In this paper we find viscosity solutions to a system with two parabolic obstacle-type equations that involve two normalized \(p-\)Laplacian operators. We analyze a two-player zero-sum game played on two boards (with different rules in each board), in which at each board one of the two players has the choice of playing in that board or switching to the other board and then play. We prove that the game has a value and show that these value functions converge uniformly (when a parameter that controls the size of the steps made in the game goes to zero) to a viscosity solution of a system in which one component acts as an obstacle for the other component and vice versa. In this way, we find solutions to the parabolic two-membranes problem.
