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On Quasi-stationary Mean Field Games Models

On Quasi-stationary Mean Field Games Models Appl Math Optim https://doi.org/10.1007/s00245-018-9484-y Charafeddine Mouzouni © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We explore a mechanism of decision-making in mean field games with myopic players. At each instant, agents set a strategy which optimizes their expected future cost by assuming their environment as immutable. As the system evolves, the players observe the evolution of the system and adapt to their new environment with- out anticipating. With a specific cost structures, these models give rise to coupled systems of partial differential equations of quasi-stationary nature. We provide suf- ficient conditions for the existence and uniqueness of classical solutions for these systems, and give a rigorous derivation of these systems from N -players stochastic differential games models. Finally, we show that the population can self-organize and converge exponentially fast to the ergodic mean field games equilibrium, if the initial distribution is sufficiently close to it and the Hamiltonian is quadratic. Keywords Mean field games · Quasi-stationary models · Nonlinear coupled PDE systems · Long time behavior · Self-organization · N-person games · Nash equilibria · Myopic equilibrium Mathematics Subject Classification 35Q91 · 49N70 · 35B40 1 Introduction The mean field games formalism has been introduced some http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

On Quasi-stationary Mean Field Games Models

Mouzouni, Charafeddine
Applied Mathematics and Optimization , Volume OnlineFirst – Feb 22, 2018
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References (37)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-018-9484-y
Publisher site
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Abstract

Appl Math Optim https://doi.org/10.1007/s00245-018-9484-y Charafeddine Mouzouni © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We explore a mechanism of decision-making in mean field games with myopic players. At each instant, agents set a strategy which optimizes their expected future cost by assuming their environment as immutable. As the system evolves, the players observe the evolution of the system and adapt to their new environment with- out anticipating. With a specific cost structures, these models give rise to coupled systems of partial differential equations of quasi-stationary nature. We provide suf- ficient conditions for the existence and uniqueness of classical solutions for these systems, and give a rigorous derivation of these systems from N -players stochastic differential games models. Finally, we show that the population can self-organize and converge exponentially fast to the ergodic mean field games equilibrium, if the initial distribution is sufficiently close to it and the Hamiltonian is quadratic. Keywords Mean field games · Quasi-stationary models · Nonlinear coupled PDE systems · Long time behavior · Self-organization · N-person games · Nash equilibria · Myopic equilibrium Mathematics Subject Classification 35Q91 · 49N70 · 35B40 1 Introduction The mean field games formalism has been introduced some

Journal

Applied Mathematics and Optimization – Springer Journals

Published: Feb 22, 2018

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