On the Impossibility of Black-Box Transformations in Mechanism Design

TL;DR

This paper proves fundamental limitations on black-box reductions in mechanism design, showing that such reductions cannot always produce truthful mechanisms with preserved approximation guarantees for various objectives.

Contribution

It establishes impossibility results for black-box transformations in mechanism design, highlighting fundamental barriers in converting algorithms into truthful mechanisms without explicit problem knowledge.

Findings

Black-box reduction for social welfare with worst-case guarantees is impossible.

No black-box reduction exists for makespan objective with Bayesian truthfulness and average-case guarantees.

Fundamental limitations are shown for transforming algorithms into truthful mechanisms without explicit constraints.

Abstract

We consider the problem of converting an arbitrary approximation algorithm for a single-parameter optimization problem into a computationally efficient truthful mechanism. We ask for reductions that are black-box, meaning that they require only oracle access to the given algorithm and in particular do not require explicit knowledge of the problem constraints. Such a reduction is known to be possible, for example, for the social welfare objective when the goal is to achieve Bayesian truthfulness and preserve social welfare in expectation. We show that a black-box reduction for the social welfare objective is not possible if the resulting mechanism is required to be truthful in expectation and to preserve the worst-case approximation ratio of the algorithm to within a subpolynomial factor. Further, we prove that for other objectives such as makespan, no black-box reduction is possible even if we only require Bayesian truthfulness and an average-case performance guarantee.