A simple and approximately optimal mechanism for an additive Buyer

  • Babaioff M
  • Immorlica N
  • Lucier B
 et al. 
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Abstract

We consider a monopolist seller with $n$ heterogeneous items, facing a single buyer. The buyer has a value for each item drawn independently according to (non-identical) distributions, and his value for a set of items is additive. The seller aims to maximize his revenue. It is known that an optimal mechanism in this setting may be quite complex, requiring randomization [HR12] and menus of infinite size [DDT13]. Hart and Nisan [HN12] have initiated a study of two very simple pricing schemes for this setting: item pricing, in which each item is priced at its monopoly reserve; and bundle pricing, in which the entire set of items is priced and sold as one bundle. Hart and Nisan [HN12] have shown that neither scheme can guarantee more than a vanishingly small fraction of the optimal revenue. In sharp contrast, we show that for any distributions, the better of item and bundle pricing is a constant-factor approximation to the optimal revenue. We further discuss extensions to multiple buyers and to valuations that are correlated across items.

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Authors

  • Seth WeinbergDepartment of Computer Science, Princeton University

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  • Moshe Babaioff

  • Nicole Immorlica

  • Brendan Lucier

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