Competition and Equilibria of Private Toll Roads with Elastic Demand

This paper describes how there has been an increasing worldwide tendency towards the introduction of commercially and privately provided roads for the expansion of modern road system. The private sector would build and operate roads at its own expense and receive the revenue from road toll charge within some years, and then these roads will be transferred to the government. Toll road competition is one of the important issues under such a Build-Operate-Transfer (BOT) scheme, which is being encountered nowadays in many cities. When two or more competing firms operate multiple toll roads, the situation could be complicated, since their profits are interrelated due to demand inter-dependence in the network and apart from the consideration of road user responses, each firm must consider what its competitors' choices are likely to be. In this paper we develop game-theoretic approaches to the study of the road network that involves multiple toll roads operated by competitive private firms. The strategic interactions and market equilibriums among the private firms are analyzed both in determining their supply (road capacity) and price (toll level) over the network. The toll road competition problems in general traffic equilibrium networks are formulated as equilibrium program with equilibrium constraints or bi-level variational inequalities. Heuristic solution methods are proposed and their convergences are demonstrated with simple network examples. It is also shown that private pricing and competition can be both profitable and welfare-improving.