A Dynamic Axiomatic Approach to First-Price Auctions

TL;DR

This paper introduces a dynamic, axiomatic approach to understanding first-price auctions, demonstrating how simple behavioral assumptions can yield robust revenue guarantees in complex, repeated auction settings.

Contribution

It develops a dynamic framework for analyzing first-price auctions, introduces the utility-target auction, and shows how behavioral axioms lead to strong performance guarantees.

Findings

A loser raising her bid quickly ensures revenue at least as high as second-price auctions.

The utility-target auction performs well in complex environments.

Pure-strategy equilibrium exists in the utility-target auction.

Abstract

The first-price auction is popular in practice for its simplicity and transparency. Moreover, its potential virtues grow in complex settings where incentive compatible auctions may generate little or no revenue. Unfortunately, the first-price auction is poorly understood in theory because equilibrium is not {\em a priori} a credible predictor of bidder behavior. We take a dynamic approach to studying first-price auctions: rather than basing performance guarantees solely on static equilibria, we study the repeated setting and show that robust performance guarantees may be derived from simple axioms of bidder behavior. For example, as long as a loser raises her bid quickly, a standard first-price auction will generate at least as much revenue as a second-price auction. We generalize this dynamic technique to complex pay-your-bid auction settings and show that progressively stronger assumptions about bidder behavior imply progressively stronger guarantees about the auction's performance. Along the way, we find that the auctioneer's choice of bidding language is critical when generalizing beyond the single-item setting, and we propose a specific construction called the {\em utility-target auction} that performs well. The utility-target auction includes a bidder's final utility as an additional parameter, identifying the single dimension along which she wishes to compete. This auction is closely related to profit-target bidding in first-price and ascending proxy package auctions and gives strong revenue guarantees for a variety of complex auction environments. Of particular interest, the guaranteed existence of a pure-strategy equilibrium in the utility-target auction shows how Overture might have eliminated the cyclic behavior in their generalized first-price sponsored search auction if bidders could have placed more sophisticated bids.