Bicriteria Multidimensional Mechanism Design with Side Information

We develop a versatile methodology for multidimensional mechanism design that incorporates side information about agents to generate high welfare and high revenue simultaneously. Side information sources include advice from domain experts, predictions from machine learning models, and even the mechanism designer’s gut instinct. We design a tunable mechanism that integrates side information with an improved Vickrey–Clarke–Groves–like mechanism based on weakest types, which are agent types that generate the least welfare. We show that our mechanism, when its side information is of high quality, generates welfare and revenue competitive with the prior-free total social surplus, and its performance decays gracefully as the side information quality decreases. We consider a number of side information formats including distribution-free predictions, predictions that express uncertainty, agent types constrained to low-dimensional subspaces of the ambient type space, and the traditional setting with known priors over agent types. In each setting, we design mechanisms based on weakest types and prove performance guarantees. History: This paper has been accepted for the Mathematics of Operations Research Special Issue on Market Design. Funding: This work was supported by Office of Naval Research and the Vannevar Bush Faculty Fellowship [Grant ONR N00014-23-1-2876], the Army Research Office [Award W911NF2210266], the Simons Foundation [Award MPS-SICS-00826333], the National Science Foundation [Grants CCF-1733556, CCF-1910321, IIS-1901403, RI-1901403, RI-2312342, and SES-1919453], the National Institutes of Health [Grant A240108S001], and the Defense Advanced Research Projects Agency [Grant HR00112020003].