  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 (e.g., 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.
