The best-performing and most popular algorithms are often the least explainable. In parallel,
there is growing concern and evidence that sophisticated algorithms may engage, autonomously,
in prot-maximizing but welfare-damaging strategies. Drawing on the literature
on self-regulation and following recent regulatory proposals, we model a regulator who seeks to
encourage algorithmic compliance through the threat of (costly and imperfect) audits. Firms
may invest in \explainability" to better understand their own algorithms and reduce their cost of
compliance. We nd that, when audit ecacy is not aected by explainability, audit regulation
always induces investment in explainability. Mandatory disclosure of the explainability level
makes regulation even more eective, because it allows rms to signal compliance. If, instead,
explainability facilitates regulatory audits a rm may attempt to hide a potential misconduct behind
algorithmic opacity. Because of regulatory opportunism, mandatory disclosure may further
deter investment in explainability. In these cases, regulatory audits may be counterproductive
and laissez-faire or minimum explainability standards should be envisaged.