Revenue Monotonicity Under Misspecified Bidders

TL;DR

This paper examines how auction revenue guarantees are affected when the auctioneer's knowledge of bidders' distributions is partially incorrect, revealing that the feasibility environment determines whether using all distributions is beneficial.

Contribution

It establishes conditions under which auction revenue is preserved or compromised when bidders' distribution information is misspecified, especially highlighting the role of matroid constraints.

Findings

For matroid environments, using all specified distributions guarantees revenue.

For non-matroid environments, revenue guarantees can fail when distributions are misspecified.

The impact of distribution misspecification depends on the auction's feasibility constraints.

Abstract

We investigate revenue guarantees for auction mechanisms in a model where a distribution is specified for each bidder, but only some of the distributions are correct. The subset of bidders whose distribution is correctly specified (henceforth, the "green bidders") is unknown to the auctioneer. The question we address is whether the auctioneer can run a mechanism that is guaranteed to obtain at least as much revenue, in expectation, as would be obtained by running an optimal mechanism on the green bidders only. For single-parameter feasibility environments, we find that the answer depends on the feasibility constraint. For matroid environments, running the optimal mechanism using all the specified distributions (including the incorrect ones) guarantees at least as much revenue in expectation as running the optimal mechanism on the green bidders. For any feasibility constraint that is not a matroid, there exists a way of setting the specified distributions and the true distributions such that the opposite conclusion holds.