Bicriteria Multidimensional Mechanism Design with Side Information

TL;DR

This work addresses designing mechanisms that simultaneously maximize welfare and revenue in a prior-free setting when side information about agents is available. It introduces a tunable mechanism that augments the weakest-type VCG with randomized, parameterized adjustments to leverage predictive information, and proves welfare and revenue guarantees that degrade gracefully as prediction quality worsens. The framework accommodates various side-information formats, including uncertainty-encoded predictions, low-dimensional subspace structures, and known priors, and extends to affine-maximizer mechanisms. Practically, the approach offers robust, data-informed mechanism design that outperforms naive trust-or-discard strategies and provides controllable trade-offs between efficiency and revenue across prediction regimes.

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 carefully tuned, 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.

Figures (3)

• Figure 1: Two different predictions (the ellipse and polygon displayed with dashed boundaries) that are equivalent in the sense that their weakest types create the same amount of welfare $w(\widetilde{\theta}_i,\boldsymbol{\theta}_{-i}) = w(\theta_i,\boldsymbol{\theta}_{-i}) - \Delta_i$ for the system and thus generate the same weakest-type payments for agent $i$, despite the fact that one prediction (the polygon) contains the true type and the other (the ellipse) completely misses the true type. Welfare level sets are depicted by the solid black lines.
• Figure 2: An agent's expected value (as a fraction of $\theta_i[\alpha^*]$) as a function of $\zeta_i$ for problem parameters $\Delta_i^{\texttt{VCG}} = 10$, $\Delta_i^{\texttt{err}} = 2$ (conservative prediction), varying $\lambda_i\in\{2^{-100}, 2^{-10}, 2^{-1}\}$.
• Figure 3: Left: Payment as a function of $\zeta_i$ for problem parameters $\theta_i[\alpha^*] = 15$, $\Delta_i^{\texttt{VCG}} = 10$, $\Delta_i^{\texttt{err}} = 2$ (conservative prediction), varying $\lambda_i\in\{2^{-100}, 2^{-10}, 2^{-1}\}$. Right: Payment as a function of $\Delta_i^{\texttt{err}}$ for problem parameters $\theta_i[\alpha^*] = 15$, $\Delta_i^{\texttt{VCG}} = 10$ and mechanism parameter $\zeta_i = 2$, varying $\lambda_i\in\{2^{-100}, 2^{-10}, 2^{-1}\}$.

Theorems & Definitions (26)

• Theorem 2.1
• proof
• Theorem 3.1
• Proposition 3.2
• proof
• Proposition 3.3
• Example 3.4
• Theorem 3.5
• proof
• Theorem 3.6