Abstract:

We consider Mean Field Games system posed on the bounded domain $\Omega \subset \mathbb{R}^2$, which arises in Economics and Finance. In the limit as the nonlinearity exponent $p \to \infty$, we construct a multi-spikes solution via using the so-called inner-outer scheme. Notably, the spike location include both in $\Omega$ and on boundary $\partial \Omega$.

Key words: mean fields games, spiky solution, inner-outer gluing