The Price of Anarchy of Two-Buyer Sequential Multiunit Auctions

Abstract

We study the efficiency of first-/second-price sequential multiunit auctions with two buyers and complete information. Extending the primal-dual framework for obtaining efficiency bounds to this sequential setting, we obtain tight price of anarchy bounds. For general valuation functions, we show that the price of anarchy is exactly 1/ T for auctions with T items for sale. For concave valuation functions, we show that the price of anarchy is bounded below by 1 − 1/ e ≃ 0.632. This bound is asymptotically tight as the number of items sold tends to infinity.