Game of Platforms: Strategic Expansion in Two-Sided Markets

Online platforms, such as Google, Facebook, or Amazon, are constantly expanding their activities, while increasing the overlap in their service offering. In this paper, we study the scope and overlap of online platforms' activities, when they are endogenously determined. We model an expansion game between two online platforms offering two different services to users for free, while selling user clicks to advertisers. At the outset, each platform offers one service, and users may subscribe to one platform or both (multihoming). In the second stage, each platform decides whether to expand by adding the service already offered by its rival. Platforms' expansion decisions affect users' mobility, and thus the partition of users in the market, which, in turn, affects platform prices and profits. We analyze the equilibrium of the expansion game, demonstrating that, in equilibrium, platforms may decide not to expand, even though expansion is costless. Such strategic "no expansion" decisions are due to quantity and price effects of changes in user mobility, brought on by expansion. Both symmetric expansion and symmetric no-expansion equilibria may arise, as well as asymmetric expansion equilibria, even for initially symmetric platforms.