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An Analytical Study of a Two-Sided Mobility Game

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.