An Analytical Study of a Two-Sided Mobility Game

TL;DR

This paper models a two-sided mobility system as a game, analyzing stable assignments between travelers and providers, and proposes mechanisms to handle informational asymmetry with validation through simulations.

Contribution

It introduces a linear programming framework for stable matching in a mobility game considering capacity constraints and information asymmetry, advancing the understanding of such systems.

Findings

Linear program effectively finds stable assignments.

Mechanism successfully elicits truthful information.

Simulation demonstrates advantages of the proposed method.

Abstract

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.