# Bicriteria Multidimensional Mechanism Design with Side Information

## TL;DR

This paper introduces a flexible multidimensional mechanism design approach that leverages various forms of side information to optimize welfare and revenue, with performance guarantees that adapt to information quality.

## Contribution

It presents a tunable mechanism integrating side information with an improved VCG-like approach, applicable across multiple information formats, with proven performance guarantees.

## Key findings

- Mechanism performance improves with high-quality side information.
- Performance degrades gracefully as side information quality decreases.
- Applicable to diverse side information formats, including predictions and low-dimensional constraints.

## Abstract

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 VCG-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.