Related papers: Cluster formation in iterated Mean Field Games
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…
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…
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…
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,…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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, $N$…
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…
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.…
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…
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…
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…