Characterizing Optimal Adword Auctions

TL;DR

This paper models and characterizes optimal auction mechanisms for search engine advertising slots, introducing new incentive-compatible mechanisms, analyzing special cases, and proposing a superior rank-based allocation rule with computational efficiency.

Contribution

It provides a comprehensive characterization of incentive-compatible ad auction mechanisms, including new mechanisms beyond affine maximizers, and introduces a novel customized rank-based allocation rule.

Findings

New incentive-compatible mechanisms for multi-dimensional type spaces.

Efficient algorithms for revenue and efficiency maximization in special cases.

Numerical evidence showing the superiority of the customized rank-based allocation.

Abstract

We present a number of models for the adword auctions used for pricing advertising slots on search engines such as Google, Yahoo! etc. We begin with a general problem formulation which allows the privately known valuation per click to be a function of both the identity of the advertiser and the slot. We present a compact characterization of the set of all deterministic incentive compatible direct mechanisms for this model. This new characterization allows us to conclude that there are incentive compatible mechanisms for this auction with a multi-dimensional type-space that are {\em not} affine maximizers. Next, we discuss two interesting special cases: slot independent valuation and slot independent valuation up to a privately known slot and zero thereafter. For both of these special cases, we characterize revenue maximizing and efficiency maximizing mechanisms and show that these mechanisms can be computed with a worst case computational complexity $O(n^2m^2)$ and $O(n^2m^3)$ respectively, where $n$ is number of bidders and $m$ is number of slots. Next, we characterize optimal rank based allocation rules and propose a new mechanism that we call the customized rank based allocation. We report the results of a numerical study that compare the revenue and efficiency of the proposed mechanisms. The numerical results suggest that customized rank-based allocation rule is significantly superior to the rank-based allocation rules.