Who Wins When Uber and Taxis Compete? The Case for Pareto-Optimal Regulation

Ridesourcing platforms—Uber, Lyft, Didi—have fundamentally disrupted the taxi industry. Regulators worldwide now face a genuinely hard question: how do you set rules that are fair to passengers who want cheap, reliable rides; to taxi drivers who have invested in licences; to platform operators managing dynamic fleets; and to governments seeking tax revenue and safety standards—all at the same time?

The short answer, of course, is that you cannot fully satisfy everyone simultaneously. Trade-offs are inevitable. However, our recent study, "Pareto optimal regulatory strategies for coupled ridesourcing and taxi markets with impatient passengers," published in Transportation Research Part E: Logistics and Transportation Review (2026), establishes a rigorous mathematical framework to map those trade-offs explicitly and identify the complete set of Pareto-efficient regulatory policies.

The Market Structure: Two Competing Systems, One Impatient Customer

A key modelling insight in this work is that ridesourcing and taxi markets are coupled, not independent. A passenger who grows impatient waiting for a ride-hail vehicle may switch to a taxi; a taxi driver who perceives low demand may reduce supply, which in turn raises passenger wait times for taxis and sends more passengers back to the platform. This feedback loop creates complex system dynamics that single-market analyses routinely miss.

The model incorporates passenger impatience explicitly. Each passenger has a maximum acceptable wait time; beyond this threshold, they either switch mode or abandon the trip entirely. This is not merely a behavioural flourish—it fundamentally changes the equilibrium conditions and the shape of the regulatory trade-off frontier.

The Regulatory Levers: What Can a Government Actually Control?

The study examines a combined regulatory strategy consisting of three interdependent instruments:

1. Platform commission rate: The percentage of each fare retained by the ridesourcing platform.
2. Taxi licence quota: The number of taxi licences in circulation, controlling taxi supply.
3. Minimum fare floor: A price floor applied across both markets to prevent destructive price competition.

Each instrument affects the four stakeholders differently. Lowering the commission rate benefits drivers but squeezes platform profits. Tightening the licence quota protects taxi drivers but reduces competition, raising fares for passengers. The minimum fare floor protects driver income but raises consumer costs. The regulatory challenge is precisely this multi-dimensional interaction.

The Mathematical Framework: A Bi-level Black-Box Problem

The study formulates the problem as a multi-objective bi-level programme:

• Upper level (Government/Regulator): Selects the regulatory parameters to optimise a vector of stakeholder objectives simultaneously.
• Lower level (Market Equilibrium): Given the regulatory parameters, determines the equilibrium supply of taxi drivers, platform pricing, and passenger demand across both markets.

The critical computational challenge is that the lower-level equilibrium has no closed-form solution: it must be computed via simulation for every candidate regulatory vector $x$. This makes the upper-level objective a costly black-box function, and conventional gradient-based multi-objective solvers are inapplicable.

The Solution Method: Bayesian Optimisation for the Pareto Frontier

To tackle this black-box multi-objective problem efficiently, the study adapts Bayesian Optimisation (BO) with a Gaussian Process (GP) surrogate. The approach works as follows:

1. Surrogate modelling: A GP is trained on a small initial set of simulation evaluations, producing a probabilistic approximation of each objective function.
2. Acquisition function: A multi-objective acquisition criterion (based on hypervolume improvement) selects the next regulatory vector to evaluate, balancing exploitation of known good regions with exploration of uncertain regions.
3. Iterative refinement: The surrogate is updated with each new simulation result, progressively approximating the true Pareto frontier.

Key Findings: Navigating the Four-Stakeholder Trade-Off

1. There Is No Single "Best" Policy

The study confirms that the four stakeholder objectives are fundamentally in conflict. No single regulatory vector simultaneously maximises passenger welfare, driver income, platform profit, and government revenue. The Pareto frontier, however, reveals the precise shape and extent of these trade-offs, equipping regulators with a decision support tool rather than a false promise of a win-win solution.

2. Impatient Passengers Reshape the Trade-Off Geometry

When passenger impatience is low (passengers are willing to wait), the market equilibrium is relatively stable, and regulatory levers have predictable effects. However, as the impatience threshold tightens, the system becomes more sensitive to supply shocks. A small reduction in taxi quota that would be inconsequential for patient passengers can trigger a cascade of mode-switching that significantly degrades overall system performance. Regulators must therefore calibrate policies with explicit reference to the local travel culture and acceptable wait time norms.

3. Commission Rate Regulation Has Asymmetric Effects

Reducing the platform commission rate is often proposed as a pro-driver measure. Our results reveal an important asymmetry: at moderate commission rates, driver welfare does improve; however, at very low commissions, platform profitability falls below viability thresholds, potentially triggering platform exit—an outcome worse for all parties. The Pareto frontier identifies a commission rate corridor within which meaningful driver welfare improvements are achievable without threatening platform sustainability.

4. The Regulatory Interaction Effect

The three instruments interact non-additively. A minimum fare floor combined with a tight licence quota produces a different equilibrium than either instrument alone. The bi-level framework is essential for capturing these interactions, which single-instrument analyses cannot detect.

Managerial Implications for Policymakers

The practical contribution of this work is a navigable Pareto frontier that functions as a regulatory dashboard. Rather than presenting a single recommended policy, the framework allows policymakers to:

• Visualise the full efficiency-equity frontier across all four stakeholder groups.
• Identify the "price of fairness"—how much aggregate efficiency must be sacrificed to achieve a more equitable distribution of welfare.
• Conduct scenario analysis on how the frontier shifts under different passenger impatience levels, demand elasticities, or city-size parameters.

This is the kind of evidence-based decision support that urban transport regulators urgently require as ridesourcing continues to grow in market share relative to traditional taxi services.

Conclusion

The ridesourcing revolution has rendered single-stakeholder, single-instrument regulatory thinking obsolete. This study advances a multi-objective bi-level framework that treats regulatory design as the complex, coupled, multi-stakeholder problem it genuinely is. By combining Bayesian Optimisation with market equilibrium simulation, we efficiently compute the Pareto frontier of regulatory strategies—providing a rigorous, computationally tractable tool for urban transport governance.

For full model specifications, equilibrium proofs, and numerical experiments, read the complete paper in Transportation Research Part E (Vol. 208, 2026, Article 104677).