Abstract Mean Field Games provide a powerful framework to analyze the dynamics of a large number of controlled objects in interaction. Though these models are much simpler than the underlying differential games they describe in some limit, their behavior is still far from being fully understood. When the system is confined, a notion of “ergodic state” has been introduced that characterizes most of the dynamics for long optimization times. Here we consider a class of models without such an ergodic state, and show the existence of a scaling solution that plays a similar role. Its universality and scaling behavior can be inferred from a mapping to an electrostatic problem.

中文翻译：

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非平稳平均场博弈中的普遍行为

Abstract Mean Field Games提供了一个强大的框架来分析交互中大量受控对象的动力学。尽管这些模型比它们在某些限制下描述的底层微分博弈简单得多，但它们的行为仍远未完全被理解。当系统受限时，引入了“遍历状态”的概念，该概念表征了长优化时间的大部分动态。在这里，我们考虑一类没有这种遍历状态的模型，并展示了具有类似作用的缩放解决方案的存在。从映射到静电问题可以推断出它的普遍性和缩放行为。