Vickrey Auctions for Irregular Distributions

TL;DR

This paper extends Bulow and Klemperer's classic result to settings with bidders whose values are drawn from non-i.i.d. irregular distributions, showing that recruiting extra bidders from each group and running a Vickrey auction guarantees at least half of the optimal revenue.

Contribution

It models irregular distributions as convex combinations of regular ones and proves a revenue guarantee for Vickrey auctions in this setting.

Findings

Recruitment of one extra bidder per group yields at least half the optimal revenue.

Modeling irregular distributions as convex combinations of regular distributions.

Extension of Bulow and Klemperer's result to non-i.i.d. irregular distributions.

Abstract

The classic result of Bulow and Klemperer \cite{BK96} says that in a single-item auction recruiting one more bidder and running the Vickrey auction achieves a higher revenue than the optimal auction's revenue on the original set of bidders, when values are drawn i.i.d. from a regular distribution. We give a version of Bulow and Klemperer's result in settings where bidders' values are drawn from non-i.i.d. irregular distributions. We do this by modeling irregular distributions as some convex combination of regular distributions. The regular distributions that constitute the irregular distribution correspond to different population groups in the bidder population. Drawing a bidder from this collection of population groups is equivalent to drawing from some convex combination of these regular distributions. We show that recruiting one extra bidder from each underlying population group and running the Vickrey auction gives at least half of the optimal auction's revenue on the original set of bidders.