论文标题
与时间相关的平均野外游戏的存在和不存在
Existence and non-existence for time-dependent mean field games with strong aggregation
论文作者
论文摘要
我们研究了具有本地局部且强烈降低$-σm^α$，$α\ ge 2/n $的二阶二次平均含量游戏系统的经典解决方案的存在，其中$ m $是人口密度，$ n $是州空间的维度。在假设$σ$足够小的假设下，我们证明了解决方案的存在。对于大$σ$，我们表明，每当Time Horizon $ t $大的情况下，存在可能会失败。
We investigate the existence of classical solutions to second-order quadratic Mean-Field Games systems with local and strongly decreasing couplings of the form $-σm^α$, $α\ge 2/N$, where $m$ is the population density and $N$ is the dimension of the state space. We prove the existence of solutions under the assumption that $σ$ is small enough. For large $σ$, we show that existence may fail whenever the time horizon $T$ is large.
