Lower Bounds on Revenue of Approximately Optimal Auctions [chapter]

Balasubramanian Sivan, Vasilis Syrgkanis, Omer Tamuz
2012 Lecture Notes in Computer Science  
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
more » ... neric 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.
doi:10.1007/978-3-642-35311-6_42 fatcat:dxwamfg2vbd5xou3slctzc5oxa