Optimal Allocation Mechanisms When Bidders Ranking for the Objects is Common

Search engines commonly use “sponsored links”, where certain advertisers’ links are promoted to be placed above others in return for monetary payment. It is natural to assume that all providers value a higher ranked placement more than lower ranked ones. Then how should the seller optimally sell these ranked slots is critical for the search engines. In this paper we study the seller’s (search engine) optimal selling mechanism in the following setting: buyers (advertisers), each of whom has unit demand, compete for positions offered by the seller. While each buyer’s valuation for each position is private and independent, the ranking for these positions is common among all the buyers. However the rate at which these valuations change might be different. We begin with 4 simplified scenarios specifying how buyers valuations change for different positions, namely,“parallel”, “convergent”, “divergent”, and “convergent then divergent”. We find that the optimal incentive compatible allocation mechanism is quite different in determining the “pivot” types and the order to fill in the positions. Under some conditions, these mechanisms are even efficient in terms of maximizing the total welfare of the auctioneer and bidders. When the buyers’ valuations for lower positions decrease at different rates, the seller earns more than the case of simple second-price sequential auction. ∗University of Florida, Warrington College of Business. I am grateful to Kalyan Chatterjee for his invaluable guidance and support. I also thank Anthony Kwasnica, Tomas Sjostrom, Hemant Bhargava, David Sappington, Motty Perry, Max Shen and Anand Paul for their insightful comments. All the remaining errors are mine. Optimal Allocation Mechanisms When Bidders Ranking for the Objects is Common