Strategic Pricing and Ranking in Recommendation Systems with Seller Competition

We study recommendation systems where sellers compete for visibility by o?ering commissions to a platform that curates a personalized ranked menu and sets item prices. Customers interact with the menu under a cascade click model (e.g., as in [1, 3]), scanning the items sequentially from top to bottom. The seller–platform interaction is formulated as a Stackelberg game with sellers as leaders and the platform as a follower. We consider two variants: in the Order and Pricing (OP) game, the platform chooses both ranking and prices, while in the Order at Set-Prices (OS) game, sellers pre-fix prices and the platform decides only the ranking.