Inter-Platform Competition in a Regulated Ride-Hail Market With Pooling

Abstract

This paper studies an aggregate ride-hail market in which two platforms competing with each other, as well as with transit, under different supply and regulatory conditions. The duopoly is built on a general market equilibrium model that explicitly characterizes the physical matching process, including pairing two passengers for a pooling ride. To account for the similarities between ride-hail services, a passenger's mode choice is represented using a Nested Logit model. Depending on whether drivers' work affiliation with a platform is exclusive or not, the duopoly is said to have a single- or multi-homing supply mode. We describe the outcome of the duopoly pricing game as a Nash Equilibrium (NE) and solve it by transforming it into a variational inequality problem (VIP). When a regulatory constraint is imposed, the duopoly equilibrium becomes a generalized NE, which corresponds to a quasi VIP. Through numerical experiments constructed using data from Chicago, we find multi-homing may lead to disastrous outcomes in an unregulated duopoly. Specifically, passenger and driver surplus, as well as platform profits, are all significantly lower in a multi-homing duopoly than in a single-homing counterpart. This disaster arises because the multi-homing duopoly is locked in a self-destructive pricing war analogous to the prisoner's dilemma. We show that the negative consequences of such a dilemma can be mitigated by (i) discouraging multi-homing behavior; (ii) imposing a minimum wage on both platforms; and (iii) encouraging the platforms to specialize in different services. The results also show the efficiency in matching passengers and drivers is a more crucial asset for platform competition than that in pairing pooling passengers, more so in a multi-homing duopoly. In general, the platform with a higher matching efficiency ends up making more money and providing a better level of service.