  On-demand mobility sharing, provided by one or several transportation network
companies (TNCs), is realized by real-time optimization algorithms to connect
trips among tens of thousands of drivers and fellow passengers. In a market of
mobility sharing comprised of TNCs, there are two competing principles, the
economies of network scale and the healthy competition between TNCs, which can
lead to "segmentation" of market. To understand the substantiality and
relationship of the two competing principles, we need to answer how much
efficiency loss is generated due to the segmentation of market, and which
factors are related to it. Here we show how four critical factors of market
structure and characteristics of mobility sharing services -- density of trips
(thickness), maximum detour allowed for sharing (tightness), market shares
(unevenness), and spatial segregation of the TNCs (dissolvedness) -- are
associated with the efficiency loss, represented as the difference in vehicle
miles traveled (VMT) under different market structures. We found that 1) while
VMT shows a simple power function with thickness, the corresponding exponent
term can be expressed as a non-monotonic function with tightness -- essentially
showing how economies and diseconomies of scale in this market arise, and
appearing a very similar form to the Lennard--Jones model in inter-molecular
potentials; and 2) the efficiency loss is higher when unevenness is closer to
0.5 (50-50 market share) and dissolvedness is larger. Our results give a
comprehensive analysis of how the inefficiency of market segmentation is
generated, and how potentially it may be avoided through market mechanism
design.
