A Game-theoretical Model of Road Pricing with Endogenized User-equilibrium

Abstract

This paper presents an optimization-based game-theoretical model of road pricing. The model incorporates elastic user-demand, multiple user-classes, and an endogenized demand and pathchoice user-equilibrium. After providing a generic model formulation, we apply it to a singleplayer optimization problem to find optimal tolls for a government subjected to user-equilibrium. We propose a post-processing method that avoids unfavorable outcomes caused by the nonuniqueness of user-equilibrium path flows. We use the single-player optimization problem to develop a game-theoretical framework to solve different competition scenarios. The model is applied to two fictional case-studies. The first involves a two-player game-theoretical problem and four competition scenarios are elaborated, and the second involves user-class specific instruments and demonstrates the relevance of the post-processing.