  We study the problem of automated mechanism design with partial verification,
where each type can (mis)report only a restricted set of types (rather than any
other type), induced by the principal's limited verification power. We prove
hardness results when the revelation principle does not necessarily hold, as
well as when types have even minimally different preferences. In light of these
hardness results, we focus on truthful mechanisms in the setting where all
types share the same preference over outcomes, which is motivated by
applications in, e.g., strategic classification. We present a number of
algorithmic and structural results, including an efficient algorithm for
finding optimal deterministic truthful mechanisms, which also implies a faster
algorithm for finding optimal randomized truthful mechanisms via a
characterization based on convexity. We then consider a more general setting,
where the principal's cost is a function of the combination of outcomes
assigned to each type. In particular, we focus on the case where the cost
function is submodular, and give generalizations of essentially all our results
in the classical setting where the cost function is additive. Our results
provide a relatively complete picture for automated mechanism design with
partial verification.
