On the Existence of Solutions for Stationary Mean-Field Games with Congestion
On the Existence of Solutions for Stationary Mean-Field Games with Congestion
复制标题
拥塞稳态平均场博弈解的存在性
DOI：
10.1007/s10884-017-9615-1
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发表时间：
2016
影响因子：
1.3
通讯作者：
D. Gomes
中科院分区：
文献类型：
--
作者：
David Evangelista;D. Gomes
平均场博弈（Mean-field games，MFG）是一种由大量理性主体组成的模型，这些理性主体试图优化一个目标函数，该目标函数考虑了它们的位置和剩余主体的分布。在这里，我们考虑平稳的MFG与拥塞，并证明了稳定的解决方案的存在性。由于在拥挤的地区移动是困难的，代理更喜欢在非拥挤的地区移动。结果，模型在零密度附近变得奇异。由于一个非常特殊的身份，稳定的解决方案的存在性先前获得的MFG与二次哈密顿。在这里，我们开发强大的估计，给出了一般次二次哈密顿的解决方案的存在。
Mean-field games (MFGs) are models of large populations of rational agents who seek to optimize an objective function that takes into account their location and the distribution of the remaining agents. Here, we consider stationary MFGs with congestion and prove the existence of stationary solutions. Because moving in congested areas is difficult, agents prefer to move in non-congested areas. As a consequence, the model becomes singular near the zero density. The existence of stationary solutions was previously obtained for MFGs with quadratic Hamiltonians thanks to a very particular identity. Here, we develop robust estimates that give the existence of a solution for general subquadratic Hamiltonians.