[Paper Review] Economies and Diseconomies of Scale in Segmented Mobility Sharing Markets

Hongmou Zhang, Xiaotong Guo+1 more|arXiv (Cornell University)|Apr 5, 2022

Transportation and Mobility Innovations6 citations

TL;DR

This paper develops a closed-form model to quantify efficiency loss in segmented mobility sharing markets due to market fragmentation between competing transportation network companies (TNCs). Using Manhattan taxi data, it models vehicle miles traveled (VMT) under monopoly and duopoly conditions, revealing that inefficiency arises from trip density, detour tolerance, market share imbalance, and spatial segregation—with a non-monotonic relationship between detour limits and VMT that mirrors the Lennard-Jones potential in molecular physics.

ABSTRACT

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.

Motivation & Objective

• To understand the trade-off between economies of scale in centralized mobility sharing and diseconomies from market segmentation due to multiple competing TNCs.
• To quantify the efficiency loss in vehicle miles traveled (VMT) caused by market segmentation in on-demand mobility platforms.
• To identify how four structural factors—trip density, detour tolerance, market share imbalance, and spatial segregation—affect this inefficiency.
• To propose a mechanistic model that explains the competing forces of scale economies and diseconomies in sharing markets using a formal, analytically tractable framework.

Proposed method

• Constructed a complete shareability network from Manhattan taxi data (301,430 trips) using shortest-path distances on a street network with 100m spatial resolution.
• Defined a shareability network with edges between trips if they could be shared within a maximum delay of 10 minutes (Δ = 600 seconds).
• Generated sub-networks by sampling nodes and edges based on trip density (ν), detour tolerance (δ), market share (σ), and spatial dissolvedness (ρ) to simulate monopoly and duopoly market conditions.
• Calculated VMT under monopoly (VMT₁) and duopoly (VMT₂) by subtracting maximum weight matching savings from total trip distance (VMT₀), using a polynomial-time algorithm.
• Used maximum weight matching to compute optimal sharing efficiency, with edge weights representing VMT savings from shared trips.
• Modelled the efficiency loss as ℓ = VMT₂ − VMT₁, and derived its functional dependence on ν, δ, σ, and ρ, revealing a non-monotonic power-law relationship with δ.

Experimental results

Research questions

• RQ1 How does market segmentation between two TNCs affect the efficiency of mobility sharing, measured by vehicle miles traveled (VMT)?
• RQ2 What is the functional relationship between VMT and the key market parameters: trip density (ν), detour tolerance (δ), market share imbalance (σ), and spatial dissolvedness (ρ)?
• RQ3 How do economies of scale and diseconomies of scale interact to shape the overall efficiency of segmented mobility markets?
• RQ4 To what extent does the efficiency loss depend on the balance of market shares and the spatial overlap of TNC service areas?

Key findings

• The relationship between VMT and trip density (ν) follows a power law, with the exponent depending non-monotonically on detour tolerance (δ), indicating that economies and diseconomies of scale coexist and compete in a complex manner.
• The efficiency loss (ℓ = VMT₂ − VMT₁) is minimized when market shares are highly uneven (σ ≈ 0 or 1) and maximized when shares are balanced (σ ≈ 0.5), indicating that 50-50 competition causes the highest inefficiency.
• Spatial dissolvedness (ρ) has a positive, increasing effect on efficiency loss—higher spatial segregation between TNCs leads to greater VMT inefficiency.
• The functional form of VMT as a function of δ exhibits a non-monotonic curve that closely resembles the Lennard-Jones potential in intermolecular forces, suggesting a deep analogy between social and physical systems.
• The model demonstrates that cross-platform coordination—such as a central broker or mutual trip trading—could recover up to 30–40% of the lost efficiency, depending on market structure.
• The model provides a closed-form analytical framework that quantifies the trade-off between network-scale economies and competitive fragmentation, applicable beyond mobility to other sharing markets.