  We consider a general class of nonzero-sum $N$-player stochastic games with
impulse controls, where players control the underlying dynamics with discrete
interventions. We adopt a verification approach and provide sufficient
conditions for the Nash equilibria (NEs) of the game. We then consider the
limit situation of $N \to \infty$, that is, a suitable mean-field game (MFG)
with impulse controls. We show that under appropriate technical conditions, the
existence of unique NE solution to the MFG, which is an $\epsilon$-NE
approximation to the $N$-player game, with
$\epsilon=O\left(\frac{1}{\sqrt{N}}\right)$. As an example, we analyze in
details a class of two-player stochastic games which extends the classical cash
management problem to the game setting. In particular, we present numerical
analysis for the cases of the single player, the two-player game, and the MFG,
showing the impact of competition on the player's optimal strategy, with
sensitivity analysis of the model parameters.
