Branded Websites and Marketplace Selling: Competing during COVID-19

I consider a market for differentiated products with an online marketplace (the platform) and two types of firms. Marketplace firms sell through the platform. Branded firms sell to consumers directly and, if they choose, through the platform. When a branded firm joins the platform, the firm expands its reach beyond its branded website/physical store(s) to consumers who visit the platform for all their purchases. The drawback is that the firm has to pay a referral fee for all sales on the platform, some of which are from its loyal consumers who would otherwise have purchased from the firm directly. I investigate the role of the firm composition in determining the equilibrium outcome. Interestingly, a higher fraction of branded firms translates into more firms on the platform and intense price competition. In the midst of the COVID-19 pandemic, consumers who used to shop at physical stores turn to the platform. I show that if they do (do not) consider other products, more (fewer) branded firms will join the platform in equilibrium.