相关论文: An Inverse Problem With the Final Overdeterminatio…

This paper investigates the well-posedness of a type of state constraint ergodic Mean Field Game system in a bounded domain in which the Hamilton-Jacobi-Bellman equation is paired with an infinite Dirichlet boundary condition. In this…

This paper is devoted to the study of Mean-field Games (MFG) systems in the mass critical exponent case. We firstly establish the optimal Gagliardo-Nirenberg type inequality associated with the potential-free MFG system. Then, under some…

In this paper we study a mean-field games system with Dirichlet boundary conditions in a closed domain and in a mean-field of control setting, that is in which the dynamics of each agent is affected not only by the average position of 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…

We prove the global-in-time well-posedness for a broad class of mean field game problems, which is beyond the special linear-quadratic setting, as long as the mean field sensitivity is not too large. Through the stochastic maximum…

Predictions for physical systems often rely upon knowledge acquired from ensembles of entities, e.g., ensembles of cells in biological sciences. For qualitative and quantitative analysis, these ensembles are simulated with parametric…

Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…

In this paper we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or the consumer choice behaviour in the free market. The corresponding…

We present a new combined \textit{mean field control game} (MFCG) problem which can be interpreted as a competitive game between collaborating groups and its solution as a Nash equilibrium between groups. Players coordinate their strategies…

In this paper, we introduce a natural learning rule for mean field games with finite state and action space, the so-called myopic adjustment process. The main motivation for these considerations are the complex computations necessary to…

We develop a foundational framework for inverse problems governed by evolutionary partial differential equations (PDEs) on the Wasserstein space of probability measures. While the forward problems for such transport-type PDEs have been…

We address counterfactual analysis in empirical models of games with partially identified parameters, and multiple equilibria and/or randomized strategies, by constructing and analyzing the counterfactual predictive distribution set (CPDS).…

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…

The theory of Mean-Field Games is interested in the behaviour of interacting particle systems in which the individual interaction between particles (players) decreases as the size of the population increases. In recent years, it was…

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…

This paper is devoted to a class of finite horizon deterministic mean field games with Grushin type dynamics, state constraints and nonlocal coupling. First, we consider the optimal control problem that each agent aims to solve when the…

We study the generalized conditional gradient (GCG) method for time-dependent second-order mean field games (MFG) with local coupling terms. While explicit convergence rates of the GCG method were previously established only for globally…

The standard formulation of the PDE system of Mean Field Games (MFG) requires the differentiability of the Hamiltonian. However in many cases, the structure of the underlying optimal problem leads to a convex but nondifferentiable…

The large amounts of data from molecular biology and neuroscience have lead to a renewed interest in the inverse Ising problem: how to reconstruct parameters of the Ising model (couplings between spins and external fields) from a number of…

This paper studies the convergence of mean field games with finite state space to mean field games with a continuous state space. We examine a space discretization of a diffusive dynamics, which is reminiscent of the Markov chain…