Continuous Time Finite State Mean Field Games
Continuous Time Finite State Mean Field Games
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DOI：
10.1007/s00245-013-9202-8
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发表时间：
2013-08-01
影响因子：
1.8
通讯作者：
Souza, Rafael Rigao
中科院分区：
文献类型：
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作者：
Gomes, Diogo A.;Mohr, Joana;Souza, Rafael Rigao
在这篇文章中，我们考虑对称对策，其中大量的玩家可以处于d个状态中的任何一个。我们导出了一个极限平均场模型，并刻画了它的主要性质。这个平均场极限是一个具有初末数据的耦合常微分方程组。对于这个平均场问题，我们证明了一个趋向平衡定理，即在适当的极限下收敛到定常解。然后，我们研究了平均场模型试图逼近的N+1人问题。我们的主要结果是平均场模型的收敛为N-gt；a，并给出了收敛速度的估计。最后，我们给出了一些潜在平均场对策的进一步例子。
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N -> a of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.