  In recent years, we have witnessed a remarkable surge of usage in shared
vehicles in our cities. Shared mobility offers a future of no congestion in
busy city roads with increasing populations of travelers, passengers, and
drivers. Given the behavioral decision-making of travelers and the shared
vehicles' operators, however, the question is "how can we ensure a
socially-acceptable assignment between travelers and vehicles?" In other words,
how can we design a shared mobility system that assigns each traveler to the
"right" vehicle? In this paper, we design a shared mobility market consisted of
travelers and vehicles in a transportation network. We formulate a linear
programming problem and derive the optimal assignment between travelers and
vehicles. In addition, we provide the necessary and sufficient conditions for
the stable traveler-vehicle profit allocation. Our goal is twofold: maximize
the social welfare of all travelers with the optimal assignment while ensuring
the feasibility and stability of the traveler-vehicle profit allocation while
respecting the decision-making of both the travelers and the vehicles'
operators.
