Asymptotically optimal repeated auctions for sponsored search

• Authors: Nicolas S. Lambert;Yoav Shoham
• Venue: Proceedings of the ninth international conference on Electronic commerce
• Year: 2007

We investigate asymptotically optimal keyword auctions, that is, auctions which maximize revenue as the number of bidders grows. We do so under two alternative behavioral assumptions. The first explicitly models the repeated nature of keyword auctions. It introduces a novel assumption on individual bidding, namely that bidders never overbid their value, and bid their actual value if shut out for long enough. Under these conditions we present a broad class of repeated auctions that are asymptotically optimal among all sequential auctions (a superset of repeated auctions). Those auctions have varying payment schemes but share the ranking method. The Google auction belongs to this class, but not the Yahoo auction, and indeed we show that the latter is not asymptotically optimal. (Nonetheless, with some additional distributional assumptions, the Yahoo auction can be shown to belong to a broad category of auctions that are asymptotically optimal among all auction mechanisms that do not rely on ad relevance.) We then look at the one-shot keyword auction, which can be taken to model repeated auctions in which relatively myopic bidders converge on the equilibrium of the full-information stage game. In this case we show that the Google auction remains asymptotically optimal and the Yahoo auction suboptimal. The distributional assumptions under which our theorems hold are quite general. We do however show that the Google auction is not asymptotically revenue-maximizing for general distributions.