The Value of Knowing Your Enemy

TL;DR

This paper analyzes anonymous auction mechanisms, showing their limitations and potential, especially when bidder identities can be inferred, and introduces simple, near-optimal mechanisms for digital goods and related settings.

Contribution

It characterizes the structure and limitations of anonymous auctions and proposes a simple, asymptotically optimal mechanism that extends to various auction formats.

Findings

No anonymous mechanism can guarantee better than O(n) approximation in worst case.

Posted price mechanisms match the approximation bounds of general anonymous mechanisms.

Inferring bidder identities improves auction performance, achieving an O(k) approximation when confusion is limited.

Abstract

Many auction settings implicitly or explicitly require that bidders are treated equally ex-ante. This may be because discrimination is philosophically or legally impermissible, or because it is practically difficult to implement or impossible to enforce. We study so-called {\em anonymous} auctions to understand the revenue tradeoffs and to develop simple anonymous auctions that are approximately optimal. We consider digital goods settings and show that the optimal anonymous, dominant strategy incentive compatible auction has an intuitive structure --- imagine that bidders are randomly permuted before the auction, then infer a posterior belief about bidder i's valuation from the values of other bidders and set a posted price that maximizes revenue given this posterior. We prove that no anonymous mechanism can guarantee an approximation better than O(n) to the optimal revenue in the worst case (or O(log n) for regular distributions) and that even posted price mechanisms match those guarantees. Understanding that the real power of anonymous mechanisms comes when the auctioneer can infer the bidder identities accurately, we show a tight O(k) approximation guarantee when each bidder can be confused with at most k "higher types". Moreover, we introduce a simple mechanism based on n target prices that is asymptotically optimal and build on this mechanism to extend our results to m-unit auctions and sponsored search.