On the Power of Randomization in Algorithmic Mechanism Design

Abstract

In many settings the power of truthful mechanisms is severely bounded. In this paper we use randomization to overcome this problem in the multi-unit auction setting. In particular, we construct a fully polynomial-time approximation scheme (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 leverage the FPTAS to show for the first time that truthful in expectation polynomial-time mechanisms are provably stronger than polynomial-time universally truthful mechanisms. Specifically, we show that there is a setting, related to multi-unit auctions, in which (1) there is a nonpolynomial 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.