[Paper Review] Flow Equilibria via Online Surge Pricing

Amos Fiat, Yishay Mansour+1 more|arXiv (Cornell University)|Apr 25, 2018

Transportation and Mobility InnovationsEngineering19 references4 citations

TL;DR

This paper proposes an online surge pricing mechanism that induces passenger-taxicab equilibria to maximize social welfare in dynamic ride-sharing systems. By setting location-specific surge prices based on real-time supply and demand, it ensures strategic taxicabs and passengers act in ways that minimize total travel cost while maximizing service efficiency, achieving a (1−δ)-competitive ratio in online settings with poly-time computation.

ABSTRACT

We explore issues of dynamic supply and demand in ride sharing services such as Lyft and Uber, where demand fluctuates over time and geographic location. We seek to maximize social welfare which depends on taxicab and passenger locations, passenger valuations for service, and the distances between taxicabs and passengers. Our only means of control is to set surge prices, then taxicabs and passengers maximize their utilities subject to these prices. We study two related models: a continuous passenger-taxicab setting, similar to the Wardrop model, and a discrete passenger-taxicab setting. In the continuous setting, every location is occupied by a set of infinitesimal strategic taxicabs and a set of infinitesimal non-strategic passengers. In the discrete setting every location is occupied by a set of strategic agents, taxicabs and passengers, passengers have differing values for service. We expand the continuous model to a time-dependent setting and study the corresponding online environment. Surge prices are in passenger-taxicab equilibrium if there exists a min cost flow that moves taxicabs about such that (a) every taxicab follows a best response, (b) all strategic passengers at $v$ with value above the surge price $r_v$ for $v$, are served and (c) no strategic passengers with value below $r_v$ are served (non-strategic infinitesimal passengers are always served). This paper computes surge prices such that resulting passenger-taxicab equilibrium maximizes social welfare, and the computation of such surge prices is in poly time. Moreover, it is a dominant strategy for passengers to reveal their true values. We seek to maximize social welfare in the online environment, and derive tight competitive ratio bounds to this end. Our online algorithms make use of the surge prices computed over time and geographic location, inducing successive passenger-taxicab equilibria.

Motivation & Objective

• To maximize social welfare in dynamic ride-sharing systems where supply and demand fluctuate over time and space.
• To design a surge pricing mechanism that induces passenger-taxicab equilibria in both continuous and discrete models.
• To ensure that truthful valuation reporting is a dominant strategy for passengers.
• To provide poly-time algorithms for computing optimal surge prices that achieve near-optimal social welfare in online environments.
• To derive tight competitive ratio bounds for online algorithms under time-dependent demand and supply shifts.

Proposed method

• Models the system as a min-cost flow problem where taxicabs and passengers are assigned based on surge prices to minimize total travel cost.
• Defines a passenger-taxicab equilibrium where all strategic agents follow best responses: taxicabs choose routes maximizing (surge price − distance), and passengers only accept rides if value > surge price.
• Uses the earthmover distance metric to quantify the cost of moving supply from one distribution to another across time and locations.
• Applies the online algorithm 'match' which sets supply equal to previous demand, ensuring (1−δ)-competitiveness under total variation drift.
• Extends the model to general metrics with bounded edge lengths, proving (1−δℓ_max)-competitiveness under such constraints.
• Proves existence of equilibria and shows that truthful reporting of passenger valuations is a dominant strategy under the proposed mechanism.

Experimental results

Research questions

• RQ1 Can online surge pricing be designed to maximize social welfare in time-varying ride-sharing systems?
• RQ2 What competitive ratio can be achieved by online algorithms in dynamic supply-demand environments?
• RQ3 How can surge prices be computed in poly time to induce equilibria that maximize social welfare?
• RQ4 Is truthful reporting of passenger valuations a dominant strategy under the proposed pricing mechanism?
• RQ5 What are the theoretical limits of online performance in terms of competitive ratio for such systems?

Key findings

• The proposed online algorithm 'match' achieves a (1−δ)-competitive ratio when edge lengths are 1, where δ is the total variation drift of demand over time.
• For general metrics with maximum edge length ℓ_max, the competitive ratio is (1−δℓ_max), showing dependence on metric scale.
• No online algorithm can achieve a competitive ratio better than (1−δ/4), establishing a theoretical lower bound.
• Surge prices can be computed in polynomial time to induce equilibria that maximize social welfare in both continuous and discrete models.
• Truthful reporting of passenger valuations is a dominant strategy, ensuring incentive compatibility.
• The model supports personalized costs for taxicabs, enabling inclusion of start-up costs and private cost structures under Bayesian assumptions.