The Brushing Game in Online Marketplaces.

We study a pervasive fraudulent strategy, called "brushing," employed by retailers operating in e-commerce platforms: Retailers place fake orders of their own products to inflate sales and boost the visibility of their store links in search results. Using a duopolistic pricing game with heterogeneous consumer search behavior, we show that the retailer at a more prominent position in product listing enjoys greater profit as well as an advantage in future position allocation if the platform charges a per-sale commission fee and uses a sales-based ranking mechanism to display store-link positions. To fight for better visibility, retailers may employ brushing to boost their sales metrics. We characterize the equilibrium brushing behavior for the position competition game between the retailers. Under a sufficiently high commission rate, the game has a pure-strategy equilibrium and entails no-brushing outcome. Otherwise, retailers fully engage in brushing activity and the brushing equilibrium exists only in mixed strategies. Model extensions incorporating heterogeneities in wholesale cost and product quality show that retailers with cost and quality advantages are able to gain profit improvement at a less prominent position and thereby have less incentive to invest in brushing. Our results provide platform managers and retailers with economic insights to better understand the logic for brushing fraud and strategic decisions in online marketplaces.