相关论文: Second order local minimal-time Mean Field Games

We introduce a general probabilistic framework for discrete-time, infinite-horizon discounted Mean Field Type Games (MFTGs) with both global common noise and team-specific common noises. In our model, agents are allowed to use randomized…

In this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study a class of deterministic mean field games and master equations, where the interaction of the agents happens…

We consider stochastic differential games with a large number of players, with the aim of quantifying the gap between closed-loop, open-loop and distributed equilibria. We show that, under two different semi-monotonicity conditions, the…

We consider a couple of integrodifferential PDEs arising from a stochastic Markovian control problem subjected to initial-terminal conditions. These equations correspond to the MFG system for a controlled jump-diffusion process. We prove…

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…

The Parallel Minority Game (PMG) is a synchronous adaptive multi-agent model that exhibits active-absorbing transitions characteristic of non-equilibrium statistical systems. We perform a comprehensive numerical study of the PMG under two…

We show the convergence of finite state symmetric N-player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled…

We discuss the system of Fokker-Planck and Hamilton-Jacobi-Bellman equations arising from the finite horizon control of McKean-Vlasov dynamics. We give examples of existence and uniqueness results. Finally, we propose some simple models for…

In this paper, using variational approaches, we investigate the first order planning problem arising in the theory of mean field games. We show the existence and uniqueness of weak solutions of the problem in the case of a large class of…

In this paper, we study deterministic mean field games for agents who operate in a bounded domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of…

Mean field games (MFGs) describe the limit, as $n$ tends to infinity, of stochastic differential games with $n$ players interacting with one another through their common empirical distribution. Under suitable smoothness assumptions that…

We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian behaves like a power of its arguments as they tend to infinity,…

Mean Field Games with state constraints are differential games with infinitely many agents, each agent facing a constraint on his state. The aim of this paper is to provide a meaning of the PDE system associated with these games, the…

Mean-Field Games are games with a continuum of players that incorporate the time-dimension through a control-theoretic approach. Recently, simpler approaches relying on the Best Reply Strategy have been proposed. They assume that the agents…

In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary…

We consider a finite-time stochastic drift control problem with the assumption that the control is bounded and the system is controlled until the state process leaves the half-line. Assuming general conditions, it is proved that the…

Mean-field games (MFGs) are a modeling framework for systems with a large number of interacting agents. They have applications in economics, finance, and game theory. Normalizing flows (NFs) are a family of deep generative models that…

By following the study in [24], we consider an inverse boundary problem for the mean field game system where a probability density constraint is enforced on the game agents. That is, we consider the case that reflective boundary conditions…

Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players…

We propose a control-theoretic framework for evolutionary clustering based on Mean Field Games (MFG). Moving beyond static or heuristic approaches, we formulate the problem as a population dynamics game governed by a coupled…