Online market platforms play an increasingly powerful role in the economy. An empirical phenomenon is that platforms, such as Amazon, Apple, and DoorDash, also enter their own marketplaces, imitating successful products developed by third-party sellers. We formulate a Stackelberg model, where the platform acts as the leader by committing to an entry policy: when will it enter and compete on a product? We study this model through a theoretical and computational framework. We begin with a single seller, and consider different kinds of policies for entry. We characterize the seller's optimal explore-exploit strategy via a Gittins-index policy, and give an algorithm to compute the platform's optimal entry policy. We then consider multiple sellers, to account for competition and information spillover. Here, the Gittins-index characterization fails, and we employ deep reinforcement learning to examine seller equilibrium behavior. Our findings highlight the incentives that drive platform entry and seller innovation, consistent with empirical evidence from markets such as Amazon and Google Play, with implications for regulatory efforts to preserve innovation and market diversity.

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