We present an example of symmetric ergodic N-players differential games, played in memory strategies on the position of the players, for which the limit set, as \(N\rightarrow +\infty \), of Nash equilibrium payoffs is large, although the game has a single mean field game equilibrium. This example is in sharp contrast with a result by Lacker (On the convergence of closed-loop Nash equilibria to the mean field game limit, 2018. arXiv:1808.02745) for finite horizon problems.

中文翻译：

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遍历微分博弈中多个平均场限制的示例

我们提供了一个对称遍历N玩家差分游戏的示例，该博弈以玩家位置上的记忆策略进行，其纳什均衡收益的极限设置为\（N \ rightarrow + \ infty \），尽管该博弈具有单个均值博弈均衡。该示例与Lacker（关于闭环Nash均衡到平均场博弈极限的收敛，2018年。arXiv：1808.02745）形成的鲜明对比。