Model and Analysis of Provider-User Games

by Soterwood, Jeanine Michelle.

This dissertation studies the competitive dynamics between two non-identical providers competing for customers seeking low-cost and quick service. Providers have generic delay functions where, as demand received by each provider grows, so does delay in processing customers’ requests. Given a pricing or capacity decision by each provider, customers determine the proportion of demand to send to each provider by minimizing generalized cost (monetary cost plus delay cost). This problem is formulated as a bilevel optimization, with providers competing at the upper level subject to the customers’ decisions at the lower level. Occurrence of Nash equilibria between the providers is studied. First studied is the providers’ problem of making decisions on capacities, while competing for a single customer. Conditions are derived for one provider to claim the entire market share, and for the occurrence of an equilibrium where both providers receive positive demand. A numerical example in which no equilibrium exists is presented. Both the inelastic and elastic demand cases are studied for this scenario. In a second model, providers make pricing decisions with capacity fixed. Under some assumptions, it is shown that a Nash equilibrium between providers always exists and a numerical example is presented. These models are then combined, in which providers make capacity decisions where prices equilibrate based on the results from the second model. Two competing customers with demand for a homogeneous product are then introduced, where providers choose prices as they compete for customers. This model is extended to an application along a highway corridor with a high-occupancy/toll (HOT) lane in parallel with a free road and transit line. A government agency chooses the transit service frequency while a private toll operator competes by choosing a toll to charge single-occupancy vehicles who wish to use the HOT lane. This scenario is 14 also modeled as a bilevel program. For the lower level, a new dynamic equilibration process where homogeneous users make mode choice decisions based on previous generalized costs of using a particular mode is developed. Two numerical examples are presented showing a unique Nash equilibrium between the providers and an example in which multiple equilibria exist. 15