Economies and Diseconomies of Scale in Segmented Mobility Sharing Markets

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.