论文标题
平均野外游戏理论中NASH平衡的存在和独特性
The Existence and Uniqueness of a Nash Equilibrium in Mean Field Game Theory
论文作者
论文摘要
在最近和过去的工作中，通常在动作功能的每个部分都假定凸度，以证明在某个间隔[0，t]上表现出NASH平衡的存在和唯一性（这意味着每个Hessian被认为是非负性的）。特别是为了量化T的较小性，提出了一定的假设。该项目的贡献是扩展这一点，关键见解是，一个人不需要每个部分的凸度，而只是仅需要适当的组合，而这些组合本质上将“补偿”以使其他两个项在动作中产生凸度。 这在纯净和应用的设置中都是有意义的，因为它概括了纳什均衡的存在和唯一性，但更重要的是，更重要的是，与现实世界的应用略微匹配，因为实际上，在许多设置中，动作的每个部分都不是均匀的。因此，对于平均现场游戏理论的现代应用是更准确的。
In recent and past works, convexity is usually assumed on each individual part of the action functional in order to demonstrate the existence and uniqueness of a Nash equilibrium on some interval [0, T] (this meant that each hessian was assumed to be nonnegative). Particularly, a certain assumption was imposed in order to quantify the smallness of T. The contribution of this project is to expand on this with the key insight being that one does not need the convexity of each part of the action, but rather just an appropriate combination of them, which will essentially "compensate" for the other two terms to yield convexity in the action. This is meaningful in both the pure and applied settings as it generalizes the existence and uniqueness of a Nash equilibrium slightly more, but maybe more importantly matches real world application slightly closer, as in reality there are many settings in which not each part of the action have convexity. Thus, it is more accurate for modern application of Mean Field Game Theory.
