相关论文: Finite state N-agent and mean field control proble…

The goal of this paper is to provide a selection principle for potential mean field games on a finite state space and, in this respect, to show that equilibria that do not minimize the corresponding mean field control problem should be…

The paper studies the convergence, as $N$ tends to infinity, of a system of $N$ coupled Hamilton-Jacobi equations, the Nash system. This system arises in differential game theory. We describe the limit problem in terms of the so-called…

We propose two numerical methods for the optimal control of McKean-Vlasov dynamics in finite time horizon. Both methods are based on the introduction of a suitable loss function defined over the parameters of a neural network. This allows…

We consider a Mean Field Games model where the dynamics of the agents is subdiffusive. According to the optimal control interpretation of the problem, we get a system involving fractional time-derivatives for the Hamilton-Jacobi-Bellman and…

First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit as the number of agents tends to infinity. The known results…

Agents attempt to maximize expected profits earned by selling multiple units of a perishable product where their revenue streams are affected by the prices they quote as well as the distribution of other prices quoted in the market by other…

In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by 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 study the optimal control of mean-field systems with heterogeneous and asymmetric interactions. This leads to considering a family of controlled Brownian diffusion processes with dynamics depending on the whole collection of marginal…

We introduce a new numerical method to approximate the solution of a finite horizon deterministic optimal control problem. We exploit two Hamilton-Jacobi-Bellman PDE, arising by considering the dynamics in forward and backward time. This…

In this paper we provide the existence of classical solutions to stationary mean field game systems in the whole space $\mathbb{R}^N$, with coercive potential and aggregating local coupling, under general conditions on the Hamiltonian. The…

This paper studies a class of time-inconsistent mean field control (MFC) problems in the presence of common noise under non-exponential discount and joint law dependence of both state and control. We investigate the closed-loop…

We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this…

We study a degenerate second order mean field game (MFG) system in a Hilbert space $H$ which couples a Fokker--Planck equation describing the evolution of probability measures on $H$ with a Hamilton--Jacobi--Bellman (HJB) equation for the…

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…

This paper studies the $N$-particle systems as well as the HJB/master equations for a class of generalized mean field control (MFC) problems and the corresponding potential mean field games of control (MFGC). A local in time classical…

We consider a class of systems of time dependent partial differential equations which arise in mean field type models with congestion. The systems couple a backward viscous Hamilton-Jacobi equation and a forward Kolmogorov equation both…

This paper analyzes and explicitly solves a class of long-term average impulse control problems with a specific mean-field interaction. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The…

We show the existence of "mild solutions" for a first-order mean field game of controls under the state constraint that trajectories be confined in a closed and bounded set in euclidean space. This extends the results of Cannarsa and…

This paper deals with a class of neural SDEs and studies the limiting behavior of the associated sampled optimal control problems as the sample size grows to infinity. The neural SDEs with $N$ samples can be linked to the $N$-particle…