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Networks and Heterogeneous Media

2012, Volume 7, Issue 2: 279-301. doi: 10.3934/nhm.2012.7.279
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Long time average of mean field games

  • 1.
    Ceremade, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16
  • 2.
    56 Rue d'Assas, 75006 Paris
  • 3.
    Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scienti ca 1, 00133 Roma
  • Received: 01 November 2011 Revised: 01 March 2012

  • Primary: 35B40; Secondary: 35K55.

  • We consider a model of mean field games system defined on a time interval $[0,T]$ and investigate its asymptotic behavior as the horizon $T$ tends to infinity. We show that the system, rescaled in a suitable way, converges to a stationary ergodic mean field game. The convergence holds with exponential rate and relies on energy estimates and the Hamiltonian structure of the system.

    Citation: Pierre Cardaliaguet, Jean-Michel Lasry, Pierre-Louis Lions, Alessio Porretta. Long time average of mean field games[J]. Networks and Heterogeneous Media, 2012, 7(2): 279-301. doi: 10.3934/nhm.2012.7.279

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  • We consider a model of mean field games system defined on a time interval $[0,T]$ and investigate its asymptotic behavior as the horizon $T$ tends to infinity. We show that the system, rescaled in a suitable way, converges to a stationary ergodic mean field game. The convergence holds with exponential rate and relies on energy estimates and the Hamiltonian structure of the system.


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Networks and Heterogeneous Media
1.2 1.8

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