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This paper is concerned with non-zero sum differential games of mean-field stochastic differential equations with partial information and convex control domain. First, applying the classical convex variations, we obtain stochastic maximum…

Optimization and Control · Mathematics 2016-01-11 Hua Xiao , Shuaiqi Zhang

We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To…

Probability · Mathematics 2020-06-02 Carsten Chong , Claudia Klüppelberg

We study a system of partial differential equations used to describe Bertrand and Cournot competition among a continuum of producers of an exhaustible resource. By deriving new a priori estimates, we prove the existence of classical…

Analysis of PDEs · Mathematics 2015-09-01 P. Jameson Graber , Alain Bensoussan

In this article we consider finite Mean Field Games (MFGs), i.e. with finite time and finite states. We adopt the framework introduced in Gomes Mohr and Souza in 2010, and study two seemly unexplored subjects. In the first one, we analyze…

Optimization and Control · Mathematics 2018-05-16 Saeed Hadikhanloo , Francisco José Silva

We study first order evolutive Mean Field Games whose operators are non-coercive. This situation occurs, for instance, when some directions are `forbidden' to the generic player at some points. Under some regularity assumptions, we…

Analysis of PDEs · Mathematics 2019-03-14 Paola Mannucci , Claudio Marchi , Carlo Mariconda , Nicoletta Tchou

The mean field games system is a coupled pair of nonlinear partial differential equations arising in differential game theory, as a limit as the number of agents tends to infinity. We prove existence and uniqueness of classical solutions…

Analysis of PDEs · Mathematics 2020-01-28 David M. Ambrose

In this paper, we study a class of linear-quadratic (LQ) mean-field games in which the individual control process is constrained in a closed convex subset $\Gamma$ of full space $\mathbb{R}^m$. The decentralized strategies and consistency…

Optimization and Control · Mathematics 2016-10-20 Ying Hu , Huang Jianhui , Xun Li

We establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type,…

Probability · Mathematics 2017-07-25 Boualem Djehiche , Said Hamadène

The objective of this paper is to analyze the existence of equilibria for a class of deterministic mean field games of controls. The interaction between players is due to both a congestion term and a price function which depends on the…

Optimization and Control · Mathematics 2022-01-19 Joseph Frédéric Bonnans , Justina Gianatti , Laurent Pfeiffer

Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…

Probability · Mathematics 2015-04-09 Rene Carmona , Daniel Lacker

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…

Optimization and Control · Mathematics 2023-06-21 Mattia Bongini , Francesco Salvarani

The \emph{stationary set splitting game} is a game of perfect information of length $\omega_{1}$ between two players, \unspls and \spl, in which \unspls chooses stationarily many countable ordinals and \spls tries to continuously divide…

Logic · Mathematics 2010-03-15 Paul Larson , Saharon Shelah

In a mean field game of controls, players seek to minimize a cost that depends on the joint distribution of players' states and controls. We consider an ergodic problem for second-order mean field games of controls with state constraints,…

Analysis of PDEs · Mathematics 2026-04-10 Jameson Graber , Kyle Rosengartner

This paper establishes the existence of relaxed solutions to mean field games (MFGs for short) with singular controls. We also prove approximations of solutions results for a particular class of MFGs with singular controls by solutions,…

Optimization and Control · Mathematics 2017-08-04 Guanxing Fu , Ulrich Horst

An existence result for a class of mean field games of controls is provided. In the considered model, the cost functional to be minimized by each agent involves a price depending at a given time on the controls of all agents and a…

Optimization and Control · Mathematics 2019-06-24 J. Frédéric Bonnans , Saeed Hadikhanloo , Laurent Pfeiffer

This paper is devoted to path-dependent kinetics equations arising, in particular, from the analysis of the coupled backward - forward systems of equations of mean field games. We present local well-posedness, global existence and some…

Probability · Mathematics 2013-03-25 Vassili Koloklotsov , Wei Yang

In this paper, we develop a Mean Field Games approach to Cluster Analysis. We consider a finite mixture model, given by a convex combination of probability density functions, to describe the given data set. We interpret a data point as an…

Numerical Analysis · Mathematics 2019-12-24 Laura Aquilanti , Simone Cacace , Fabio Camilli , Raul De Maio

We study some systems of interacting fields whose evolution is given by some singular stochastic partial differential equations of mean field type. We provide a robust setting for their study and prove a well-posedness result and a…

Probability · Mathematics 2026-04-15 I. Bailleul , N. Moench

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…

Probability · Mathematics 2018-02-01 Alekos Cecchin , Markus Fischer

In this paper, we investigate the robustness of stationary mean-field equilibria in the presence of model uncertainties, specifically focusing on infinite-horizon discounted cost functions. To achieve this, we initially establish…

Systems and Control · Electrical Eng. & Systems 2026-04-10 Uğur Aydın , Naci Saldi