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The Competition Complexity of an auction measures how much competition is needed for the revenue of a simple auction to surpass the optimal revenue. A classic result from auction theory by Bulow and Klemperer [11], states that the Competition Complexity of VCG, in the case of n i.i.d. buyers and a single item, is 1. In other words, it is better to invest in recruiting one extra buyer and run a second price auction than to invest in learning exactly the buyers’ underlying distribution and run the revenue-maximizing auction tailored to this distribution.

In this paper we study the Competition Complexity of dynamic auctions. Consider the following problem: a monopolist is auctioning off m items in m consecutive stages to n interested buyers. A buyer realizes her value for item k in the beginning of stage k. How many additional buyers are necessary and sufficient for a second price auction at each stage to extract revenue at …