A Game Theoretic Analysis of High Occupancy Toll Lane Design

Abstract

In this article, we study the optimal design of High Occupancy Toll (HOT) lanes. The traffic authority determines the road capacity allocation between HOT lanes and ordinary lanes, as well as the toll price charged for travelers using HOT lanes who do not meet the high-occupancy eligibility criteria. We develop a game-theoretic model to analyze the decisions of travelers with heterogeneous preference parameters in values of time and carpool disutilities. These travelers choose between paying or forming carpools to use the HOT lanes, or taking the ordinary lanes. Travelers' welfare depends on the congestion cost of the lane they use, the toll payment, and the carpool disutilities. For highways with a single entrance and exit node, we provide a complete characterization of equilibrium strategies and a comparative statics analysis of how the equilibrium vehicle flow and travel time change with HOT capacity and toll price. We then extend the single segment model to highways with multiple entrance and exit nodes. We extend the equilibrium concept and propose various design objectives considering traffic congestion, toll revenue, and social welfare. Using the data collected from the HOT lane of the California Interstate Highway 880 (I-880), we formulate a convex program to estimate the travel demand and approximate the distribution of travelers' preference parameters. We then compute the optimal toll design of five segments for I-880 for achieve each one of the four objectives, and compare the optimal solution with the current toll pricing.