Anomalous supply shortages from dynamic pricing in on-demand mobility

Complex engineered systems can exhibit unintended collective dynamical states that disrupt function. In urban mobility, such phenomena include congestion and cascading failures. As on-demand mobility becomes digitized, providers increasingly rely on dynamic pricing both to reflect base cost changes and to equilibrate supply–demand imbalances by raising prices when demand exceeds supply. Yet reports from ride-hailing suggest dynamic pricing may instead create imbalances. This study asks: (1) What incentives lead drivers to induce anomalous supply shortages under dynamic pricing, and under what conditions do they emerge? (2) Do such non-equilibrium dynamics appear at other locations, and how can they be identified from price data alone?

Prior work documents unintended collective dynamics in complex systems (e.g., congestion, cascading failures) and widespread use of dynamic pricing across industries including e-commerce and mobility. Ride-hailing platforms implement surge pricing to balance supply and demand. Media and empirical reports have alleged driver-induced artificial surge events at Washington Reagan National Airport and other U.S. locations. Theoretical research on surge mechanisms and pricing has explored algorithmic pricing and incentives. Related mobility literature examines ride-sharing efficiency, minimum fleet sizing, and labor flexibility of drivers; broader systems research discusses smart grid pricing and demand-side management, highlighting the potential for inelastic demand components to complicate control.

Data: The authors recorded approximately 28 million Uber price estimates for 137 routes in 59 urban areas across six continents between 2019-05-31 and 2019-06-25. Routes were categorized by origin: 63 airports, 23 convention centers, 12 train stations, and 39 city trips. For each route, total fare estimates were polled every 2–30 seconds via Uber’s price estimate API, capturing lower and upper total fare, estimated distance and duration, and timestamps. Product metadata (booking fee, price per minute/mile, distance unit, minimum fees, currency) was obtained via Uber’s products API. Prices were converted to USD using ECB exchange rates. Analyses used the lower estimate of the local economy product (UberX or UberGO). Base cost extraction: Base cost P_base(t) was computed as p0 + p_t Δt + p_l Δl (pickup fee plus trip fees proportional to duration and distance), with surcharges treated as constant per trip. The surge fee time series was then estimated as total fare minus base cost. Airport demand estimation: For the 63 airport routes, aircraft arrivals (times, call signs, aircraft type) were collected via flightradar24’s open API; seat configurations were obtained from flightera.net. Demand was proxied by the number of arriving seats. Time series were smoothed to 1-minute resolution using a 5-minute moving average for both deplanements and surge fee. Cross-correlation between deplanements and surge fee was computed to assess demand–surge coupling. Timescale separation of price changes: The total fare was normalized by the contemporaneous base cost to form an effective surge factor. Per-minute changes Δp(t) between consecutive time points were computed. The distribution of Δp was modeled as a mixture: a Dirac delta at zero (Δp^2 < 1e-7) plus two zero-mean Gaussian components, representing slow base-cost variations and fast surge-driven changes. A maximum-likelihood Gaussian mixture fit yielded the weight W_surge and standard deviation σ_surge (normalized surge strength) characterizing surge activity per route. Game-theoretic modeling: A minimal two-player static game captured driver incentives. Drivers choose ON/OFF (temporarily switching off the app) against fixed average demand D∈[1,2]. The fare follows a piecewise-linear response with base cost P_base and maximum surge fee P_e. With elastic demand, D'(p') = D(1 − δ (p' − P_base)), elasticity δ ∈ {0, 0.15, 0.30}. Payoff matrices yield Nash equilibria across demand and maximum surge fee, producing a phase diagram with regimes: ON–ON (prisoner’s dilemma), multiple equilibria (stag hunt), OFF–OFF (both induce a shortage), and partial shortages (one offline). Dynamic multiplayer simulation: A continuous-time model with N=160 drivers at a single origin considered stochastic round-trip times (uniform within ±5 min around a base value t_b varying with rush hours). Base cost depends linearly on t_b. Surge pricing depends on the number of online drivers N_online relative to a threshold N_thresh = ⟨t⟩ given Poisson demand at rate λ=2 requests/min. Customers have heterogeneous willingness-to-pay; they wait and retry if price is too high or no drivers are available, leaving after 10 minutes. Drivers follow a mean-field optimal strategy: they switch OFF only if enough peers are willing to induce a surge and price is below the driver-optimal level; OFF durations are capped at 20 minutes to avoid indefinite idleness. The simulation reproduces rush-hour sustained surges due to congestion (without coordinated OFF behavior) and short repeated surges during off-peak hours due to coordinated OFF behavior.

• Empirical evidence of non-equilibrium surge dynamics: At Washington Reagan National Airport (DCA), repeated short evening surge peaks occur while base costs are stable and without correlation to estimated demand from deplanements, consistent with supply-driven anomalies.
• Generic incentive structure: A two-player game reveals regions where drivers benefit from coordinated temporary OFF decisions, leading to artificial supply shortages and surge fees. The phase diagram shows transitions from prisoner’s dilemma to stag hunt to coordinated OFF–OFF equilibria as demand and maximum surge fee increase; with higher demand elasticity, incentives to induce surges shrink and partial shortages may arise.
• Ubiquity across locations: Timescale analysis of price changes for 137 routes in 59 urban areas identifies multiple locations worldwide (e.g., Warsaw, Montreal, Chicago, New York City, Chennai) exhibiting high surge strength (σ_surge) and high surge contribution (W_surge), with surge-fee time series qualitatively similar to DCA (frequent evening surge peaks), suggesting widespread anomalous supply shortages.
• Separation of timescales: Price-change distributions decompose into slow base-cost variations and fast surge-fee jumps, enabling classification using only price time series without direct supply data.
• Policy-relevant insight: Capping the maximum surge fee may not prevent and can even exacerbate incentives for artificial shortages when demand is highly elastic; increasing price elasticity (e.g., via alternative transport options) or effectively lowering demand (e.g., ride-sharing) can reduce incentives to induce surges.
• Scale of analysis: ~28 million price estimates collected across six continents; modeling and simulations (N=160 drivers) qualitatively reproduce observed patterns.

The findings address the central paradox: dynamic pricing designed to equilibrate supply and demand can itself create incentives for coordinated supply withholding, producing anomalous surges. The phase diagram clarifies when drivers face prisoner’s dilemma versus coordination regimes; under many realistic conditions, temporary OFF decisions are payoff-dominant, explaining observed repeated surge peaks in evening off-peak periods. The timescale-based classification method allows detection of likely anomalies globally using only price time series, bypassing the lack of public supply data. These insights generalize to other algorithmically priced, fast-timescale markets with inelastic demand components (e.g., smart grids), emphasizing the need to design pricing rules that avoid collective-action incentives that destabilize systems. For mobility, enhancing demand elasticity (public transport availability) and reducing effective demand (ride-sharing) mitigate anomalous surges more effectively than capping surge fees.

Dynamic pricing in on-demand mobility can induce non-equilibrium states characterized by anomalous supply shortages. Through game-theoretic analysis, large-scale empirical time series, and dynamic simulations, the study demonstrates generic incentives for drivers to coordinate temporary supply withholding and provides a timescale-based method to identify such dynamics across cities worldwide. The work informs the design and regulation of pricing schemes to avoid perverse incentives. Future research should incorporate direct observations of driver supply, extend modeling to heterogeneous agents and multi-region settings, test alternative pricing algorithms robust to coordination, and explore cross-industry applications such as power systems and platform-mediated services.

Direct observation of driver supply (number and location of online drivers) was not available; identification of anomalies relies on price dynamics and inferred demand proxies, requiring external confirmation for causal attribution. Exact surge algorithm details and local policy factors are unknown, potentially affecting interpretation. Base-cost estimates assume constant surcharges and rely on rounded API fare data, limiting precision for short trips. Theoretical models use simplified price responses, linear demand elasticity, and mean-field strategies; while capturing incentives generically, they abstract from heterogeneity, communication, and platform interventions.