Urban networks with ring roads: Two-level, three-player game

The integrated traffic control and traffic assignment problem is studied for a situation with two road authorities. Road authorities try to optimize their own objectives, and the same is done by road users. The result is a two-level, three-player multistage optimization problem with complete information. Game theory gives a suitable framework to analyze the problem and to find solutions for different situations such as no cooperation, cooperation between the two authorities, and a system optimum in which all actors cooperate to minimize the total costs for all travelers. Two approaches are used: an analytical approach and one based on a simulation and assignment framework. Both approaches are described and used to study a simple example, for which the results are given and discussed. The results show that separate or integrated anticipatory control gives better results than iterative reaction to the current situation. If one road authority takes the lead and anticipates the reactions of both the road users and the other road authority, a suboptimum is reached. The model calculations provide evidence that cooperation of road authorities improves utilization of the infrastructure and that global optimization does not necessarily result in a worse situation for one road authority.