Lower Bounds on Revenue of Approximately Optimal Auctions

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 v_(max) =  max{V_1,V_2,…,V_n} achieves a revenue of at least a 1/e fraction of the geometric expectation of v_(max). This generic bound is a measure of how revenue improves/degrades as a function of the concentration/spread of v_(max). 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 v_(max).

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