A game theoretical approximation for a parabolic/elliptic system with different operators

In this paper we find viscosity solutions to a coupled system composed by two equations, the first one is parabolic and driven infinity Laplacian while second elliptic involves usual Laplacian. We prove that there two-player zero-sum game played in different boards with rules each board (in play Tug-of-War taking number of plays into consideration move at random) whose value functions converge uniformly solution PDE system.