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Related papers: Graphon Mean Field Games and the GMFG Equations

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In this paper we discuss a class of mean field linear-quadratic-Gaussian (LQG) games for large population system which has never been addressed by existing literature. The features of our works are sketched as follows. First of all, our…

Probability · Mathematics 2013-08-09 Jianhui Huang , Xun Li , Tianxiao Wang

We address the generalized Nash equilibrium seeking problem for a population of agents playing aggregative games with affine coupling constraints. We focus on semi-decentralized communication architectures, where there is a central…

Optimization and Control · Mathematics 2022-06-16 Giuseppe Belgioioso , Sergio Grammatico

We study the mean field game problem for a nervous system consisting of a large number of neurons with mean-field interaction. In this system, each neuron can modulate its spiking activity by controlling its membrane potential to…

Optimization and Control · Mathematics 2024-12-18 Lijun Bo , Dongfang Yang , Shihua Wang

This paper introduces and analyses some models in the framework of Mean Field Games describing interactions between two populations motivated by the studies on urban settlements and residential choice by Thomas Schelling. For static games,…

Analysis of PDEs · Mathematics 2016-07-18 Yves Achdou , Martino Bardi , Marco Cirant

We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are represented either by the…

Neurons and Cognition · Quantitative Biology 2016-11-25 Javier Baladron , Diego Fasoli , Olivier Faugeras , Jonathan Touboul

Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been…

Computer Science and Game Theory · Computer Science 2014-04-08 Hamidou Tembine

Non-cooperative and cooperative games with a very large number of players have many applications but remain generally intractable when the number of players increases. Introduced by Lasry and Lions, and Huang, Caines and Malham\'e, Mean…

Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and…

Computer Science and Game Theory · Computer Science 2023-12-19 Kai Cui , Gökçe Dayanıklı , Mathieu Laurière , Matthieu Geist , Olivier Pietquin , Heinz Koeppl

We investigate how the framework of mean-field games may be used to investigate strategic interactions in large heterogeneous populations. We consider strategic interactions in a population of players which may be partitioned into…

Optimization and Control · Mathematics 2025-02-19 Rama Cont , Anran Hu

We address the problem of regularity of solutions $u^i(t, x^1, \dots, x^N)$ to a family of semilinear parabolic systems of $N$ equations, which describe closed-loop equilibria of some $N$-player differential games with Lagrangian having…

Analysis of PDEs · Mathematics 2025-06-19 Marco Cirant , Davide Francesco Redaelli

This paper is concerned with linear quadratic graphon field social control problem where the noises of individual agents are correlated. Compared with the well-studied mean field system, the graphon field system consists of a large number…

Optimization and Control · Mathematics 2024-12-30 De-xuan Xu , Zhun Gou , Nan-jing Huang

We establish the existence and uniqueness of distributed equilibria to possibly nonsymmetric $N$ player differential games with interactions through controls under displacement semimonotonicity assumptions. Surprisingly, the nonseparable…

Analysis of PDEs · Mathematics 2026-04-01 Hei Jie Lam , Alpár R. Mészáros

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

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

We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. Particular instances of the problem considered here are mean…

Optimization and Control · Mathematics 2022-12-21 Justina Gianatti , Francisco J. Silva

We study mean field games and corresponding $N$-player games in continuous time over a finite time horizon where the position of each agent belongs to a finite state space. As opposed to previous works on finite state mean field games, we…

Probability · Mathematics 2018-02-01 Alekos Cecchin , Markus Fischer

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

In Evolutionary Game Theory (EGT), a population reaches a Nash equilibrium when none of the agents can improve its objective by solely changing its strategy on its own. Roughly speaking, this equilibrium is a protection against betrayal.…

Computer Science and Game Theory · Computer Science 2025-04-24 Alejandro Luque-Cerpa , Miguel A. Gutiérrez-Naranjo

This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with merely monotone and restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method…

Optimization and Control · Mathematics 2025-07-18 Tatiana Tatarenko , Angelia Nedich

We formulate the MFG limit for $N$ interacting agents with a common noise as a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. We prove that any its (regular enough) solution…

Probability · Mathematics 2022-04-21 Vassili Kolokoltsov , Marianna Troeva