On the Power of Randomization in Algorithmic Mechanism Design

TL;DR

This paper demonstrates that randomization can significantly enhance the power of truthful mechanisms in algorithmic design, enabling near-optimal solutions where deterministic mechanisms cannot.

Contribution

It introduces an FPTAS for multi-unit auctions that is truthful in expectation, proving that such mechanisms are strictly more powerful than universally truthful ones.

Findings

An FPTAS for multi-unit auctions that is truthful in expectation.

Proof that truthful in expectation mechanisms outperform universally truthful mechanisms in certain settings.

Existence of non-polynomial truthful mechanisms achieving optimal solutions.

Abstract

In many settings the power of truthful mechanisms is severely bounded. In this paper we use randomization to overcome this problem. In particular, we construct an FPTAS for multi-unit auctions that is truthful in expectation, whereas there is evidence that no polynomial-time truthful deterministic mechanism provides an approximation ratio better than 2. We also show for the first time that truthful in expectation polynomial-time mechanisms are \emph{provably} stronger than polynomial-time universally truthful mechanisms. Specifically, we show that there is a setting in which: (1) there is a non-polynomial time truthful mechanism that always outputs the optimal solution, and that (2) no universally truthful randomized mechanism can provide an approximation ratio better than 2 in polynomial time, but (3) an FPTAS that is truthful in expectation exists.