Auction Design in an Auto-bidding Setting: Randomization Improves Efficiency Beyond VCG

TL;DR

This paper introduces a randomized auction that improves efficiency over VCG in auto-bidding settings with two bidders, but establishes fundamental limits on efficiency improvements as the number of bidders grows.

Contribution

It presents a prior-free randomized auction achieving better PoA than VCG for two bidders and proves an asymptotic PoA lower bound of 2 for larger bidder sets.

Findings

Randomized auction achieves PoA of approximately 1.896 for two bidders.

Impossibility result: no anonymous truthful auction can have PoA better than 2 asymptotically.

Improvement over VCG is possible only in small bidder settings without additional value information.

Abstract

Auto-bidding is an area of increasing importance in the domain of online advertising. We study the problem of designing auctions in an auto-bidding setting with the goal of maximizing welfare at system equilibrium. Previous results showed that the price of anarchy (PoA) under VCG is 2 and also that this is tight even with two bidders. This raises an interesting question as to whether VCG yields the best efficiency in this setting, or whether the PoA can be improved upon. We present a prior-free randomized auction in which the PoA is approx. 1.896 for the case of two bidders, proving that one can achieve an efficiency strictly better than that under VCG in this setting. We also provide a stark impossibility result for the problem in general as the number of bidders increases -- we show that no (randomized) anonymous truthful auction can have a PoA strictly better than 2 asymptotically as the number of bidders per query increases. While it was shown in previous work that one can improve on the PoA of 2 if the auction is allowed to use the bidder's values for the queries in addition to the bidder's bids, we note that our randomized auction is prior-free and does not use such additional information; our impossibility result also applies to auctions without additional value information.