The Balloon Popping Problem Revisited: Lower and Upper Bounds
We consider the balloon popping problem introduced by Immorlica et al. (Proceedings of FOCS'07, pp. 104-112, 2007). This problem is directly related to the problem of profit maximization in online auctions, where an auctioneer is selling a collection of identical items to anonymous unit-demand bidders. The auctioneer has the full knowledge of bidders' private valuations for the items and tries to maximize his profit. Compared with the profit of fixed price schemes, the competitive ratio of Immorlica et al.'s algorithm was in the range [1.64,4.33]. In this paper, we narrow the gap to [1.6595,2].
upper bound auction lower bound ballot theorem