Fake Sales and Ranking Algorithms in Online Retail Marketplace with Sponsored Advertising

We study the optimal algorithm decisions of a platform on ranking products sold by sellers--who may use fake sales to boost the rankings of their products--and the impact on consumers and sellers. We design a model of an online retail marketplace with competing sellers. The platform decides whether to tolerate fake sales and whether to rank its organic results based on sellers' qualities or popularities. The sellers decide whether to buy fake sales and how much to bid for sponsored advertising on the platform. We show a platform may strategically tolerate or even encourage popularity-boosting fake sales by a seller when the seller's quality level is extreme relative to competitors. With a low-quality seller, allowing fake sales may benefit the platform through reducing differentiation between sellers and intensifying competition for the sponsored ads (i.e., "feeding the puppy dog"). With a high-quality seller, it benefits the platform by increasing differentiation between the two sellers and softening price competition, which improves the platform's commission revenue (i.e., "feeding the fat cat"). Furthermore, fake sales may benefit consumers by increasing price competition and may also benefit competing sellers by reducing the high-quality seller's dominance