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This paper has two central aims: first, to provide simple conditions under which the generalized games in choice form and, consequently, the abstract economies, admit equilibrium; second, to study the solvability of several types of systems…

Optimization and Control · Mathematics 2016-05-17 Monica Patriche

Here, we study a one-dimensional, non-local mean-field game model with congestion. When the kernel in the non-local coupling is a trigonometric polynomial we reduce the problem to a finite dimensional system. Furthermore, we treat the…

Analysis of PDEs · Mathematics 2017-03-14 Levon Nurbekyan

A linear quadratic (LQ) stochastic optimization problem with delay involving weakly-coupled large population is investigated in this paper. Different to classic mean field (MF) game, here agents cooperate with each other to minimize the…

Optimization and Control · Mathematics 2023-01-18 Tianyang Nie , Shujun Wang , Zhen Wu

We study the short-time existence and uniqueness of solutions to a coupled system of partial differential equations arising in mean field game theory. It has the generic form $$ \left\{ \begin{array}{c} -\partial_t u - \Delta u +…

Analysis of PDEs · Mathematics 2015-03-27 Philip Jameson Graber

This paper investigates the non-zero-sum linear-quadratic stochastic Stackelberg differential games with affine constraints, which depend on both the follower's response and the leader's strategy. With the help of the stochastic Riccati…

Optimization and Control · Mathematics 2024-12-30 Zhun Gou , Nan-Jing Huang , Xian-Jun Long , Jian-Hao Kang

The goal of this paper is to demonstrate that common noise may serve as an exploration noise for learning the solution of a mean field game. This concept is here exemplified through a toy linear-quadratic model, for which a suitable form of…

Optimization and Control · Mathematics 2023-11-03 François Delarue , Athanasios Vasileiadis

In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the…

Analysis of PDEs · Mathematics 2013-11-26 Diogo A. Gomes , Edgard Pimentel , Héctor Sánchez-Morgado

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…

Optimization and Control · Mathematics 2019-01-01 Piermarco Cannarsa , Rossana Capuani , Pierre Cardaliaguet

We introduce the concept of mean field games for agents using Forward utilities of CARA type to study a family of portfolio management problems under relative performance concerns. Under asset specialization of the fund managers, we solve…

Portfolio Management · Quantitative Finance 2020-09-09 Goncalo dos Reis , Vadim Platonov

The mean-field theory for lossy nonlinear composites, described by complex and field-dependent dielectric functions, is presented. By using the spectral representation of linear composites with identical microstructure, we develop…

Soft Condensed Matter · Physics 2007-05-23 K. W. Yu

This paper proposes a new equilibrium concept "robust perfect equilibrium" for non-cooperative games with a continuum of players, incorporating three types of perturbations. Such an equilibrium is shown to exist (in symmetric mixed…

Theoretical Economics · Economics 2021-05-06 Enxian Chen , Lei Qiao , Xiang Sun , Yeneng Sun

In this paper, we consider linear quadratic optimal control with mean-field type for discrete-time stochastic systems with state and control dependent noise. An optimal control problem is studied for a linear mean-field stochastic…

Optimization and Control · Mathematics 2022-10-06 Arzu Ahmadova , Nazim I. Mahmudov

We establish the existence and uniqueness of a solution to the master equation for a mean field game of controls with absorption. The mean field game arises as a continuum limit of a dynamic game of exhaustible resources modeling Cournot…

Analysis of PDEs · Mathematics 2022-08-25 P. Jameson Graber , Ronnie Sircar

The goal of this paper is to study a Mean Field Game (MFG) system stemming from the harvesting of resources. Modelling the latter through a reaction-diffusion equation and the harvesters as competing rational agents, we are led to a…

Analysis of PDEs · Mathematics 2024-06-11 Ziad Kobeissi , Idriss Mazari-Fouquer , Domènec Ruiz-Balet

In this technical note, we consider the linear-quadratic time-inconsistent mean-field type leader-follower Stackelberg differential game with an adapted open-loop information structure. The objective functionals of the leader and the…

Optimization and Control · Mathematics 2019-11-12 Jun Moon , Hyun Jong Yang

While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward-forward problem is still poorly understood - even in the one-dimensional setting.…

Analysis of PDEs · Mathematics 2016-06-30 Diogo Gomes , Levon Nurbekyan , Marc Sedjro

Mean field games allow to describe tractable models of dynamic games with a continuum of players, explicit interaction and heterogeneous states. Thus, these models are of great interest for socio-economic applications. A particular class of…

Optimization and Control · Mathematics 2020-10-20 Berenice Anne Neumann

We show the existence of "mild solutions" for a first-order mean field game of controls under the state constraint that trajectories be confined in a closed and bounded set in euclidean space. This extends the results of Cannarsa and…

Optimization and Control · Mathematics 2023-01-24 Jameson Graber , Sergio Mayorga

We consider a deterministic mean field games problem in which a typical agent solves an optimal control problem where the dynamics is affine with respect to the control and the cost functional has a growth which is polynomial with respect…

Optimization and Control · Mathematics 2023-05-03 Justina Gianatti , Francisco J. Silva , Ahmad Zorkot

The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…

Optimization and Control · Mathematics 2020-03-11 Yves Achdou , Mathieu Laurière