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On Quasi-stationary Mean Field Games Models

  • Charafeddine MouzouniEmail author
Article

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 without anticipating. With a specific cost structures, these models give rise to coupled systems of partial differential equations of quasi-stationary nature. We provide sufficient 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 

Notes

Acknowledgements

This work was supported by LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program ”Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR), and partially supported by project (ANR-16-CE40-0015-01) on mean field games. The author would like to thank Martino Bardi and Pierre Cardaliaguet for fruitful discussions.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Univ Lyon, École centrale de Lyon, CNRS UMR 5208, Institut Camille JordanEcully CedexFrance

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