Truthfulness via smoothed complexity

Abstract

Recently, Dobzinski and Dughmi (FOCS '09) defined a class of truthful-in-expectation VCG-based mechanisms they termed maximal-in-distributional-range (MIDR). Using MIDR mechanisms, they derived the first truthful-in-expectation FPTAS for multi-unit auctions, and showed the first separation between the power of truthful-in-expectation and truthful mechanisms. Since then, there has been much speculation on whether exploiting randomization allows general positive results that have eluded deterministic mechanism design. We answer this question in the affirmative for the class of essentially all packing problems that admit an FPTAS. Using techniques from smoothed algorithm analysis, we show a black box reduction that converts an FPTAS for such a problem to a truthful-in-expectation FPTAS of the MIDR variety. Our techniques and results may hold promise for unlocking the powers of truthful-in-expectation algorithms for strongly NP-hard problems.