  We show that all maximal almost disjoint families have pseudocompact Vietoris
hyperspace if and only if $\mathsf{MA}_\mathfrak c (\mathcal
P(\omega)/\mathrm{fin})$ holds. We further study the question whether there is
a maximal almost disjoint family whose hyperspace is pseudocompact and prove
that consistently such families do not exist \emph{genericaly}, by constructing
a consistent example of a maximal almost disjoint family $\mathcal A$ of size
less than $\mathfrak c$ whose hyperspace is not pseudocompact.
