Learning Valuation Distributions from Partial Observation

Auction theory traditionally assumes that bidders’ valuation distributions are known to the auctioneer, such as in the celebrated, revenue-optimal Myerson auction [Myerson, 1981]. However, this theory does not describe how the auctioneer comes to possess this information. Recently, Cole and Roughgarden [2014] showed that an approximation based on a finite sample of independent draws from each bidder’s distribution is sufficient to produce a near-optimal auction. In this work, we consider the problem of learning bidders’ valuation distributions from much weaker forms of observations. Specifically, we consider a setting where there is a repeated, sealed-bid auction with n bidders, but all we observe for each round is who won, but not how much they bid or paid. We can also participate (i.e., submit a bid) ourselves, and observe when we win. From this information, our goal is to (approximately) recover the inherently recoverable part of the underlying bid distributions. We also consider extensions where different subsets of bidders participate in each round, and where bidders’ valuations have a common-value component added to their independent private values. Supported in part by the National Science Foundation under grants CCF-1101215, CCF-1116892, CCF-1331175, and IIS1065251. Email: [email protected] This research was supported in part by The Israeli Centers of Research Excellence (I-CORE) program, (Center No. 4/11), by a grant from the Israel Science Foundation (ISF), by a grant from United States-Israel Binational Science Foundation (BSF), and by a grant from the Israeli Ministry of Science (MoS). Email: [email protected] Supported in part by the National Science Foundation under grants CCF-1116892, CCF-1331175 and IIS-1065251 and by a Simons Award for Graduate Students in Theoretical Computer Science. Email: [email protected]