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Designing High-Occupancy Toll Lanes: A Game-Theoretic Analysis

Zhanhao Zhang, Ruifan Yang, Manxi Wu

TL;DR

The paper analyzes optimal HOT lane design via a game-theoretic Wardrop framework where travelers have continuous heterogeneity in value of time $\beta$ and carpool disutility $\gamma$, and a planner chooses HOT capacity $\rho$ and toll $\tau$. It first characterizes a complete equilibrium for single-segment roads, revealing two regimes determined by design parameters, then extends to multi-segment networks with multiple occupancy levels and segment-specific tolls, proving existence and generic uniqueness. The authors calibrate latency and preference distributions using California I-880 data through inverse optimization and convex programming, and solve a design problem over five road segments to achieve objectives such as congestion reduction and toll revenue across different times of day. The empirical findings show trade-offs between congestion metrics and revenue, and demonstrate substantial potential gains from optimal tolling and capacity allocation, guiding practical HOT-lane design and policy analysis.

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.

Designing High-Occupancy Toll Lanes: A Game-Theoretic Analysis

TL;DR

The paper analyzes optimal HOT lane design via a game-theoretic Wardrop framework where travelers have continuous heterogeneity in value of time and carpool disutility , and a planner chooses HOT capacity and toll . It first characterizes a complete equilibrium for single-segment roads, revealing two regimes determined by design parameters, then extends to multi-segment networks with multiple occupancy levels and segment-specific tolls, proving existence and generic uniqueness. The authors calibrate latency and preference distributions using California I-880 data through inverse optimization and convex programming, and solve a design problem over five road segments to achieve objectives such as congestion reduction and toll revenue across different times of day. The empirical findings show trade-offs between congestion metrics and revenue, and demonstrate substantial potential gains from optimal tolling and capacity allocation, guiding practical HOT-lane design and policy analysis.

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.
Paper Structure (15 sections, 5 theorems, 36 equations, 8 figures, 2 tables)

This paper contains 15 sections, 5 theorems, 36 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The basic model
  3. Equilibrium characterization and comparative statics
  4. Equilibrium characterization
  5. Comparative statics
  6. Extensions to multiple segments and occupancy levels
  7. Design HOT on California I-880
  8. Data description
  9. Model calibration
  10. Latency functions.
  11. Calibration of preference distribution.
  12. Optimal design of toll price and HOT capacity at 5-6pm
  13. Hourly optimal toll pricing
  14. Concluding remarks
  15. Proof of Results

Key Result

Lemma 1

If $\tau > 0$, then $\ell_{\delta}(\sigma^*_{}, \rho) > 0$, $\sigma^*_{\mathrm{pool}} > 0$, and $\sigma^*_{\mathrm{o}} > 0$.

Figures (8)

  • Figure 1: Characterization of best response strategies
  • Figure 2: Equilibrium outcomes in each regime.
  • Figure 3: Interstate 880 (I-880) Highway from Dixon Landing Rd to Lewelling Blvd (Highlighted in Blue). The nodes separating the segments are marked in bold text.
  • Figure 4: Average travel time (min) and 95% confidence interval of the HOT and ordinary lanes from Auto Mall Pkwy to Hesperian Blvd in each hour of a workday.
  • Figure 5: Fractions of agents on HOT lanes taking each occupancy level per day.
  • ...and 3 more figures

Theorems & Definitions (7)

  • Definition 1
  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Theorem 2
  • Definition 2
  • Theorem 3