Revenue Comparisons of Auctions with Ambiguity Averse Sellers

TL;DR

This paper compares auction revenues when sellers are ambiguity averse, developing a new methodology based on a weak single-crossing condition, and finds that first-price auctions outperform others under certain beliefs.

Contribution

It introduces a novel revenue comparison methodology for ambiguity-averse sellers using a weak single-crossing condition, challenging the Linkage Principle.

Findings

First-price auction outperforms second-price and all-pay auctions under IID beliefs.

Second-price and all-pay auctions outperform war of attrition.

Methodology applies to ambiguity-averse settings, contrasting traditional results.

Abstract

We study the revenue comparison problem of auctions when the seller has a maxmin expected utility preference. The seller holds a set of priors around some reference belief, interpreted as an approximating model of the true probability law or the focal point distribution. We develop a methodology for comparing the revenue performances of auctions: the seller prefers auction X to auction Y if their transfer functions satisfy a weak form of the single-crossing condition. Intuitively, this condition means that a bidder's payment is more negatively associated with the competitor's type in X than in Y. Applying this methodology, we show that when the reference belief is independent and identically distributed (IID) and the bidders are ambiguity neutral, (i) the first-price auction outperforms the second-price and all-pay auctions, and (ii) the second-price and all-pay auctions outperform the war of attrition. Our methodology yields results opposite to those of the Linkage Principle.