For a class of finite horizon first order mean field games and associated N-player games, we give a simple proof of convergence of symmetric N-player Nash equilibria in distributed open-loop strategies to solutions of the mean field game in Lagrangian form. Lagrangian solutions are then connected with those determined by the usual mean field game system of two coupled first order PDEs, and convergence of Nash equilibria in distributed Markov strategies is established.

中文翻译：

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一阶均值场博弈的渐近性质

对于一类有限水平一阶均值场博弈和相关的N玩家博弈，我们给出了对称的N玩家纳什均衡在分布式开环策略中收敛到拉格朗日形式的均值博弈解的简单证明。然后将拉格朗日解与由两个耦合的一阶PDE的通常平均场博弈系统确定的解联系起来，并建立了分布式马尔可夫策略中纳什均衡的收敛性。