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Related papers: Cluster formation in iterated Mean Field Games

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We consider the one-dimensional stationary first-order mean-field game (MFG) system with the coupling between the Hamilton-Jacobi equation and the transport equation. In both cases that the coupling is strictly increasing and decreasing…

Analysis of PDEs · Mathematics 2018-05-29 Yiru Cai , Haobo Qi , Yi Tan , Xifeng Su

We study a model of a population making a binary decision based on information spreading within the population, which is fully connected or covering a square grid. We assume that a fraction of the population wants to make the choice of the…

Physics and Society · Physics 2016-05-24 Petter Holme , Hang-Hyun Jo

This paper addresses a linear-quadratic Stackelberg mean field (MF) games and teams problem with arbitrary population sizes, where the game among the followers is further categorized into two types: non-cooperative and cooperative, and the…

Optimization and Control · Mathematics 2024-12-24 Wenyu Cong , Jingtao Shi , Bingchang Wang

Mean Field Games (MFG) theory describes strategic interactions in differential games with a large number of small and indistinguishable players. Traditionally, the players' control impacts only the drift term in the system's dynamics,…

Analysis of PDEs · Mathematics 2024-07-31 Vincenzo Ignazio , Michele Ricciardi

We consider mean-field models for data--clustering problems starting from a generalization of the bounded confidence model for opinion dynamics. The microscopic model includes information on the position as well as on additional features of…

Numerical Analysis · Mathematics 2020-03-16 Michael Herty , Lorenzo Pareschi , Giuseppe Visconti

We introduce a minimal model of multilevel selection on structured populations, considering the interplay between game theory and population dynamics. Through a bottleneck process, finite groups are formed with cooperators and defectors…

Populations and Evolution · Quantitative Biology 2023-10-02 Jeferson J. Arenzon , Luca Peliti

This work shows that the formation of a finite number of coalitions in a nonatomic network congestion game benefits everyone. At the equilibrium of the composite game played by coalitions and individuals, the average cost to each coalition…

Computer Science and Game Theory · Computer Science 2015-03-20 Cheng Wan

The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…

Probability · Mathematics 2014-08-13 Daniel Lacker

We consider the spread of infectious diseases through a Mean Field Game version of a SIR compartmental model with social structure, in which individuals are grouped by their age class and interact together in different settings. In our game…

Physics and Society · Physics 2022-12-14 Louis Bremaud , Denis Ullmo

Motivated by the climate crisis that is currently ravaging the planet, we propose and analyze a novel framework for the evolution of anthropogenic climate impact in which the evolution of human environmental behavior and environmental…

Dynamical Systems · Mathematics 2022-11-22 Kathinka Frieswijk , Lorenzo Zino , A. Stephen Morse , Ming Cao

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…

Dynamical Systems · Mathematics 2016-01-07 Martin Ritchie , Luc Berthouze , Istvan Z. Kiss

In this paper, we consider both finite and infinite horizon discounted dynamic mean-field games where there is a large population of homogeneous players sequentially making strategic decisions and each player is affected by other players…

Computer Science and Game Theory · Computer Science 2019-10-23 Deepanshu Vasal

In stochastic dynamic games, when the number of players is sufficiently large and the interactions between agents depend on empirical state distribution, one way to approximate the original game is to introduce infinite-population limit of…

Optimization and Control · Mathematics 2019-08-26 Naci Saldi

We study coalition structure formation with intra and inter-coalition externalities in the introduced family of nested non-cooperative simultaneous finite games. A non-cooperative game embeds a coalition structure formation mechanism, and…

Computer Science and Game Theory · Computer Science 2021-07-05 Dmitry Levando

In this paper we consider a distributed coordination game played by a large number of agents with finite information sets, which characterizes emergence of a single dominant attribute out of a large number of competitors. Formally, $N$…

Economics · Quantitative Finance 2016-12-21 S. Agarwal , D. Ghosh , A. S. Chakrabarti

Mean field games is a recent area of study introduced by Lions and Lasry in a series of seminal papers in 2006. Mean field games model situations of competition between large number of rational agents that play non-cooperative dynamic games…

Optimization and Control · Mathematics 2011-03-18 Diogo A. Gomes , Joana Mohr , Rafael R. Souza

The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…

Optimization and Control · Mathematics 2019-03-19 Bruce Hajek , Michael Livesay

When a prediction algorithm serves a collection of users, disparities in prediction quality are likely to emerge. If users respond to accurate predictions by increasing engagement, inviting friends, or adopting trends, repeated learning…

Machine Learning · Computer Science 2025-11-27 Eden Saig , Nir Rosenfeld

We introduce and study a nonlinear discrete dynamical system describing the evolution of a resource distribution among interacting agents. The model generalizes several classical mean-field and opinion-dynamics frameworks and is defined on…

Dynamical Systems · Mathematics 2026-04-28 Oksana Satur

We investigate mean-field games (MFG) in which agents can actively control their speed of access to information. Specifically, the agents can dynamically decide to obtain observations with reduced delay by accepting higher observation…

Optimization and Control · Mathematics 2025-06-03 Dirk Becherer , Christoph Reisinger , Jonathan Tam