The generalized Nash equilibrium model for oligopolistic transit market with elastic demand

This paper presents a bilevel transit fare equilibrium model for a deregulated transit system. In the upper-level problem, the transit competition is portrayed as an n-player, non-cooperative game by changing the fare structure of each of a set of transit lines separately so as to maximize the profit of each transit operator within the oligopolistic market. We show that there exists a generalized Nash game between transit operators, which can be formulated as a quasi-variational inequality problem. In the lower-level problem, the passengers' response to the equilibrium fare structure of the transit operators is represented by the stochastic user equilibrium transit assignment model with elastic OD demand. As a result, the bilevel transit fare equilibrium problem is presented in the Stackelberg form and solved by a heuristic solution algorithm based on a sensitivity analysis approach. A numerical example is given to illustrate the competition mechanism on the transit network and some useful findings are presented on competitive operations.