Dynamic Pricing Provides Robust Equilibria in Stochastic Ridesharing Networks (2205.09679v1)

Abstract: Ridesharing markets are complex: drivers are strategic, rider demand and driver availability are stochastic, and complex city-scale phenomena like weather induce large scale correlation across space and time. At the same time, past work has focused on a subset of these challenges. We propose a model of ridesharing networks with strategic drivers, spatiotemporal dynamics, and stochasticity. Supporting both computational tractability and better modeling flexibility than classical fluid limits, we use a two-level stochastic model that allows correlated shocks caused by weather or large public events. Using this model, we propose a novel pricing mechanism: stochastic spatiotemporal pricing (SSP). We show that the SSP mechanism is asymptotically incentive-compatible and that all (approximate) equilibria of the resulting game are asymptotically welfare-maximizing when the market is large enough. The SSP mechanism iteratively recomputes prices based on realized demand and supply, and in this sense prices dynamically. We show that this is critical: while a static variant of the SSP mechanism (whose prices vary with the market-level stochastic scenario but not individual rider and driver decisions) has a sequence of asymptotically welfare-optimal approximate equilibria, we demonstrate that it also has other equilibria producing extremely low social welfare. Thus, we argue that dynamic pricing is important for ensuring robustness in stochastic ride-sharing networks.

• The paper introduces a two-level stochastic model that integrates spatiotemporal dynamics and correlated shocks to capture ridesharing market complexities.
• The paper demonstrates that the Stochastic Spatiotemporal Pricing mechanism dynamically adjusts fares based on real-time data to maintain incentive compatibility and optimal social welfare.
• The paper contrasts dynamic pricing with static approaches, showing that iterative updates provide more robust and socially optimal outcomes in large-scale ridesharing networks.

The paper, "Dynamic Pricing Provides Robust Equilibria in Stochastic Ridesharing Networks," addresses the complexity inherent in ridesharing markets by proposing a novel model that incorporates strategic drivers, spatiotemporal dynamics, and stochastic elements. These elements include shocks correlated with weather or large public events. Traditional approaches have largely tackled these challenges in isolation, but the authors aim to create a more integrated and flexible model that can handle large-scale, city-wide phenomena.

The authors present a two-level stochastic model that allows for correlated shocks. This is particularly important for appropriately capturing the influence of external factors, such as weather, which can simultaneously affect driver availability and rider demand across various locations and times.

Central to their proposal is the Stochastic Spatiotemporal Pricing (SSP) mechanism. The SSP mechanism dynamically updates prices based on real-time data of demand and supply. This dynamic adjustment is crucial for maintaining incentive compatibility and ensuring all approximate equilibria are welfare-maximizing in large markets. Essentially, the SSP mechanism ensures that drivers and riders make decisions that, when aggregated, lead to optimal outcomes in terms of social welfare.

The paper contrasts this dynamic pricing mechanism with a static variant, where prices adjust only according to broader market-level scenarios rather than individual rider or driver decisions. While the static model can achieve welfare-optimal equilibria under certain conditions, it is also shown to have equilibria that lead to significantly lower social welfare, demonstrating the importance of dynamic adjustments.

The results underscore that dynamic pricing is essential for robustness in stochastic ridesharing networks. Static pricing mechanisms can lead to unreliable outcomes, whereas the iterative recalculations of SSP based on real-time conditions more consistently steer the market towards welfare-maximizing equilibria. In summary, the SSP mechanism offers a more resilient and effective approach to managing the intricate, variable conditions of ridesharing markets, leading to improved overall social welfare.