On the impact of congestion pricing onto different classes of users: A game-theoretic approach

Traffic congestion in road networks creates a negative externality that justifies the intervention of a public authority to restore Pareto-efficiency. Such an intervention can take the form of congestion pricing, whereby a time-varying toll is levied on certain roads of the network during the rush hour.; Most traffic models used today predict that user choices are made according to the so-called Wardrop principle, whereby a departure pattern (i.e. a set of itinerary and departure time decisions from all commuters) is in equilibrium if it yields identical costs to all (identical) users. However, this paradigm is incapable of addressing the issues of multiple classes of users with different preferences.; Additionally, a more general equilibrium condition based on a strict Nash equilibrium is to be ruled out, even in mixed strategies, due to strategy-dependent discontinuities in the pay-off functions.; In this dissertation, we propose an orginal approach to find an {dollar}epsilon{dollar}-Nash equilibrium of the morning commute problem, using an analagous problem known as the shipment problem. We examine the algorithmic implications of this theory on the simple case of two classes of users, and illustrate our findings on two numerical examples.