This paper studies an aggregate ride-hail market in which two platforms compete 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. 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. We show that multi-homing may lead to disastrous outcomes in an unregulated duopoly and demonstrate it through numerical experiments constructed using data from Chicago. 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 (i) the multi-homing duopoly is locked in a self-destructive pricing war analogous to the tragedy of the commons; and (ii) the competition among passengers limits economy of scale in trip production. We show that the negative consequences of this tragedy 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 crucial asset for a platform’s competitiveness, 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.