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Related papers: Computational Mean-field Games on Manifolds

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Mean Field Game systems describe equilibrium configurations in differential games with infinitely many infinitesimal interacting agents. We introduce a learning procedure (similar to the Fictitious Play) for these games and show its…

Optimization and Control · Mathematics 2015-08-03 Pierre Cardaliaguet , Saeed Hadikhanloo

This paper investigates a novel class of mean field games involving a major agent and numerous minor agents, where the agents' functionals are recursive with nonlinear backward stochastic differential equation (BSDE) representations. We…

Optimization and Control · Mathematics 2024-12-17 Jianhui Huang , Wenqiang Li , Harry Zheng

In this paper we examine fully nonlinear mean-field games associated with a minimization problem. The variational setting is driven by a functional depending on its argument through its Hessian matrix. We work under fairly natural…

Analysis of PDEs · Mathematics 2020-10-30 Pêdra D. S. Andrade , Edgard A. Pimentel

We show the convergence of finite state symmetric N-player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled…

Probability · Mathematics 2018-12-05 Alekos Cecchin , Guglielmo Pelino

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

Computing Nash equilibria for strategic multi-agent systems is challenging for expensive black box systems. Motivated by the ubiquity of games involving exploitation of common resources, this paper considers the above problem for potential…

Computer Science and Game Theory · Computer Science 2018-11-16 Anup Aprem , Stephen J. Roberts

This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and affected by the aggregate behavior…

Systems and Control · Computer Science 2016-11-15 Sergio Grammatico , Francesca Parise , Marcello Colombino , John Lygeros

The goal of the paper is to introduce a formulation of the mean field game with major and minor players as a fixed point on a space of controls. This approach emphasizes naturally the role played by McKean-Vlasov dynamics in some of the…

Probability · Mathematics 2016-10-19 Rene Carmona , Peiqi Wang

In a game theoretic framework, we study energy markets with a continuum of homogenous producers who produce energy from an exhaustible resource such as oil. Each producer simultaneously optimizes production rate that drives her revenues, as…

Economics · Quantitative Finance 2017-10-17 Michael Ludkovski , Xuwei Yang

Mean field games models describing the limit of a large class of stochastic differential games, as the number of players goes to $+\infty$, have been introduced by J.-M. Lasry and P.-L. Lions. We use a change of variables to transform the…

Numerical Analysis · Mathematics 2011-06-17 Olivier Guéant

This article considers a mean field game model inspired by crowd motion models in which agents aim at reaching a given target set and wish to minimize a cost consisting of an individual running cost, an individual cost depending on the…

Optimization and Control · Mathematics 2026-02-20 Guilherme Mazanti , Laurent Pfeiffer , Saeed Sadeghi Arjmand

We study mean field portfolio games with consumption. For general market parameters, we establish a one-to-one correspondence between Nash equilibria of the game and solutions to some FBSDE, which is proved to be equivalent to some BSDE.…

Mathematical Finance · Quantitative Finance 2022-12-08 Guanxing Fu

We study a general class of fully coupled backward-forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the…

Probability · Mathematics 2020-03-03 Yinggu Chen , Boualem Djehiche , Said Hamadene

We propose and analyze a framework for mean-field Markov games under model uncertainty. In this framework, a state-measure flow describing the collective behavior of a population affects the given reward function as well as the unknown…

Optimization and Control · Mathematics 2024-10-16 Johannes Langner , Ariel Neufeld , Kyunghyun Park

In this paper, we study the well-posedness (existence and uniqueness) of the Master Equation of Mean Field Games under invariance-type conditions, otherwise known as viability conditions for the controlled dynamics. The interior regularity…

Analysis of PDEs · Mathematics 2022-11-15 Antonios Zitridis

A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action pairs. This article presents some…

Optimization and Control · Mathematics 2017-11-30 Boualem Djehiche , Alain Tcheukam , Hamidou Tembine

We propose a single-level numerical approach to solve Stackelberg mean field game (MFG) problems. In Stackelberg MFG, an infinite population of agents play a non-cooperative game and choose their controls to optimize their individual…

Optimization and Control · Mathematics 2024-04-24 Gokce Dayanikli , Mathieu Lauriere

In this paper we consider extended stationary mean field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean field…

Analysis of PDEs · Mathematics 2013-05-14 Diogo A. Gomes , Stefania Patrizi , Vardan Voskanyan

Mean Field Game is a rather new field initially developed in applied mathematics and engineering in order to deal with the dynamics of a large number of controlled agents or objects in interaction. For a large class of these models, there…

Physics and Society · Physics 2021-08-25 Thibault Bonnemain , Thierry Gobron , Denis Ullmo

This paper studies a large population dynamic game involving nonlinear stochastic dynamical systems with agents of the following mixed types: (i) a major agent, and (ii) a population of $N$ minor agents where $N$ is very large. The major…

Optimization and Control · Mathematics 2013-06-07 Mojtaba Nourian , Peter E. Caines