Core-competitive Auctions

Abstract

One of the major drawbacks of the celebrated VCG auction is its low (or zero) revenue even when the agents have high value for the goods and a competitive outcome would have generated a significant revenue. A competitive outcome is one for which it is impossible for the seller and a subset of buyers to 'block' the auction by defecting and negotiating an outcome with higher payoffs for themselves. This corresponds to the well-known concept of core in cooperative game theory. In particular, VCG revenue is known to be not competitive when the goods being sold have complementarities. Complementary goods are present in many application domains including spectrum, procurement, and ad auctions. The absence of good revenue from VCG auction poses a real hurdle when trying to design auctions for these settings. Given the importance of these application domains, researchers have looked for alternate auction designs. One important research direction that has come from this line of thinking is that of the design of core-selecting auctions (See Ausubel and Milgrom, Day and Milgrom, Day and Cramton, Ausubel and Baranov). Core-selecting auctions are combinatorial auctions whose outcome implements competitive prices even when the goods are complements. While these auction designs have been implemented in practice in various scenarios and are known for having good revenue properties, they lack the desired incentive-compatibility property of the VCG auction. A bottleneck here is an impossibility result showing that there is no auction that simultaneously achieves competitive prices (a core outcome) and incentive-compatibility. In this paper we try to overcome the above impossibility result by asking the following natural question: is it possible to design an incentive-compatible auction whose revenue is comparable (even if less) to a competitive outcome? Towards this, we define a notion of core-competitive auctions. We say that an incentive-compatible auction is α-core-competitive if its revenue is at least 1/α fraction of the minimum revenue of a core-outcome. We study one of the most commonly occurring setting in Internet advertisement with complementary goods, namely that of the Text-and-Image setting. In this setting, there is an ad slot which can be filled with either a single image ad or k text ads. We design an O(ln ln k) core-competitive randomized auction and an O(√ln k) competitive deterministic auction for the Text-and-Image setting. We also show that both factors are tight.