  We consider the situation where multiple transportation service providers
cooperate to offer an integrated multi-modal platform to enhance the
convenience to the passengers through ease in multi-modal journey planning,
payment, and first and last mile connectivity. This market structure allows the
multi-modal platform to coordinate profits across modes and also provide
incentives to the passengers. Accordingly, in this paper, we use cooperative
game theory coupled with the hyperpath-based stochastic user equilibrium
framework to study such a market. We assume that the platform sets incentive
(subsidy or tax) along every edge in the transportation network. We derive the
continuity and monotonicity properties of the equilibrium flow with respect to
the incentives along every edge. The optimal incentives that maximize the
profit of the platform are obtained through a two time-scale stochastic
approximation algorithm. We use the asymmetric Nash bargaining solution to
design a fair profit sharing scheme among the service providers. We show that
the profit for each service provider increases after cooperation on such a
platform. We complement the theoretical results through two numerical
simulations.
