On the Inefficiency of Standard Multi-Unit Auctions

TL;DR

This paper analyzes the inefficiency of standard multi-unit auctions, providing bounds on their Price of Anarchy for various bidder valuation models, including subadditive functions, and demonstrates their near efficiency in practice.

Contribution

It offers improved bounds on auction inefficiency for multiple valuation types, including the first analysis for subadditive bidders, enhancing understanding of auction performance.

Findings

Auctions are nearly efficient under various valuation models.

New bounds significantly improve previous inefficiency estimates.

First analysis of bidders with subadditive valuations in these auction formats.

Abstract

We study two standard multi-unit auction formats for allocating multiple units of a single good to multi-demand bidders. The first one is the Discriminatory Auction, which charges every winner his winning bids. The second is the Uniform Price Auction, which determines a uniform price to be paid per unit. Variants of both formats find applications ranging from the allocation of state bonds to investors, to online sales over the internet, facilitated by popular online brokers. For these formats, we consider two bidding interfaces: (i) standard bidding, which is most prevalent in the scientific literature, and (ii) uniform bidding, which is more popular in practice. In this work, we evaluate the economic inefficiency of both multi-unit auction formats for both bidding interfaces, by means of upper and lower bounds on the Price of Anarchy for pure Nash equilibria and mixed Bayes-Nash equilibria. Our developments improve significantly upon bounds that have been obtained recently in [Markakis, Telelis, ToCS 2014] and [Syrgkanis, Tardos, STOC 2013] for submodular valuation functions. Moreover, we consider for the first time bidders with subadditive valuation functions for these auction formats. Our results signify that these auctions are nearly efficient, which provides further justification for their use in practice.