Learning to Price Vehicle Service with Unknown Demand

TL;DR

This paper develops a learning-based pricing policy for vehicle services that balances exploration and exploitation, ensuring near-optimal revenue over time despite initially unknown demand and the need for vehicle flow balance.

Contribution

It introduces a novel pricing and supply policy for spatial vehicle pricing with unknown demand, providing theoretical guarantees on its performance.

Findings

The policy achieves a sublinear regret bound of O((ln D)^0.5 D^(-0.25)).

The expected payoff loss diminishes as the number of days increases.

The approach effectively balances demand learning and revenue maximization.

Abstract

It can be profitable for vehicle service providers to set service prices based on users' travel demand on different origin-destination pairs. The prior studies on the spatial pricing of vehicle service rely on the assumption that providers know users' demand. In this paper, we study a monopolistic provider who initially does not know users' demand and needs to learn it over time by observing the users' responses to the service prices. We design a pricing and vehicle supply policy, considering the tradeoff between exploration (i.e., learning the demand) and exploitation (i.e., maximizing the provider's short-term payoff). Considering that the provider needs to ensure the vehicle flow balance at each location, its pricing and supply decisions for different origin-destination pairs are tightly coupled. This makes it challenging to theoretically analyze the performance of our policy. We analyze the gap between the provider's expected time-average payoffs under our policy and a clairvoyant policy, which makes decisions based on complete information of the demand. We prove that after running our policy for D days, the loss in the expected time-average payoff can be at most O((ln D)^0.5 D^(-0.25)), which decays to zero as D approaches infinity.