An Online Multi-unit Auction with Improved Competitive Ratio

TL;DR

This paper presents an improved online multi-unit auction algorithm with a competitive ratio approaching 1, applicable to general bidders with decreasing marginal utilities, enhancing revenue maximization in online settings.

Contribution

It introduces a new online auction algorithm with a better competitive ratio and extends reduction techniques to general bidder cases, advancing auction design theory.

Findings

Competitive ratio improved from 1/4 to 1/2.

Algorithm's competitive ratio tends to 1 with smoother bid profiles.

Provides reduction for truthful auction design in general multi-unit settings.

Abstract

We improve the best known competitive ratio (from 1/4 to 1/2), for the online multi-unit allocation problem, where the objective is to maximize the single-price revenue. Moreover, the competitive ratio of our algorithm tends to 1, as the bid-profile tends to ``smoothen''. This algorithm is used as a subroutine in designing truthful auctions for the same setting: the allocation has to be done online, while the payments can be decided at the end of the day. Earlier, a reduction from the auction design problem to the allocation problem was known only for the unit-demand case. We give a reduction for the general case when the bidders have decreasing marginal utilities. The problem is inspired by sponsored search auctions.