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We introduce Mean-Field Game (MFG) epidemiological models, in which immunity either wanes with time in a fully observable way or disappears instantaneously with no direct observation (making a previously recovered individual fully…

Optimization and Control · Mathematics 2026-04-08 Carlos Doebeli , Alexander Vladimirsky

Zero-sum Markov Games (MGs) has been an efficient framework for multi-agent systems and robust control, wherein a minimax problem is constructed to solve the equilibrium policies. At present, this formulation is well studied under tabular…

Machine Learning · Computer Science 2022-12-06 Yangang Ren , Yao Lyu , Wenxuan Wang , Shengbo Eben Li , Zeyang Li , Jingliang Duan

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

Multi-agent reinforcement learning (MARL) becomes more challenging in the presence of more agents, as the capacity of the joint state and action spaces grows exponentially in the number of agents. To address such a challenge of scale, we…

Machine Learning · Computer Science 2021-05-19 Yan Li , Lingxiao Wang , Jiachen Yang , Ethan Wang , Zhaoran Wang , Tuo Zhao , Hongyuan Zha

The article provides a solution algorithm for the linear programming problem (LPP) with the latter being presented as an antagonistic matrix game so the game's further solution is based on the iterative method. The algorithm is presented as…

Optimization and Control · Mathematics 2019-05-15 Vilisov V. Ya

Value-based methods for reinforcement learning lack generally applicable ways to derive behavior from a value function. Many approaches involve approximate value iteration (e.g., $Q$-learning), and acting greedily with respect to the…

Machine Learning · Computer Science 2020-08-27 Alan Chan , Kris de Asis , Richard S. Sutton

We introduce two Smoothed Policy Iteration algorithms (\textbf{SPI}s) as rules for learning policies and methods for computing Nash equilibria in second order potential Mean Field Games (MFGs). Global convergence is proved if the coupling…

Optimization and Control · Mathematics 2023-04-18 Qing Tang , Jiahao Song

Mean Field Control Games (MFCG), introduced in [Angiuli et al., 2022a], represent competitive games between a large number of large collaborative groups of agents in the infinite limit of number and size of groups. In this paper, we prove…

Optimization and Control · Mathematics 2024-06-05 Andrea Angiuli , Jean-Pierre Fouque , Mathieu Laurière , Mengrui Zhang

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

In this paper we formulate the now classical problem of optimal liquidation (or optimal trading) inside a Mean Field Game (MFG). This is a noticeable change since usually mathematical frameworks focus on one large trader in front of a…

Trading and Market Microstructure · Quantitative Finance 2017-09-22 Pierre Cardaliaguet , Charles-Albert Lehalle

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

In this paper, we consider the problem of optimization and learning for constrained and multi-objective Markov decision processes, for both discounted rewards and expected average rewards. We formulate the problems as zero-sum games where…

Optimization and Control · Mathematics 2021-03-05 Ather Gattami , Qinbo Bai , Vaneet Agarwal

We consider zero-sum stochastic games with finite state and action spaces, perfect information, mean payoff criteria, without any irreducibility assumption on the Markov chains associated to strategies (multichain games). The value of such…

Optimization and Control · Mathematics 2012-08-03 Marianne Akian , Jean Cochet-Terrasson , Sylvie Detournay , Stéphane Gaubert

We investigate an iterative mean value method for the inverse (and highly ill-posed) problem of solving the heat equation backwards in time. Semi-group theory is used to rewrite the solution of the inverse problem as the solution of a fixed…

Numerical Analysis · Mathematics 2020-12-01 A. Leitao

Strategy iteration is a technique frequently used for two-player games in order to determine the winner or compute payoffs, but to the best of our knowledge no general framework for strategy iteration has been considered. Inspired by…

Logic in Computer Science · Computer Science 2022-12-14 Paolo Baldan , Richard Eggert , Barbara König , Tommaso Padoan

This manuscript discusses planning problems for first- and second-order one-dimensional mean-field games (MFGs). These games are comprised of a Hamilton-Jacobi equation coupled with a Fokker-Planck equation. Applying Poincar\'e's Lemma to…

Analysis of PDEs · Mathematics 2021-04-27 Tigran Bakaryan , Rita Ferreira , Diogo Gomes

We investigate an infinite-horizon time-inconsistent mean-field game (MFG) in a discrete time setting. We first present a classic equilibrium for the MFG and its associated existence result. This classic equilibrium aligns with the…

Optimization and Control · Mathematics 2024-09-13 Erhan Bayraktar , Zhenhua Wang

Learning by experience in Multi-Agent Systems (MAS) is a difficult and exciting task, due to the lack of stationarity of the environment, whose dynamics evolves as the population learns. In order to design scalable algorithms for systems…

Optimization and Control · Mathematics 2020-02-24 Romuald Elie , Julien Pérolat , Mathieu Laurière , Matthieu Geist , Olivier Pietquin

We consider online reinforcement learning in Mean-Field Games (MFGs). Unlike traditional approaches, we alleviate the need for a mean-field oracle by developing an algorithm that approximates the Mean-Field Equilibrium (MFE) using the…

Machine Learning · Computer Science 2023-04-12 Muhammad Aneeq uz Zaman , Alec Koppel , Sujay Bhatt , Tamer Başar

In this paper, we propose an initial value fomulation of the discrete mean field games on finite graphs (Graph MFG), and design a neural network based approach to solve it. Graph MFG describes infinite, non-cooperative and interactive…

Numerical Analysis · Mathematics 2026-04-08 Yaxin Feng , Yang Xiang , Haomin Zhou