论文标题
某些平均现场游戏系统与聚合和羊群模型的收敛
Convergence of some Mean Field Games systems to aggregation and flocking models
论文作者
论文摘要
对于两类的平均现场游戏系统，我们研究解决方案的收敛性，因为成本功能的利率变得非常大，建模代理只关心非常短的时间率，并且控制的成本变得非常便宜。在这两种情况下，极限是质量密度演变的单个一阶整体差分方程。第一个模型是具有消失粘度的第二阶MFG系统，极限是聚合方程。结果对集体动物行为和人群动态的模型有一种解释。第二类问题是加速度的一阶MFG，极限是与Cucker-Smale模型相关的动力学方程。第一个问题是通过PDE方法分析的，而第二个问题是通过轨迹概率度量的变异方法研究的。
For two classes of Mean Field Game systems we study the convergence of solutions as the interest rate in the cost functional becomes very large, modeling agents caring only about a very short time-horizon, and the cost of the control becomes very cheap. The limit in both cases is a single first order integro-partial differential equation for the evolution of the mass density. The first model is a 2nd order MFG system with vanishing viscosity, and the limit is an aggregation equation. The result has an interpretation for models of collective animal behaviour and of crowd dynamics. The second class of problems are 1st order MFGs of acceleration and the limit is the kinetic equation associated to the Cucker-Smale model. The first problem is analyzed by PDE methods, whereas the second is studied by variational methods in the space of probability measures on trajectories.
