  In this paper we find viscosity solutions to the two membranes problem (that
is a system with two obstacle-type equations) with two different $p-$Laplacian
operators taking limits of value functions of a sequence of games. We analyze
two-player zero-sum games that are played in two boards with different rules in
each board. At each turn both players (one inside each board) have the choice
of playing without changing board or to change to the other board (and then
play one round of the other game). We show that the value functions
corresponding to this kind of games converge uniformly to a viscosity solution
of the two membranes problem. If in addition the possibility of having the
choice to change boards depends on a coin toss we show that we also have
convergence of the value functions to the two membranes problem that is
supplemented with an extra condition inside the coincidence set.
