A Model of Search Intermediaries and Paid Referrals

Abstract

In this paper we pursue three main objectives: (1) to develop a model of an intermediated search market in which matching between consumers and firms takes place primarily via paid referrals; (2) to address the important managerial question (for a search intermediary) of finding a suitable mechanism for selling referrals to firms; and (3) to characterize and analyze the firms' resulting equilibrium bidding strategies given consumers' equilibrium search behavior. To achieve these objectives we develop a two-stage model of search intermediaries in a vertically differentiated product market. In the first stage an intermediary chooses a search engine design that specifies to which extent a firm's search rank is determined by its bid and to which extent it is determined by the product offering's overall performance. In the second stage, based on the search engine design, competing firms place their open bids to be paid for each referral by the search engine. We find that the revenue-maximizing search engine design bases rankings on a weighted average of relative product performance and bid amount. The firms' bid amounts are generally nonmonotonic in product performance and a nonzero pure-strategy equilibrium of the underlying discontinuous bidding game does not exist. We derive the unique mixed-strategy Nash equilibrium and show that firms of low product performance tend to fully dissipate their rents. These rents are fully appropriated by the search intermediary and the better firm, and are therefore not socially wasteful. However, the intermediary's design choice, by attributing a positive weight to the firms' bids, generally obfuscates search results and reduces overall consumer surplus compared to the socially optimal design of providing fully transparent results ranked purely on product performance.

Keywords: All-Pay Auction, Intermediaries, Rent Dissipation, Search

JEL Classification: C72, D43, D49, D83, M21