Dynamic Matching for Ride-sharing with Deadlines

Ride-sharing systems, which enable private car drivers to offer rides to passengers heading in the same direction, have gained popularity as a cost-effective urban transportation solution. We consider the market design problem, where drivers and riders dynamically enter the system over time, requiring transportation to specific destinations within certain deadlines. This study focuses on a simple but representative case, wherein all agents, i.e., drivers and riders, share a common origin but possess different destinations that define their types. Agents exhibit flexibility in their willingness to wait for a match, and matching agents of the same type generates higher utility than matching different types. Initially, we address the full information scenarios where agents reveal their true types to the platform and must accept the matching proposed by the platform. Given that the optimal matching for this problem requires solving an MDP with exponential complexity, we propose a computationally simple mechanism that matches a different-type pair only when one agent is about to leave immediately, and the other cannot wait beyond a threshold number of time periods. We theoretically prove that this mechanism has near-optimal performance, particularly under balanced demand and supply. Subsequently, we shift focus to the incentive properties of the mechanism in more practical scenarios where selfish agents can be non-cooperative with the platform, i.e., reject low-value different-type matchings hoping to get better ones in the future, and non-truth-telling, i.e., declare a different destination. We study the incentive compatibility of two interesting payment schemes and prove the Price-of-Anarchy.