We study a market mechanism that sets edge prices to incentivize strategic agents to organize trips that efficiently share limited network capacity. This market allows agents to form groups to share trips, make decisions on departure times and route choices, and make payments to cover edge prices and other costs. We develop a new approach to analyze the existence and computation of market equilibrium, building on theories of combinatorial auctions and dynamic network flows. Our approach tackles the challenges in market equilibrium characterization arising from: (a) integer and network constraints on the dynamic flow of trips in sharing limited edge capacity; (b) heterogeneous and private preferences of strategic agents. We provide sufficient conditions on the network topology and agents' preferences that ensure the existence and polynomial-time computation of market equilibrium. We identify a particular market equilibrium that achieves maximum utilities for all agents, and is equivalent to the outcome of the classical Vickery Clark Grove mechanism. Finally, we extend our results to general networks with multiple populations and apply them to compute dynamic tolls for efficient carpooling in San Francisco Bay Area.

翻译：我们研究了一种市场机制，通过设定边价格激励策略性代理高效组织行程以共享有限网络容量。该市场允许代理组成团体共享行程、决定出发时间与路线选择，并支付边价格与其他成本。我们基于组合拍卖与动态网络流理论，开发了一种分析市场均衡存在性与计算的新方法。该方法解决了以下因素导致的市场均衡表征挑战：(a) 共享有限边容量时行程动态流所涉及的整数约束与网络约束；(b) 策略性代理的异质性私有偏好。我们给出了确保市场均衡存在且可在多项式时间内求解的充分条件，该条件涉及网络拓扑结构与代理偏好。我们识别出一种特殊的市场均衡，该均衡能为所有代理实现最大效用，且等价于经典维克里-克拉克-格罗夫斯机制的结果。最后，我们将结论推广至包含多群体的通用网络，并应用于计算旧金山湾区的动态拼车收费。