Finite-Sample Average Bid Auction

TL;DR

This paper introduces a new auction design framework based on statistical samples, focusing on average bid auctions, and demonstrates improved performance in small sample scenarios through an adaptive estimator.

Contribution

It develops a novel framework combining statistical decision theory with mechanism design, introducing the average bid auction and an adaptive estimator with strong asymptotic properties.

Findings

Average bid auction sets reservation prices based on historical samples.

The adaptive estimator outperforms traditional methods in small samples.

Theoretical analysis links the auction to Gamma distribution assumptions.

Abstract

The paper studies the problem of auction design in a setting where the auctioneer accesses the knowledge of the valuation distribution only through statistical samples. A new framework is established that combines the statistical decision theory with mechanism design. Two optimality criteria, maxmin, and equivariance, are studied along with their implications on the form of auctions. The simplest form of the equivariant auction is the average bid auction, which set individual reservation prices proportional to the average of other bids and historical samples. This form of auction can be motivated by the Gamma distribution, and it sheds new light on the estimation of the optimal price, an irregular parameter. Theoretical results show that it is often possible to use the regular parameter population mean to approximate the optimal price. An adaptive average bid estimator is developed under this idea, and it has the same asymptotic properties as the empirical Myerson estimator. The new proposed estimator has a significantly better performance in terms of value at risk and expected shortfall when the sample size is small.