Learning Valuation Distributions from Partial Observation

TL;DR

This paper investigates how to learn bidders' valuation distributions in repeated sealed-bid auctions using only winner information and self-participation, extending to scenarios with shared values and varying participant sets.

Contribution

It introduces methods to recover valuation distributions from minimal observations, addressing a gap in auction theory where distribution data is weak or incomplete.

Findings

Effective algorithms for distribution recovery from winner-only data

Extensions to common-value and variable-participant settings

Insights into the limits of distribution learning with partial information

Abstract

Auction theory traditionally assumes that bidders' valuation distributions are known to the auctioneer, such as in the celebrated, revenue-optimal Myerson auction. 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.