Multihoming and Oligopolistic Platform Competition

We provide a general framework to analyze competition between any number of two-sided platforms, in which buyers and sellers can multihome, and platforms compete on transaction fees charged on both sides. The framework allows buyers and sellers to have heterogenous benefits from using platforms for transactions, and additionally, buyers to have idiosyncratic preferences over using the different platforms. We highlight that multihoming in participation is not the only thing driving market outcomes; one has to also take into account buyers' preferences over which platform they transact on. We show how key primitives such as the number of platforms, the fraction of buyers that find multihoming costly, the value of transactions for buyers and sellers, and the degree of buyer heterogeneity jointly determine the level and structure of platform fees