Smoothness and Pricing: Near-Optimal Outcomes in Markets Large and Small
summary
Shows that simple posted prices achieve a constant (about 1/2) of optimal expected welfare for Bayes settings with XOS/submodular valuations by reading prices off smoothness proofs (single-item intuition: post vi/2; 2 bidders U[0,1] posting 1/3 gives ~16/27 welfare). Prices are computable by sampling, yield dominant-strategy incentive compatibility given demand queries, and extend to dynamic pricing. In large markets with many copies and noisy arrivals, treating bidders as price takers makes simultaneous uniform-price auctions converge to full efficiency with error shrinking roughly like 1/√n.
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