Spatial Matching under Resource Competition

Motivated by ride-hailing marketplaces, we present a model of two-sided matching platforms that participate in a duopoly market with spatial frictions. Both platforms face disjoint streams of service requests, but they share the same resources on the supply side, i.e., suppliers multi-home. Due to spatial frictions, supply efficiency requires an admission control to maintain a buffer of available suppliers to balance matching distances with other supply costs. We consider two types of platform admissions controls, protection and distance thresholds, under a large-market stochastic model. For both controls, we find that a duopoly equilibrium entails at least one platform undercutting, by accepting all requests, to gain market share. When both platforms undercut, the supply buffer is not maintained and inefficiencies ensue. In contrast, when just one platform undercuts, then the duopoly is asymptotically as efficient as a monopolist. For the protection thresholds, we provide a classifier of market characteristics that delineates the two regimes and allows us to characterize the prices of anarchy and stability in these settings