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

In this paper the integrated traffic control and traffic assignment problem is studied for a situation with two road authorities. The road authorities try to optimize their own objectives and the same is done by the road users. This leads to a two-level three-player, multi-stage optimization problem with complete information. Game theory gives a suitable framework to analyze the problem and to find solutions for different situations, e.g. no cooperation, cooperation between the two authorities and a system optimum where all actors cooperate to minimize the total costs for all travelers. In this paper two approaches are used: an analytical one and an approach 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 reacting 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 sub-optimum is reached. The model calculations give evidence that cooperation of road administrators improves the utilization of the infrastructure and that a global optimization does not necessarily give a worse situation for one road administrator.