One-Dimensional Stationary Mean-Field Games with Local Coupling
One-Dimensional Stationary Mean-Field Games with Local Coupling
复制标题
具有局部耦合的一维固定平均场博弈
DOI：
10.1007/s13235-017-0223-9
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发表时间：
2016
影响因子：
1.5
通讯作者：
Mariana Prazeres
中科院分区：
文献类型：
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作者：
D. Gomes;L. Nurbekyan;Mariana Prazeres
在平均场博弈（MFG）理论中的一个标准假设是，哈密顿-雅可比方程和输运方程之间的耦合是单调非递减的人口密度。在许多情况下，这个假设意味着解的存在性和唯一性。在这里，我们放弃了这个假设，并构造了一维MFG的显式解。这些解决方案表现出的现象不存在于单调增加的MFG：低规律性，非唯一性，并形成区域没有代理。
A standard assumption in mean-field game (MFG) theory is that the coupling between the Hamilton–Jacobi equation and the transport equation is monotonically non-decreasing in the density of the population. In many cases, this assumption implies the existence and uniqueness of solutions. Here, we drop that assumption and construct explicit solutions for one-dimensional MFGs. These solutions exhibit phenomena not present in monotonically increasing MFGs: low-regularity, non-uniqueness, and the formation of regions with no agents.