Connections between coupling and Ishii-Lions methods for tug-of-war with noise stochastic games

We present a streamlined account of two different regularity methods as well as their connections. We consider the coupling method in the context of tug-of-war with noise stochastic games, and consider viscosity solutions of the $p$-Laplace equation in the context of the Ishii-Lions method.
Comment: 28 pages, comments are welcome