Extreme value theorems for optimal multidimensional pricing

Our algorithm for bounded distributions applies probabilistic techniques to understand the statistical properties of revenue distributions, obtaining a reduction in the algorithm's search space via dynamic programming. Adapting this approach to MHR and regular distributions requires the proof of novel extreme-value theorems for such distributions. As a byproduct, we show that, for all n, a constant or a polylogarithmic (in n) number of distinct prices suffice for near-optimal revenue for MHR and regular distributions, respectively.