相关论文: Convexification Numerical Method for the Retrospec…

In recent years, mean field games (MFGs) have garnered considerable attention and emerged as a dynamic and actively researched field across various domains, including economics, social sciences, finance, and transportation. The inverse…

We generalize the notion of convexity and average-convexity to the notion of weighted average-convexity. We show several results on the relation between weighted average-convexity and cooperative games. First, we prove that if a game is…

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…

The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…

In this paper we consider ill-posed inverse problems, both linear and nonlinear, by a heavy ball method in which a strongly convex regularization function is incorporated to detect the feature of the sought solution. We develop ideas on how…

In this paper we study second order stationary Mean Field Game systems under density constraints on a bounded domain $\Omega \subset \mathbb{R}^d$. We show the existence of weak solutions for power-like Hamiltonians with arbitrary order of…

In this short note, we consider an inverse problem to a mean-field games system where we are interested in reconstructing the state-independent running cost function from observed value-function data. We provide an elementary proof of a…

We study the forward-backward system of stochastic partial differential equations describing a mean field game for a large population of small players subject to both idiosyncratic and common noise. The unique feature of the problem is that…

In this article, we study a simplified version of a density-dependent first-order mean field game, in which the players face a penalization equal to the population density at their final position. We consider the problem of finding an…

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…

In a series of publications of the second author, including some with coauthors, globally strictly convex Tikhonov-like functionals were constructed for some nonlinear ill-posed problems. The main element of such a functional is the…

We propose a simple variant of the generalized Frank-Wolfe method for solving strongly convex composite optimization problems, by introducing an additional averaging step on the dual variables. We show that in this variant, one can choose a…

We consider mean field games with discrete state spaces (called discrete mean field games in the following) and we analyze these games in continuous and discrete time, over finite as well as infinite time horizons. We prove the existence of…

Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean…

The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…

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…

Recent applications that arise in machine learning have surged significant interest in solving min-max saddle point games. This problem has been extensively studied in the convex-concave regime for which a global equilibrium solution can be…

Optimizing strategic decisions (a.k.a. computing equilibrium) is key to the success of many non-cooperative multi-agent applications. However, in many real-world situations, we may face the exact opposite of this game-theoretic problem --…

This paper revisits the well-studied \emph{optimal stopping} problem but within the \emph{large-population} framework. In particular, two classes of optimal stopping problems are formulated by taking into account the \emph{relative…

This paper studies an inverse problem for a multipopulation mean field game (MFG) system where the objective is to reconstruct the running and terminal cost functions of the system that couples the dynamics of different populations. We…