论文标题
在平均野外游戏的单调条件下
On monotonicity conditions for Mean Field Games
论文作者
论文摘要
在本文中，我们提出了两个新的单调性条件，这些条件可以作为平均野外游戏中纳什均衡性唯一性的足够条件。在这项研究中，我们的目标是$无条件\唯一性$，它独立于时间范围的长度，代理的起始分布的规律性或非分类特质噪声的正则化效果。通过一系列简单的例子，我们表明，这些新条件不仅在二分法中，而且还与文献中两个广泛研究的单调性条件相同，Lasry-Lions单调性和位移单调性条件。
In this paper we propose two new monotonicity conditions that could serve as sufficient conditions for uniqueness of Nash equilibria in mean field games. In this study we aim for $unconditional\ uniqueness$ that is independent of the length of the time horizon, the regularity of the starting distribution of the agents, or the regularization effect of a non-degenerate idiosyncratic noise. Through a rich class of simple examples we show that these new conditions are not only in dichotomy with each other, but also with the two widely studied monotonicity conditions in the literature, the Lasry-Lions monotonicity and displacement monotonicity conditions.
