发表机构
Aarhus University; Google Research（奥胡斯大学; 谷歌研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究机器人出租车分配博弈中的确定性斯塔克尔伯格策略，提出整数线性规划及近似算法，证明NP难性，并给出直线情形精确算法，实验验证算法实用高效。
AI 中文摘要
在自主出行双寡头市场中，平台基于车辆距离竞争乘客。一个关键的运营挑战——由防御市场进入者的在位者所面临——是如何调度车队以最小化被反应性竞争对手抢走的需求。我们将这种竞争建模为零和机器人出租车分配博弈，重点研究计算领导者最优确定性斯塔克尔伯格策略。我们将该问题表述为一个精确的单层整数线性规划，并利用其松弛设计了一种多项式时间近似算法，实现与最优解的加性误差。我们通过证明判断严格正收益是否可实现是NP完全的，以及将最优收益近似到与乘客数量线性相关的加性误差是NP难的，论证了该结果接近最优可能。我们还提供了一种精确的多项式时间动态规划算法，用于在乘客和车辆位于欧几里得直线上时计算最优斯塔克尔伯格收益。最后，我们使用真实网约车数据进行了实证评估，补充了理论发现。实验表明，我们基于线性规划的算法在实践中显著优于其最坏情况保证，而轻量级启发式算法以可忽略的计算开销实现了极具竞争力的收益，为大规模部署提供了实用解决方案。
英文摘要
In autonomous mobility duopolies, platforms compete for riders based on vehicle proximity. A critical operational challenge---faced by an incumbent proactively defending against a market entrant---is how to dispatch fleets to minimize demand poached by a reactive competitor. We model this competition as a zero-sum robotaxi assignment game, focusing on computing optimal deterministic Stackelberg strategies for the leader. We formulate this problem as an exact single-level integer linear program and use its relaxation to design a polynomial-time approximation algorithm achieving an additive error from the optimum. We argue that this is not far from best possible by proving that deciding whether a strictly positive payoff is achievable is NP-complete, and that approximating the optimal payoff within an additive error scaling linearly with the number of riders is NP-hard. We also provide an exact polynomial-time dynamic programming algorithm for computing the optimal Stackelberg payoff when riders and vehicles are on the Euclidean line. Finally, we complement our theoretical findings with an empirical evaluation using real-world ride-hailing data. The experiments demonstrate that our LP-based algorithm significantly outperforms its worst-case guarantee in practice, while lightweight heuristics achieve highly competitive payoffs with negligible computational overhead, offering practical solutions for large-scale deployments.
