Stationary focusing mean-field games
Stationary focusing mean-field games
复制标题
固定聚焦平均场游戏
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Marco Cirant
中科院分区：
文献类型：
--
作者：
Marco Cirant
摘要考虑了局部、递减和无界耦合情形下的定常粘性平均场对策系统。这些系统出现在遍历MFG理论和描述纳什均衡的游戏与大量的代理人旨在聚集。我们展示了状态空间的维数、耦合的行为和无穷远处的哈密顿量如何影响正则解的存在性和不存在性。我们的方法依赖于Sobolev正则性的不变测度的研究和爆破过程，校准系统的标度特性。在非常特殊的情况下，我们观察到解的唯一性。最后，我们应用我们的方法获得新的存在性结果的MFG系统的竞争，即，当耦合是本地和增加。
ABSTRACT We consider stationary viscous mean-field games (MFG) systems in the case of local, decreasing and unbounded coupling. These systems arise in ergodic MFG theory and describe Nash equilibria of games with a large number of agents aiming at aggregation. We show how the dimension of the state space, the behavior of the coupling, and the Hamiltonian at infinity affect the existence and nonexistence of regular solutions. Our approach relies on the study of Sobolev regularity of the invariant measure and a blow-up procedure that is calibrated on the scaling properties of the system. In very special cases, we observe uniqueness of solutions. Finally, we apply our methods to obtain new existence results for MFG systems with competition, namely, when the coupling is local and increasing.