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Annals of Applied Probability, ISSN 1050-5164, 04/2017, Volume 27, Issue 2, pp. 757 - 810
Mean field games are limit models for symmetric N-player games with interaction of mean field type as N -> infinity. The limit relation is often understood in... 
Weak convergence | Nash equilibrium | Optimal control | McKean-Vlasov limit | Mean field game | Martingale problem | mean field game | martingale problem | NONLINEAR PARABOLIC EQUATIONS | optimal control | STATISTICS & PROBABILITY | weak convergence | Mathematics - Probability
Journal Article
Physics Reports, ISSN 0370-1573, 04/2016, Volume 624, pp. 1 - 60
Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of... 
MEAN-FIELD | STATISTICAL-MECHANICS | RENORMALIZATION-GROUP | PHYSICS, MULTIDISCIPLINARY | PHASE-TRANSITIONS | ISING-MODEL | COMPETING ASSOCIATIONS | CRITICAL-BEHAVIOR | 2 X-2 GAMES | PRISONERS-DILEMMA | CRITICAL EXPONENTS | Game theory | Analysis
Journal Article
SIAM Journal on Control and Optimization, ISSN 0363-0129, 2013, Volume 51, Issue 4, pp. 2705 - 2734
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2010, Volume 48, Issue 3, pp. 1136 - 1162
Mean field type models describing the limiting behavior, as the number of players tends to + ∞, of stochastic differential game problems, have been recently... 
Discrete problems | Approximation | Real numbers | Applied mathematics | Numerical methods | Uniqueness | Homogenization | Mathematical functions | Game theory | Finite difference schemes | Mean field games | mean field games | EQUATIONS | MATHEMATICS, APPLIED | finite difference schemes | HOMOGENIZATION | Studies | Numerical analysis | Finite element analysis | Differential equations
Journal Article
AIMS Electronics and Electrical Engineering, ISSN 2578-1588, 2017, Volume 1, Issue 1, pp. 18 - 73
A mean-field-type game is a game in which the instantaneous payoffs and/or the statedynamics functions involve not only the state and the action profile but... 
mean-field-type game| electrical| computer| mechanical| civil| general engineering
Journal Article
Automatica, ISSN 0005-1098, 11/2018, Volume 97, pp. 200 - 213
Journal Article
IEEE Transactions on Automatic Control, ISSN 0018-9286, 01/2020, Volume 65, Issue 1, pp. 12 - 27
We consider mean field games between a dominant leader and many followers, such that each follower is subject to a heterogeneous delay effect from the leader's... 
mean field games (MFGs) | stocashtic optimal control | Delay effects | Delay systems | Sociology | Stochastic processes | Games | Differential equations | stochastic systems | Delays | nonlinear system | Statistics | ENGINEERING, ELECTRICAL & ELECTRONIC | SYSTEMS | AUTOMATION & CONTROL SYSTEMS
Journal Article
IEEE Transactions on Automatic Control, ISSN 0018-9286, 12/2017, Volume 62, Issue 12, pp. 6310 - 6323
Within the realm of smart buildings and smart cities, dynamic response management is playing an ever-increasing role, thus attracting the attention of... 
Asymptotic stability | stochastic stability | Mean-field games | power networks | Sociology | Stochastic processes | Games | Vehicle dynamics | Statistics | Power networks | Stochastic stability | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Game theory | Analysis
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 03/2018, Volume 35, Issue 2, pp. 443 - 480
We consider a class of systems of time dependent partial differential equations which arise in mean field type models with congestion. The systems couple a... 
Weak solutions | Congestion models | Mean field games | Local coupling | Existence and uniqueness | EXISTENCE | MATHEMATICS, APPLIED | NONLINEAR PARABOLIC EQUATIONS
Journal Article
SIAM Journal on Control and Optimization, ISSN 0363-0129, 2016, Volume 54, Issue 2, pp. 1030 - 1055
In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but... 
Mean-field games | Random variables methods | Hamilton Jacobi equations | Deterministic control | Differential games | Hamilton-Jacobi equations | MATHEMATICS, APPLIED | random variables methods | deterministic control | differential games | mean-field games | AUTOMATION & CONTROL SYSTEMS
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 01/2017, Volume 27, Issue 1, pp. 75 - 113
This paper introduces and analyzes some models in the framework of mean field games (MFGs) describing interactions between two populations motivated by the... 
finite difference methods | systems of parabolic equations | multi-populations models | Mean field games | segregation | large populations limit | NUMERICAL-METHODS | MATHEMATICS, APPLIED | RESIDENTIAL SEGREGATION | EQUATIONS | DYNAMICAL-SYSTEMS | CONVERGENCE | BOUNDARY | AGENTS | SEMI-LAGRANGIAN SCHEME
Journal Article
Dynamic Games and Applications, ISSN 2153-0785, 9/2016, Volume 6, Issue 3, pp. 277 - 303
Journal Article
IEEE Transactions on Automatic Control, ISSN 0018-9286, 03/2017, Volume 62, Issue 3, pp. 1062 - 1077
Journal Article
COMMUNICATIONS IN MATHEMATICAL SCIENCES, ISSN 1539-6746, 2015, Volume 13, Issue 4, pp. 911 - 933
We propose a simple model of inter-bank borrowing and lending where the evolution of the log-monetary reserves of N banks is described by a system of diffusion... 
MATHEMATICS, APPLIED | Nash equilibrium | Systemic risk | Mean Field Game | inter-bank borrowing and lending | stochastic games
Journal Article
The Annals of Probability, ISSN 0091-1798, 11/2016, Volume 44, Issue 6, pp. 3740 - 3803
Journal Article