相关论文: A Modest Proposal for MFG with Density Constraints

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…

We provide a unifying, black-box tool for establishing existence of approximate equilibria in weighted congestion games and, at the same time, bounding their Price of Stability. Our framework can handle resources with general…

Traditional solvable game theory and mean-field-type game theory (risk-aware games) predominantly focus on quadratic costs due to their analytical tractability. Nevertheless, they often fail to capture critical non-linearities inherent in…

We formulate the MFG limit for $N$ interacting agents with a common noise as a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. We prove that any its (regular enough) solution…

Sparsity plays a central role in recent developments in signal processing, linear algebra, statistics, optimization, and other fields. In these developments, sparsity is promoted through the addition of an $L^1$ norm (or related quantity)…

Self-interested behavior in sharing economies often leads to inefficient aggregate outcomes compared to a centrally coordinated allocation, ultimately harming users. Yet, centralized coordination removes individual decision power. This…

The objective of this paper is to provide an equivalent of the theory developed in P.~Cardaliaguet, F.~Delarue, J.M.~Lasry, P.L.~Lions \cite{CDLL}, following the approach of control on Hilbert spaces introduced by the authors in…

Mean field games (MFGs) offer a powerful framework for modeling large-scale multi-agent systems. This paper addresses MFGs formulated in continuous time with discrete state spaces, where agents' dynamics are governed by continuous-time…

In this paper, we investigate a class of Mean Field Games (MFGs) in which the state dynamics are governed by multidimensional reflected stochastic differential equations (SDEs). We establish the existence of an equilibrium and show that it…

This article considers a mean field game model inspired by crowd motion models in which agents aim at reaching a given target set and wish to minimize a cost consisting of an individual running cost, an individual cost depending on the…

We consider an extension of a noncooperative game problem where players have joint binding constraints. In this case, justification of a generalized equilibrium point needs a reasonable mechanism for attaining this state. We suggest to…

Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout…

We consider deterministic mean field games in which the agents control their acceleration and are constrained to remain in a domain of R n. We study relaxed equilibria in the Lagrangian setting; they are described by a probability measure…

Mean field game (MFG) is an expressive modeling framework for systems with a continuum of interacting agents. While many approaches exist for solving the forward MFG, few have studied its \textit{inverse} problem. In this work, we seek to…

We consider the interaction among agents engaging in a driving task and we model it as general-sum game. This class of games exhibits a plurality of different equilibria posing the issue of equilibrium selection. While selecting the most…

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…

Neural network-based methods have demonstrated effectiveness in solving high-dimensional Mean-Field Games (MFG) equilibria, yet ensuring mathematically consistent density-coupled evolution remains a major challenge. This paper proposes the…

We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become…

In this paper, we address the problem of modeling the traffic flow of a heritage city whose streets are represented by a network. We consider a mean field approach where the standard forward backward system of equations is also intertwined…

In this work, we study the contraction conditions of iterative algorithms for stationary and finite-horizon discrete-time regularized mean-field games (MFGs) with multiple populations, where each population only interacts with the state…