Service differentiation under mixed transit oligopoly: A graphical analysis

In this paper, we consider a mixed transit oligopoly market and analyze strategic interactions between passengers and operators. A number of operators provide vertically differentiated transit service to passengers. Individuals choose transit based on the assumption of willingness to pay (WTP) and minimize their generalized costs. Users are generally heterogeneous in both WTP and value of time (VOT). The efficient transit market is segmented by cut-off VOTs and illustrated in the two-dimensional WTP and VOT space. The market bounds is a concave polygonal chain connected by cutoff points. We formulate the efficient transit market problem for Pareto optimal solutions and develop a randomized market bounds algorithm (RMBA). The algorithm is based on random walk Monte Carlo methods. It is a powerful tool to compute and analyze transit oligopoly. The Pareto frontier can be found by RMBA and shown to converge in probability. A case study on duopoly is conducted.