Incentive-compatible capacity pricing for congested transportation facilities: A game-theoretic approach

The central focus of this dissertation is to investigate the theory and application of market-driven models for the management of congested transportation network facilities. Computable Nash and generalized Nash equilibrium models are used to estimate the value to users of using facilities with a view to using this information for market pricing. Variational inequality and quasi-variational inequality formulations are used to solve the oligopolistic transport market models. These game-theoretic models are then used to develop a market mechanism for determining capacity allocation and price. Different users are being offered widely varying prices based on their valuation of basically the same transport service. The quality attributes of the transportation service are differentiated to allow users with different preferences to select different qualities. Two applications are included. In the first application, passenger air travel, given the total origin-destination trip demand, airport capacity and cost of each flight, the model derives the flight patterns, ticket prices, routes and carrier choice for passengers and landing priorities. The choice of travellers between competing airlines is represented by a logit model. Two models are proposed for pricing of landing slots for airlines: the first includes an exogenously determined landing/takeoff slot allocation, and the second includes an endogenous allocation of slots that depends on the value of the slot to each airline. In the second application, we present a computable equilibrium model of an internal market for track resources in a railroad. The problem of estimating the value to each train of track capacity, which in turn is used to create the actual train schedules, is formulated as a N-player, noncooperative game with nondisjoint strategy sets. In order to incorporate the effects of other traffic on a given train schedule (the mean and variance of total travel time), a new delay model for a scheduled railroad on a partially double track rail line is developed. Using this model, a game-theoretic model is developed in which each train tries to maximize its utility (defined as minimizing the deviations from their ideal schedules); the generalized Nash equilibrium for this model is found as a solution to a quasi-variational inequality problem. Finally, we formulate a nonlinear programming model in which one agent controls all train movements. This latter model is used in order to "benchmark" and judge how close the price from the market pricing system (the game-theoretic model) comes to the optimal prices. Data from a Class I railroad is used to illustrate the practical use of the model.