Collusive Bidding for Keyword Bundles With a Dual-Roled Principal

Abstract

Motivated by the trend of platforms participating directly in their markets, we examine the dualroled platform's “unethical” behaviors in algorithmic keyword auctions. We propose an algorithmic mechanism, the Optimal Resource Allocation under Second-Price Auction, comprising a first-stage second-price auction and a second-stage market game. In the first stage, we analyze the distribution of surplus in the auction of an indivisible keyword bundle when collusive behaviors are permitted. A “nested knockout algorithm” is proposed at this stage, achieving the Shapley value. In the second stage, we analyze the reallocation of keyword traffic among participants through a market game and characterize the core of the resulting two-stage mechanism. Our findings indicate that the online platform may engage in untruthful bidding to inflate the market price and decrease the aggregate utility, leading to potential systemic market inefficiencies due to its dual role as both principal and agent, and “inside job”. Numerical examples from Google's keyword click auction validate our model and theoretical predictions in real-world scenarios. Beyond the keyword traffic auction context, our results caution against “unethical” behaviors in algorithmic market design and provide policy guidelines for platform governance in general.