In this paper, we consider a mobility system of travelers and providers, and propose a ``mobility game" to study when a traveler is matched to a provider. Each traveler seeks to travel using the services of only one provider, who manages one specific mode of transportation (car, bus, train, bike). The services of each provider are capacitated and can serve up to a fixed number of travelers at any instant of time. Thus, our problem falls under the category of many-to-one assignment problems, where the goal is to find the conditions that guarantee the stability of assignments. We formulate a linear program of maximizing the social welfare of travelers and providers and show how it is equivalent to the original problem and relate its solutions to stable assignments. We also investigate our results under informational asymmetry and provide a ``mechanism" that elicits the information of travelers and providers. Finally, we investigate and validate the advantages of our method by providing a numerical simulation example.
翻译：在本文中,我们考虑旅行者和提供者的流动系统,并提出“流动游戏”,以研究旅行者与提供者相匹配的情况。每个旅行者只寻求使用一个提供者的服务,而这个提供者管理一种特定的运输方式(汽车、公共汽车、火车、自行车)。每个提供者的服务都具有能力,可以随时为固定数目的旅行者提供服务。因此,我们的问题属于许多一派任务问题,目的是找到保证任务稳定性的条件。我们制定了一个使旅行者和提供者的社会福利最大化的线性方案,并表明它如何与最初的问题相提并论,并将其解决办法与稳定的任务联系起来。我们还在信息不对称的情况下调查我们的结果,提供一种“机制性”来了解旅行者和提供者的信息。最后,我们通过提供数字模拟的例子来调查和验证我们方法的优点。
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