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 Lower Bounds on Revenue of Approximately Optimal Auctions


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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 {V 1, V 2,

.,V n} 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.



Autor: Balasubramanian Sivan; Vasilis Syrgkanis; Omer Tamuz

Fuente: https://archive.org/



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