  We consider two competing platforms operating in a two-sided market and
offering identical services to their customers at potentially different prices.
The objective of each platform is to maximize its throughput or revenue by
suitably pricing its services. We assume that customers have a preference or
loyalty to the platforms while the workers freelance for the two platforms.
Assuming that the resulting interaction between the users is such that their
aggregate utility is maximized, we show that for each value of the loyalty,
there exists a pure strategy Nash equilibrium for both the throughput and
revenue competition game and characterize it.
