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Optimal Bundle Pricing with Monotonicity Constraint A. Grigoriev a

Summary: Optimal Bundle Pricing with Monotonicity Constraint
A. Grigoriev a
, J. van Loon a
, M. Sviridenko b
, M. Uetz c,, T. Vredeveld a
aMaastricht University, Quantitative Economics,
P.O.Box 616, 6200 MD Maastricht, The Netherlands
bIBM T.J. Watson Research Center,
P.O. Box 218, Yorktown Heigths, NY 10598, USA
cUniversity of Twente, Applied Mathematics,
P.O. Box 217, 7500 AE Enschede, The Netherlands
We consider the problem to price (digital) items in order to maximize the revenue obtainable from a set of bidders.
We suggest a natural monotonicity constraint on bundle prices, show that the problem remains NP-hard, and we
derive a PTAS. We also discuss a special case, the highway pricing problem.
Key words: bundle pricing, revenue optimization, monotonicity, computational complexity, approximation algorithm
1. Introduction
We consider the situation where we want to sell a set of (digital) items to a set of bidders. Every bidder
places bids on subsets, or bundles of items, and each bidder would like to receive one or more of these
bundles (OR-bids). Bidders have valuations for each of the bundles they bid on. The valuation is the


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering