Related papers: Nonsmooth mean field games with state constraints
Many interactions result in a socially suboptimal equilibrium, or in a non-equilibrium state, from which arriving at an equilibrium through simple dynamics can be impossible of too long. Aiming to achieve a certain equilibrium, we persuade,…
A generic feature of systems with long-range interactions is the presence of {\it quasi-stationary} states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian Mean Field (HMF) model, we demonstrate that…
We investigate an infinite-horizon time-inconsistent mean-field game (MFG) in a discrete time setting. We first present a classic equilibrium for the MFG and its associated existence result. This classic equilibrium aligns with the…
Boundary constraints in physical, environmental and engineering models restrict smooth states such as temperature to follow known physical laws at the edges of their spatio-temporal domain. Examples include fixed-state or fixed-derivative…
This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…
In this chapter we look at one of the canonical driving examples for multi-agent systems: average consensus. In this scenario, a group of agents seek to agree on the average of their initial states. Depending on the particular application,…
This paper studies a discrete-time major-minor mean field game of stopping where the major player can choose either an optimal control or stopping time. We look for the relaxed equilibrium as a randomized stopping policy, which is…
In this paper, we investigate a pursuit-evasion game in which a mobile observer tries to track a target in an environment containing obstacles. We formulate the game as an optimal control problem with state inequality constraint in a simple…
Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this…
This paper studies the connections between mean-field games and the social welfare optimization problems. We consider a mean field game in functional spaces with a large population of agents, each of which seeks to minimize an individual…
Here, we consider one-dimensional forward-forward mean-field games (MFGs) with congestion, which were introduced to approximate stationary MFGs. We use methods from the theory of conservation laws to examine the qualitative properties of…
We use the recently developed probabilistic analysis of mean field games with finitely many states in the weak formulation, to set-up a principal / agent contract theory model where the principal faces a large population of agents…
We present a formal treatment of the Crowd-Anticrowd theory of Minority Games played by a population of competing agents. This theory is built around a description of the crowding which arises within the game's strategy space. Earlier works…
Congestion games model a wide variety of real-world resource congestion problems, such as selfish network routing, traffic route guidance in congested areas, taxi fleet optimization and crowd movement in busy areas. However, existing…
In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a locally compact Polish…
The Minority Game is a simple yet highly non-trivial agent-based model for a complex adaptive system. Despite its importance, a quantitative explanation of the game's fluctuations which applies over the entire parameter range of interest…
We study stochastic Mean Field Games on networks with sticky transition conditions. In this setting, the diffusion process governing the agent's dynamics can spend finite time both in the interior of the edges and at the vertices. The…
Modeling and control of agent-based models is twice cursed by the dimensionality of the problem, as both the number of agents and their state space dimension can be large. Even though the computational barrier posed by a large ensemble of…
In this paper, a distributed velocity-constrained consensus problem is studied for discrete-time multi-agent systems, where each agent's velocity is constrained to lie in a nonconvex set. A distributed constrained control algorithm is…
We study a dynamic game with a large population of players who choose actions from a finite set in continuous time. Each player has a state in a finite state space that evolves stochastically with their actions. A player's reward depends…