  Mobility-on-Demand platforms are a fast growing component of the urban
transit ecosystem. Though a growing literature addresses the question of how to
make individual MoD platforms more efficient, much less is known about the cost
of market fragmentation, i.e., the impact on welfare due to splitting the
demand between multiple independent platforms. Our work aims to quantify how
much platform fragmentation degrades the efficiency of the system. In
particular, we focus on a setting where demand is exogenously split between
multiple platforms, and study the increase in the supply rebalancing cost
incurred by each platform to meet this demand, vis-a-vis the cost incurred by a
centralized platform serving the aggregate demand. We show under a large-market
scaling, this Price-of-Fragmentation undergoes a phase transition, wherein,
depending on the nature of the exogenous demand, the additional cost due to
fragmentation either vanishes or grows unbounded. We provide conditions that
characterize which regime applies to any given system, and discuss implications
of this on how such platforms should be regulated.
