Balloon Popping With Applications to Ascending Auctions

We study the power of ascending auctions in a scenario in which a seller is selling a collection of identical items to anonymous unit-demand bidders. We show that even with full knowledge of the set of bidders’ private valuations for the items, if the bidders are ex-anteidentical, no ascending auction can extract more than a constant times the revenue of the best fixed price scheme. This problem is equivalent to the problem of coming up with an optimal strategy for blowing up indistinguishable balloons with known capacities in order to maximize the amount of contained air. We show that the algorithm which simply inflates all balloons to a fixed volume is close to optimal in this setting.