Competition between Cities: An Exploration of Response Surfaces and Possibilities for Collusion

Extending the literature on competition in the presence of cordon tolls, this article explores the implications of competition between two cities. The city authorities are assumed to maximise the welfare of their own residents whilst taking advantage of tax export mechanisms by charging traffic from the competing authority. The problem is posed as an Equilibrium Problem with Equilibrium Constraints (EPEC) which is a special form of a Nash game with a hierarchical structure. Employing a grid search to explore the response surfaces and to determine the Nash Equilibrium toll levels, we demonstrate the possibility that there may exist multiple local Nash solutions and that competition may lead to a sub-optimal outcome for one or both authorities depending on whether there exists a stronger player. We then consider the impact of elasticity of demand and other parameter assumptions on the potential number of Nash solutions. Finally incentives for collusion are studied.