  In this paper, we consider a multi-modal mobility system of travelers each
with an individual travel budget, and propose a game-theoretic framework to
assign each traveler to a ``mobility service" (each one representing a
different mode of transportation). We are interested in equity and
sustainability, thus we maximize the worst-case revenue of the mobility system
while ensuring ``mobility equity," which we define it in terms of
accessibility. In the proposed framework, we ensure that all travelers are
truthful and voluntarily participate under informational asymmetry, and the
solution respects the individual budget of each traveler. Each traveler may
seek to travel using multiple services (e.g., car, bus, train, bike). The
services 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
worst-case revenue under the constraints of mobility equity, and we fully
characterize the optimal solution.
