Optimal bundle pricing with monotonicity constraint

Abstract

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On the complexity of a bundle pricing problem

“…For the fact that the bundle pricing problem is NP-hard even for inhomogeneity arbitrarily close to 1, consider the NP-hardness reduction from Independent Set to the bundle pricing problem presented in Grigoriev et al (2008). In this reduction, all average valuations of the bundles are at least M and at most M + 1, where M is a chosen large number.…”

“…Hartline and Koltun (2005) design near-linear and near-cubic time approximation schemes under the assumption that the number of distinct items m is constant. Under the monotonicity condition that the total price of any bundle does not exceed the total price of any bigger bundle, Grigoriev et al (2008) show that the problem is still NP-hard but admits a polynomial time approximation scheme.…”

Models and algorithms for the product pricing with single-minded customers requesting bundles

“…The SMBPP considered in this work, i.e., pricing individual products with unlimited supply and customers having a budget for a single bundle, has been studied in the literature for its complexitytheoretical aspects. Grigoriev et al 2008 show that the SMBPP is NP-hard, even when bundles have size 2. From their analysis, the authors then devise a PTAS in some special cases.…”

Dynamic pricing problems with elastic demand

“…Pricing problems with posted prices are considered in the literature on Stackelberg games, see e.g. [9,10]. All later papers consider the posted prices statically while this paper deals with pricing over time.…”