  Stochastic MPECs have found increasing relevance for modeling a broad range
of settings in engineering and statistics. Yet, there seem to be no efficient
first/zeroth-order schemes equipped with non-asymptotic rate guarantees for
resolving even deterministic variants of such problems. We consider MPECs where
the parametrized lower-level equilibrium problem is given by a
deterministic/stochastic VI problem whose mapping is strongly monotone,
uniformly in upper-level decisions. We develop a zeroth-order implicit
algorithmic framework by leveraging a locally randomized spherical smoothing
scheme. We make three sets of contributions: (i) Convex settings. When the
implicit problem is convex and the lower-level decision is obtainable by
inexactly solving a strongly monotone stochastic VI to compute an
$\epsilon$-solution, we derive iteration complexity guarantees of
$\mathcal{O}\left(\tfrac{L_0^2n^2}{\epsilon^2}\right)$ (upper-level) and
$\mathcal{O}\left(\tfrac{L_0^2 n^2}{\epsilon^2} \ln(\tfrac{L_0
n}{\epsilon})\right)$ (lower-level); (ii) Exact oracles and accelerated
schemes. When the lower-level problem can be resolved exactly, employing
accelerated schemes, the complexity improves to
$\mathcal{O}(\tfrac{1}{\epsilon})$ and
$\mathcal{O}(\tfrac{1}{\epsilon^{2+\delta}})$, respectively. Notably, this
guarantee extends to stochastic MPECs with equilibrium constraints imposed in
an almost sure sense; (iii) Nonconvex regimes. When the implicit problem is not
necessarily convex and the lower-level problem can be inexactly resolved via a
stochastic approximation framework, computing an $\epsilon$-stationary point is
equipped with complexity bounds of
$\mathcal{O}\left(\tfrac{L_0^2n^2}{\epsilon}\right)$ (upper-level) and
$\mathcal{O}\left(\tfrac{L_0^6n^6}{\epsilon^3}\right)$ (lower-level). We also
provide numerical results for validating the theoretical findings in this work.
