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.

中文翻译：

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学习为需求未知的车辆服务定价

车辆服务提供商根据用户在不同起点-目的地对的出行需求来设定服务价格是有利可图的。先前对车辆服务空间定价的研究依赖于供应商了解用户需求的假设。在本文中，我们研究了一个垄断供应商，该供应商最初不知道用户的需求，需要通过观察用户对服务价格的反应来随着时间的推移了解它。我们设计了定价和车辆供应政策，考虑到探索（即了解需求）和开发（即最大化供应商的短期收益）之间的权衡。考虑到供应商需要确保每个地点的车流平衡，其对不同起点-终点对的定价和供应决策是紧密耦合的。这使得从理论上分析我们政策的表现变得具有挑战性。我们分析了在我们的政策和透视政策下提供者的预期时间平均收益之间的差距，透视政策根据需求的完整信息做出决策。我们证明，在运行我们的策略 D 天后，预期时间平均收益的损失最多为 O((ln D)^0.5 D^(-0.25))，随着 D 接近无穷大而衰减为零。