Bundle Pricing with Comparable Items

We consider a revenue maximization problem where we are selling a set of comparable items, each available in a certain quantity (possibly unlimited) to a set of bidders. Each bidder places several bids, where each bid is on one subset, or bundle of items, and she has a valuation for each of these bundles. The bidder would like to get one or more of her requested bundles. The problem is well studied whenever bundle prices are determined by the sum of single item prices, and was recently shown to be inapproximable to within a semi-logarithmic factor. We consider two scenarios for determining bundle prices that allow to break this semi-logarithmic inapproximability barrier. Both scenarios are tailored for the case of comparable items. First, we consider classical single item prices with an additional monotonicity constraint, enforcing that larger bundles are at least as expensive as smaller ones. We show that the problem remains strongly NP-hard, and we derive a PTAS. Second, motivated by...

• Type: Conference
• Year: 2007
• Where: ESA
• Authors: Alexander Grigoriev, Joyce van Loon, Maxim Sviridenko, Marc Uetz, Tjark Vredeveld
• Keywords: Bundle Prices, Comparable Items, ESA 2007, Single Item Prices