We provide a Polynomial Time Approximation Scheme (PTAS) for the Bayesian optimal multiitem multi-bidder auction problem under two conditions. First, bidders are independent, have additive valuations and are from the same population. Second, every bidder's value distributions of items are independent but not necessarily identical monotone hazard rate (MHR) distributions. For non-i.i.d. bidders, we also provide a PTAS when the number of bidders is small. Prior to our work, even for a single bidder, only constant factor approximations are known. Another appealing feature of our mechanism is the simple allocation rule. Indeed, the mechanism we use is either the second-price auction with reserve price on every item individually, or VCG allocation with a few outlying items that requires additional treatments. It is surprising that such simple allocation rules suffice to obtain nearly optimal revenue.
For a constant number (or many i.i.d.) additive buyers with monotone hazard rate (MHR) valuation distributions, Cai and Huang REF give a PTAS to the optimal mechanism.
Simple and Nearly Optimal Multi-Item Auctions
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Mathematics Computer Science