Draft Auctions

We introduce draft auctions, which is a sequential auction f ormat where at each iteration players bid for the right to buy items at a fixed price. We show that draft au ctions offer an exponential improvement in social welfare at equilibrium over sequential item aucti ons where predetermined items are auctioned at each time step. Specifically, we show that for any subaddit ive valuation the social welfare at equilibrium is anO(log(m))-approximation to the optimal social welfare, where m is the number of items. We also provide tighter approximation results for several s ubclasses. Our welfare guarantees hold for Bayes-Nash equilibria and for no-regret learning outcomes , via the smooth-mechanism framework. Of independent interest, our techniques show that in a combina tor al auction setting, efficiency guarantees of a mechanism via smoothness for a very restricted class of cardinalityvaluations, extend with a small degradation, to subadditive valuations, the largest compl e ent-free class of valuations. Variants of draft auctions have been used in practice and have been experiment ally shown to outperform other auctions. Our results provide a theoretical justification. Microsoft Research, nikdev@microsoft.com Carnegie Mellon University, jamiemmt@cs.cmu.edu Cornell University,vasilis@cs.cornell.edu, Supported in part by Simons Graduate Fellowship in Theoret ical Computer Science. Part of work done while an intern at Microsoft Research, New England.