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, modelling 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 analysed by PDE methods, whereas the second is studied by variational methods in the space of probability measures on trajectories.

对于两类平均场博弈系统，我们研究成本函数中的利率变得非常高，建模代理仅在很短的时间范围内进行关注以及控制成本变得非常便宜时，解决方案的收敛性。在这两种情况下，极限都是用于质量密度演化的单个一阶积分偏微分方程。第一个模型是粘度消失的二阶MFG系统，极限是聚集方程。结果对集体动物行为和人群动态模型进行了解释。第二类问题是一阶MFG加速度，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，