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On Profit-Maximizing Envy-free Pricing
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| Citations: | 122 - 12 self |
BibTeX
@MISC{Guruswami_onprofit-maximizing,
author = {Venkatesan Guruswami and Jason D. Hartline and Anna R. Karlin and David Kempe and et al.},
title = { On Profit-Maximizing Envy-free Pricing},
year = {}
}
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Abstract
We study the problem of pricing items for sale to consumers so as to maximize the seller’s revenue. We assume that for each consumer, we know the maximum amount he would be willing to pay for each bundle of items, and want to find pricings of the items with corresponding allocations that maximize seller profit and at the same time are envy-free, which is a natural fairness criterion requiring that consumers are maximally happy with the outcome they receive given the pricing. We study this problem for two important classes of inputs: unit demand consumers, who want to buy at most one item from among a selection they are interested in, and single-minded consumers, who want to buy one particular subset, but only if they can afford it. We show that computing envy-free prices to maximize the seller’s revenue is APX-hard in both of these cases, and give a logarithmic approximation algorithm for them. For several interesting special cases, we derive polynomial-time algorithms. Furthermore, we investigate some connections with the corresponding mechanism design problem, in which the consumer’s preferences are private values: for this case, we give a log-competitive truthful mechanism.
Keyphrases
profit-maximizing envy-free pricing seller revenue particular subset important class seller profit envy-free price private value consumer preference corresponding mechanism design problem unit demand consumer polynomial-time algorithm natural fairness criterion logarithmic approximation algorithm several interesting special case single-minded consumer maximum amount log-competitive truthful mechanism
