoshida

The emergence of the graphon theory of large networks and their infinite limits has enabled the formulation of a theory of the centralized control of dynamical systems distributed on asymptotically infinite networks (Gao and Caines, IEEE…

Optimization and Control · Mathematics 2021-12-30 Peter E. Caines , Minyi Huang

This paper proposes a novel Mean-Field Game (MFG) framework for large-scale attacker-defender systems aimed at protecting one or multiple High-Value Units (HVUs). Motivated by classical agent-wise attrition models, we introduce a…

Analysis of PDEs · Mathematics 2026-04-03 Avetik Arakelyan , Tigran Bakaryan , Davit Alaverdyan , Naira Hovakimyan , Isaac Kaminer

In this paper, we consider discrete-time partially observed mean-field games with the risk-sensitive optimality criterion. We introduce risk-sensitivity behaviour for each agent via an exponential utility function. In the game model, each…

Systems and Control · Electrical Eng. & Systems 2022-11-11 Naci Saldi , Tamer Basar , Maxim Raginsky

Max-min fairness (MMF) is a widely known approach to a fair allocation of bandwidth to each of the users in a network. This allocation can be computed by uniformly raising the bandwidths of all users without violating capacity constraints.…

Networking and Internet Architecture · Computer Science 2014-01-15 Tobias Harks , Martin Hoefer , Kevin Schewior , Alexander Skopalik

In this paper, we propose a passivity-based methodology for analysis and design of reinforcement learning in multi-agent finite games. Starting from a known exponentially-discounted reinforcement learning scheme, we show that convergence to…

Optimization and Control · Mathematics 2024-10-30 Bolin Gao , Lacra Pavel

Subject to reasonable conditions, in large population stochastic dynamics games, where the agents are coupled by the system's mean field (i.e. the state distribution of the generic agent) through their nonlinear dynamics and their nonlinear…

Optimization and Control · Mathematics 2019-05-28 Nevroz Sen , Peter E. Caines

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…

Computer Science and Game Theory · Computer Science 2022-05-04 Yurong Chen , Xiaotie Deng , Chenchen Li , David Mguni , Jun Wang , Xiang Yan , Yaodong Yang

Multi-agent reinforcement learning (MARL) addresses sequential decision-making problems with multiple agents, where each agent optimizes its own objective. In many real-world instances, the agents may not only want to optimize their…

Machine Learning · Computer Science 2023-06-14 Pragnya Alatur , Giorgia Ramponi , Niao He , Andreas Krause

We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $n$-player equilibria converges to it as $n\to\infty$. However, both the finite and…

Optimization and Control · Mathematics 2019-05-30 Marcel Nutz , Jaime San Martin , Xiaowei Tan

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…

Computer Science and Game Theory · Computer Science 2024-10-14 Jing Dong , Baoxiang Wang , Yaoliang Yu

We introduce a general probabilistic framework for discrete-time, infinite-horizon discounted Mean Field Type Games (MFTGs) with both global common noise and team-specific common noises. In our model, agents are allowed to use randomized…

Optimization and Control · Mathematics 2026-01-01 Grégoire Lambrecht , Mathieu Laurière

In this article we study the convergence of the Nash Equilibria in a N-player differential game towards the optimal strategies in the Mean Field Games, when the dynamic of the generic player includes a reflection process which guarantees…

Analysis of PDEs · Mathematics 2022-03-16 Michele Ricciardi

Mean field games (MFGs) describe the limit, as $n$ tends to infinity, of stochastic differential games with $n$ players interacting with one another through their common empirical distribution. Under suitable smoothness assumptions that…

Probability · Mathematics 2018-04-24 Francois Delarue , Daniel Lacker , Kavita Ramanan

While the topic of mean-field games (MFGs) has a relatively long history, heretofore there has been limited work concerning algorithms for the computation of equilibrium control policies. In this paper, we develop a computable policy…

Systems and Control · Electrical Eng. & Systems 2020-04-07 Muhammad Aneeq uz Zaman , Kaiqing Zhang , Erik Miehling , Tamer Başar

Entropy regularization has been extensively adopted to improve the efficiency, the stability, and the convergence of algorithms in reinforcement learning. This paper analyzes both quantitatively and qualitatively the impact of entropy…

Optimization and Control · Mathematics 2021-12-10 Xin Guo , Renyuan Xu , Thaleia Zariphopoulou

We propose a policy iteration method to solve an inverse problem for a mean-field game (MFG) model, specifically to reconstruct the obstacle function in the game from the partial observation data of value functions, which represent the…

Optimization and Control · Mathematics 2026-02-12 Kui Ren , Nathan Soedjak , Shanyin Tong

We develop a probabilistic framework to approximate Nash equilibria in symmetric $N$-player games in the large population regime, via the analysis of associated mean field games (MFGs). The approximation is achieved through the analysis of…

Probability · Mathematics 2026-04-27 Ludovic Tangpi , Nizar Touzi