Related papers: Nonsmooth mean field games with state constraints
Art heritage cities are popular tourist destinations but for many of them overcrowding is becoming an issue. In this paper, we address the problem of modeling and analytically studying the flow of tourists along the narrow alleys of the…
The recently developed mean-field game models of corruption and bot-net defence in cyber-security, the evolutionary game approach to inspection and corruption, and the pressure-resistance game element, can be combined under an extended…
In this paper we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the perceived densities of the different groups present as well…
In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is…
Mean field games (MFGs) offer a powerful framework for modeling large-scale multi-agent systems. This paper addresses MFGs formulated in continuous time with discrete state spaces, where agents' dynamics are governed by continuous-time…
Recently developed toy models for the mean-field games of corruption and botnet defence in cyber-security with three or four states of agents are extended to a more general mean-field-game model with $2d$ states, $d\in \N$. In order to…
This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence…
In this article, we introduce a new class of entropy-penalized robust mean field game problems in which the representative agent is opposed to Nature. The agent's objective is formulated as a min-max stochastic control problem, in which…
This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…
This article introduces a novel mean-field game model for multi-sector economic growth in which a dynamically evolving externality, influenced by the collective actions of agents, plays a central role. Building on classical growth theories…
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…
Mean field games and controls involve guiding the behavior of large populations of interacting agents, where each individual's influence on the group is negligible but collectively impacts overall dynamics. Hybrid systems integrate…
We study the uniqueness of solutions to systems of PDEs arising in Mean Field Games with several populations of agents and Neumann boundary conditions. The main assumption requires the smallness of some data, e.g., the length of the time…
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…
The paper considers a forward-backward system of parabolic PDEs arising in a Mean Field Game (MFG) model where every agent controls the drift of a trajectory subject to Brownian diffusion, trying to escape a given bounded domain $\Omega$ in…
Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as $n$ interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or…
This paper studies the convergence problem for mean field games with common noise. We define a suitable notion of weak mean field equilibria, which we prove captures all subsequential limit points, as $n\to\infty$, of closed-loop…
We explore a mechanism of decision-making in Mean Field Games with myopic players. At each instant, agents set a strategy which optimizes their expected future cost by assuming their environment as immutable. As the system evolves, the…
This paper studies an optimal investment-consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as…
For two classes of Mean Field Game systems we study the convergence of solutions as the interest rate in the cost functional becomes very large, modeling agents caring only about a very short time-horizon, and the cost of the control…