Strong Revenue (Non-)Monotonicity of Single-parameter Auctions

TL;DR

This paper investigates the conditions under which revenue from single-parameter auctions increases with better prior estimates, revealing limitations beyond matroid settings and providing approximate guarantees for broader classes.

Contribution

It demonstrates the failure of strong revenue monotonicity outside matroid settings and establishes that only matroid auctions satisfy it exactly, while providing approximate bounds for all single-parameter auctions.

Findings

Strong revenue monotonicity holds only for matroid auctions.

Matroid auctions are uniquely downward-closed with this property.

Provides improved sample complexity bounds for various auction constraints.

Abstract

Consider Myerson's optimal auction with respect to an inaccurate prior, e.g., estimated from data, which is an underestimation of the true value distribution. Can the auctioneer expect getting at least the optimal revenue w.r.t. the inaccurate prior since the true value distribution is larger? This so-called strong revenue monotonicity is known to be true for single-parameter auctions when the feasible allocations form a matroid. We find that strong revenue monotonicity fails to generalize beyond the matroid setting, and further show that auctions in the matroid setting are the only downward-closed auctions that satisfy strong revenue monotonicity. On the flip side, we recover an approximate version of strong revenue monotonicity that holds for all single-parameter auctions, even without downward-closedness. As applications, we get sample complexity upper bounds for single-parameter auctions under matroid constraints, downward-closed constraints, and general constraints. They improve the state-of-the-art upper bounds and are tight up to logarithmic factors.