  The zero forcing number was introduced as a combinatorial bound on the
maximum nullity taken over the set of real symmetric matrices that respect the
pattern of an underlying graph. The $Z_q$-forcing game is an analog to the
standard zero forcing game which incorporates inertia restrictions on the set
of matrices associated with a graph. This work proves an upper bound on the
$Z_q$-forcing number for trees. Furthermore, we consider the $Z_q$-forcing
number for caterpillar cycles on $n$ vertices. We focus on developing game
theoretic proofs of upper and lower bounds.
