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A lower bound on seller revenue in single buyer monopoly auctions. Arxiv preprint arXiv:1204.5551 (2012)

by O Tamuz
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Lower Bounds on Revenue of Approximately Optimal Auctions

by Balasubramanian Sivan, Vasilis Syrgkanis, Omer Tamuz
"... Abstract. We obtain revenue guarantees for the simple pricing mechanism of a single posted price, in terms of a natural parameter of the distribution of buyers ’ valuations. Our revenue guarantee applies to the single item n buyers setting, with values drawn from an arbitrary joint distribution. Spe ..."
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Abstract. We obtain revenue guarantees for the simple pricing mechanism of a single posted price, in terms of a natural parameter of the distribution of buyers ’ valuations. Our revenue guarantee applies to the single item n buyers setting, with values drawn from an arbitrary joint distribution. Specifically, we show that a single price drawn from the distribution of the maximum valuation Vmax = max{V1, V2,..., Vn} achieves a revenue of at least a 1 e fraction of the geometric expecation of Vmax. This generic bound is a measure of how revenue improves/degrades as a function of the concentration/spread of Vmax. We further show that in absence of buyers ’ valuation distributions, recruiting an additional set of identical bidders will yield a similar guarantee on revenue. Finally, our bound also gives a measure of the extent to which one can simultaneously approximate welfare and revenue in terms of the concentration/spread of Vmax.
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... of Vmax. However we show that a random price drawn from the distribution of Vmax also achieves a 1 e fraction of geometric expectation of Vmax. Related Work. For the special single buyer case, Tamuz =-=[6]-=- showed that the monopoly price obtains a constant fraction of the geometric expectation of the buyer’s value. We primarily extend this result by showing that for the n buyer setting, apart from the m...

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