Long time average of mean field games
Long time average of mean field games
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DOI：
10.3934/nhm.2012.7.279
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发表时间：
2012-06
期刊：
影响因子：
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通讯作者：
P. Cardaliaguet;J. Lasry;P. Lions;A. Porretta
中科院分区：
文献类型：
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作者：
P. Cardaliaguet;J. Lasry;P. Lions;A. Porretta
考虑了一个定义在时间区间$[0，T]$上的平均场对策系统模型，研究了当视界$T $趋于无穷大时该系统的渐近行为。我们表明，该系统，以适当的方式重新缩放，收敛到一个平稳的遍历平均场游戏。该收敛性依赖于能量估计和系统的哈密顿结构，并以指数速度保持。
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.