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In this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study a class of deterministic mean field games and master equations, where the interaction of the agents happens…

Analysis of PDEs · Mathematics 2024-03-25 P. Jameson Graber , Alpár R. Mészáros

In this paper, we consider a mean field game (MFG) with a major and $N$ minor agents. We first consider the limiting problem and allow the coefficients to vary with the conditional distribution in a nonlinear way. We use the stochastic…

Optimization and Control · Mathematics 2024-11-05 Ziyu Huang , Shanjian Tang

We study infinite horizon discounted Mean Field Control (MFC) problems with common noise through the lens of Mean Field Markov Decision Processes (MFMDP). We allow the agents to use actions that are randomized not only at the individual…

Optimization and Control · Mathematics 2021-10-14 René Carmona , Mathieu Laurière , Zongjun Tan

An iterative finite difference scheme for mean field games (MFGs) is proposed. The target MFGs are derived from control problems for multidimensional systems with advection terms. For such MFGs, linearization using the Cole-Hopf…

Optimization and Control · Mathematics 2023-04-26 Daisuke Inoue , Yuji Ito , Takahito Kashiwabara , Norikazu Saito , Hiroaki Yoshida

We study discrete-time mean-field Markov games with infinite numbers of agents where each agent aims to minimize its ergodic cost. We consider the setting where the agents have identical linear state transitions and quadratic cost…

Optimization and Control · Mathematics 2019-10-17 Zuyue Fu , Zhuoran Yang , Yongxin Chen , Zhaoran Wang

Mean-payoff games (MPGs) are infinite duration two-player zero-sum games played on weighted graphs. Under the hypothesis of perfect information, they admit memoryless optimal strategies for both players and can be solved in…

Logic in Computer Science · Computer Science 2015-04-14 Paul Hunter , Guillermo A. Pérez , Jean-François Raskin

In this paper, we consider Mean Field Games in the presence of common noise relaxing the usual independence assumption of individual random noise. We assume a simple linear model with terminal cost satisfying a convexity and a weak…

Probability · Mathematics 2016-07-05 Saran Ahuja

In this article, from the viewpoint of control theory, we discuss the relationships among the commonly used monotonicity conditions that ensure the well-posedness of the solutions arising from problems of mean field games (MFGs) and mean…

Optimization and Control · Mathematics 2024-12-09 Alain Bensoussan , Ziyu Huang , Shanjian Tang , Sheung Chi Phillip Yam

This paper presents a Gaussian Process (GP) framework, a non-parametric technique widely acknowledged for regression and classification tasks, to address inverse problems in mean field games (MFGs). By leveraging GPs, we aim to recover…

Computer Science and Game Theory · Computer Science 2023-12-27 Jinyan Guo , Chenchen Mou , Xianjin Yang , Chao Zhou

In this paper, we consider a large class of constrained non-cooperative stochastic Markov games with countable state spaces and discounted cost criteria. In one-player case, i.e., constrained discounted Markov decision models, it is…

Optimization and Control · Mathematics 2021-12-16 Anna Jaśkiewicz , Andrzej S. Nowak

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

Mean Field Games (MFGs) can potentially scale multi-agent systems to extremely large populations of agents. Yet, most of the literature assumes a single initial distribution for the agents, which limits the practical applications of MFGs.…

Machine Learning · Computer Science 2021-09-21 Sarah Perrin , Mathieu Laurière , Julien Pérolat , Romuald Élie , Matthieu Geist , Olivier Pietquin

In this paper, we investigate a partially observable zero sum games where the state process is a discrete time Markov chain. We consider a general utility function in the optimization criterion. We show the existence of value for both…

Optimization and Control · Mathematics 2022-11-16 Arnab Bhabak , Subhamay saha

We study how risk-sensitive players act in situations where the outcome is influenced not only by the state-action profile but also by the distribution of it. In such interactive decision-making problems, the classical mean-field game…

Optimization and Control · Mathematics 2015-05-26 Hamidou Tembine

Hypothesis Testing Minority Game (HMG) is a variant of the standard Minority Game (MG) that models the inertial behavior of agents in the market. In the earlier study of our group, we find that agents cooperate better in HMG than in the…

Physics and Society · Physics 2009-11-13 H. F. Chau , V. H. Chan , F. K. Chow

We study Markov potential games under the infinite horizon average reward criterion. Most previous studies have been for discounted rewards. We prove that both algorithms based on independent policy gradient and independent natural policy…

Machine Learning · Computer Science 2024-03-12 Min Cheng , Ruida Zhou , P. R. Kumar , Chao Tian

Traditional solvable game theory and mean-field-type game theory (risk-aware games) predominantly focus on quadratic costs due to their analytical tractability. Nevertheless, they often fail to capture critical non-linearities inherent in…

Optimization and Control · Mathematics 2025-05-09 Julian Barreiro-Gomez , Tyrone E. Duncan , Bozenna Pasik-Duncan , Hamidou Tembine

In this paper we propose two new monotonicity conditions that could serve as sufficient conditions for uniqueness of Nash equilibria in mean field games. In this study we aim for $unconditional\ uniqueness$ that is independent of the length…

Analysis of PDEs · Mathematics 2023-07-24 P. Jameson Graber , Alpár R. Mészáros

This paper is concerned with two-person mean-field linear-quadratic non-zero sum stochastic differential games in an infinite horizon. Both open-loop and closed-loop Nash equilibria are introduced. Existence of an open-loop Nash equilibrium…

Optimization and Control · Mathematics 2021-04-09 Xun Li , Jingtao Shi , Jiongmin Yong

We consider learning approximate Nash equilibria for discrete-time mean-field games with nonlinear stochastic state dynamics subject to both average and discounted costs. To this end, we introduce a mean-field equilibrium (MFE) operator,…

Systems and Control · Electrical Eng. & Systems 2022-11-11 Berkay Anahtarcı , Can Deha Karıksız , Naci Saldi