Expressiveness and Robustness of First-Price Position Auctions

TL;DR

This paper analyzes the expressiveness and robustness of first-price position auctions, demonstrating that a multi-dimensional bid mechanism uniquely ensures good outcomes across various informational settings and establishing equilibrium existence in complex bid spaces.

Contribution

It identifies a variant of the generalized first-price mechanism as the only standard approach achieving robustness under diverse information conditions, highlighting the importance of expressiveness beyond the type space.

Findings

A specific multi-dimensional bid mechanism guarantees good outcomes in both complete and incomplete information.

Equilibrium existence is established for complex multi-dimensional bid spaces where standard methods fail.

First-price payments can support equilibria in more circumstances than second-price payments.

Abstract

Since economic mechanisms are often applied to very different instances of the same problem, it is desirable to identify mechanisms that work well in a wide range of circumstances. We pursue this goal for a position auction setting and specifically seek mechanisms that guarantee good outcomes under both complete and incomplete information. A variant of the generalized first-price mechanism with multi-dimensional bids turns out to be the only standard mechanism able to achieve this goal, even when types are one-dimensional. The fact that expressiveness beyond the type space is both necessary and sufficient for this kind of robustness provides an interesting counterpoint to previous work on position auctions that has highlighted the benefits of simplicity. From a technical perspective our results are interesting because they establish equilibrium existence for a multi-dimensional bid space, where standard techniques break down. The structure of the equilibrium bids moreover provides an intuitive explanation for why first-price payments may be able to support equilibria in a wider range of circumstances than second-price payments.