Simultaneous Auctions are (almost) Efficient

TL;DR

This paper analyzes the efficiency of simultaneous first- and second-price auctions with subadditive bidders, showing they achieve at least 50% and 25% of optimal social welfare respectively, improving previous bounds.

Contribution

It provides improved bounds on the social welfare efficiency of Bayesian Nash equilibria in simultaneous auctions with subadditive valuations, surpassing prior logarithmic bounds.

Findings

First-price auctions achieve at least 50% of optimal welfare in equilibrium.

Second-price auctions achieve at least 25% of optimal welfare in equilibrium.

Results improve upon previous logarithmic bounds for auction efficiency.

Abstract

Simultaneous item auctions are simple procedures for allocating items to bidders with potentially complex preferences over different item sets. In a simultaneous auction, every bidder submits bids on all items simultaneously. The allocation and prices are then resolved for each item separately, based solely on the bids submitted on that item. Such procedures occur in practice (e.g. eBay) but are not truthful. We study the efficiency of Bayesian Nash equilibrium (BNE) outcomes of simultaneous first- and second-price auctions when bidders have complement-free (a.k.a. subadditive) valuations. We show that the expected social welfare of any BNE is at least 1/2 of the optimal social welfare in the case of first-price auctions, and at least 1/4 in the case of second-price auctions. These results improve upon the previously-known logarithmic bounds, which were established by [Hassidim, Kaplan, Mansour and Nisan '11] for first-price auctions and by [Bhawalkar and Roughgarden '11] for second-price auctions.