  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 incentives
(price discount or excess charge on passengers) 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. Finally, we complement the
theoretical results through two numerical simulations.
