X VCG Auctions with Reserve Prices: Lazy or Eager

VCG auctions with reserve prices are practical simple auctions with provably approximately optimal revenue, and have been crucial in the analysis of other appealing auctions. When different reserve prices are applied to different bidders, the auctioneer may choose to apply the reserves either before (eagerly) or after (lazily) the comparison of bids. Both auction forms have been studied in various settings. We show that, for VCG auctions on matroid settings, eager reserves generate both more social welfare and more revenue than lazy reserves, when monopoly reserve prices are applied. We also identify a connection between lazy reserves VCG auctions and lookahead auctions in general downward closed settings. This connection enables a perspective that yields short and elementary proofs for key steps used in several recent works. Of independent interest is our generalization of lookahead auctions to downward-closed settings. We also show a 2-approximation for its revenue in matroid settings.