Automated Mechanism Design for Classification with Partial Verification
This work addresses strategic classification and mechanism design challenges for applications where verification is partial, offering algorithmic solutions but is incremental in extending classical additive cost results to submodular cases.
The paper tackles the problem of automated mechanism design with partial verification, where agents can only misreport restricted types due to limited verification, and presents hardness results for general cases but efficient algorithms for truthful mechanisms when types share preferences, including extensions to submodular cost functions.
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.