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Iterative Recommendations based on Monte Carlo Sampling and Trust Estimation in Multi-Stage Vehicular Traffic Routing Games

Doris E. M. Brown, Venkata Sriram Siddhardh Nadendla, Sajal K. Das

TL;DR

The paper tackles urban congestion arising from selfish routing by modeling ITS-DVS interactions as a multi-stage routing game with dynamic driver trust. It introduces ROSTER, a Monte Carlo–based algorithm that updates trust beliefs and re-evaluates best responses to approximate a Bayesian Nash equilibrium. Experiments on Manhattan-inspired Pigou and Sioux Falls networks show that ROSTER reduces network congestion and driver travel time compared with LLF and TASR baselines, with the driver trust prediction converging to the true value as interactions grow. These results demonstrate a practical, trust-aware routing framework for ITS that can balance individual travel time with system-wide performance, with potential extensions to multi-driver scenarios and adaptive information design.

Abstract

The shortest-time route recommendations offered by modern navigation systems fuel selfish routing in urban vehicular traffic networks and are therefore one of the main reasons for the growth of congestion. In contrast, intelligent transportation systems (ITS) prefer to steer driver-vehicle systems (DVS) toward system-optimal route recommendations, which are primarily designed to mitigate network congestion. However, due to the misalignment in motives, drivers exhibit a lack of trust in the ITS. This paper models the interaction between a DVS and an ITS as a novel, multi-stage routing game where the DVS exhibits dynamics in its trust towards the recommendations of ITS based on counterfactual and observed game outcomes. Specifically, DVS and ITS are respectively modeled as a travel-time minimizer and network congestion minimizer, each having nonidentical prior beliefs about the network state. A novel approximate algorithm to compute the Bayesian Nash equilibrium, called ROSTER(Recommendation Outcome Sampling with Trust Estimation and Re-evaluation), is proposed based on Monte Carlo sampling with trust belief updating to determine the best response route recommendations of the ITS at each stage of the game. Simulation results demonstrate that the trust prediction error in the proposed algorithm converges to zero with a growing number of multi-stage DVS-ITS interactions and is effectively able to both mitigate congestion and reduce driver travel times when compared to alternative route recommendation strategies.

Iterative Recommendations based on Monte Carlo Sampling and Trust Estimation in Multi-Stage Vehicular Traffic Routing Games

TL;DR

The paper tackles urban congestion arising from selfish routing by modeling ITS-DVS interactions as a multi-stage routing game with dynamic driver trust. It introduces ROSTER, a Monte Carlo–based algorithm that updates trust beliefs and re-evaluates best responses to approximate a Bayesian Nash equilibrium. Experiments on Manhattan-inspired Pigou and Sioux Falls networks show that ROSTER reduces network congestion and driver travel time compared with LLF and TASR baselines, with the driver trust prediction converging to the true value as interactions grow. These results demonstrate a practical, trust-aware routing framework for ITS that can balance individual travel time with system-wide performance, with potential extensions to multi-driver scenarios and adaptive information design.

Abstract

The shortest-time route recommendations offered by modern navigation systems fuel selfish routing in urban vehicular traffic networks and are therefore one of the main reasons for the growth of congestion. In contrast, intelligent transportation systems (ITS) prefer to steer driver-vehicle systems (DVS) toward system-optimal route recommendations, which are primarily designed to mitigate network congestion. However, due to the misalignment in motives, drivers exhibit a lack of trust in the ITS. This paper models the interaction between a DVS and an ITS as a novel, multi-stage routing game where the DVS exhibits dynamics in its trust towards the recommendations of ITS based on counterfactual and observed game outcomes. Specifically, DVS and ITS are respectively modeled as a travel-time minimizer and network congestion minimizer, each having nonidentical prior beliefs about the network state. A novel approximate algorithm to compute the Bayesian Nash equilibrium, called ROSTER(Recommendation Outcome Sampling with Trust Estimation and Re-evaluation), is proposed based on Monte Carlo sampling with trust belief updating to determine the best response route recommendations of the ITS at each stage of the game. Simulation results demonstrate that the trust prediction error in the proposed algorithm converges to zero with a growing number of multi-stage DVS-ITS interactions and is effectively able to both mitigate congestion and reduce driver travel times when compared to alternative route recommendation strategies.

Paper Structure

This paper contains 19 sections, 1 theorem, 28 equations, 6 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related Work
  4. Problem Formulation
  5. Traffic Network
  6. Players and Game Progression
  7. Bayesian Nash Equilibrium
  8. Proposed Methodology
  9. Best Response of the Driver
  10. Best Response of the System
  11. Properties of the ROSTER algorithm
  12. Trust Dynamics
  13. Driver Trust Updating
  14. System Trust Prediction Updating
  15. Experimental Evaluation
  16. ...and 4 more sections

Key Result

Theorem 1

The network congestion resulting from the ROSTER algorithm is given by where $r_i^*$ is the optimal selfish route for the driver, and $r_i^\circledast$ is the route that minimizes network congestion.

Figures (6)

  • Figure 1: Three-Stage Interaction between the system (P1) and driver (P2)
  • Figure 2: Information exchange and decision-making within one driver-system interaction (as in Fig. \ref{['Fig: Negotiation Game 3 Stage']}, player P1 is the system, and player P2 the driver)
  • Figure 3: Average congestion ratios of all strategies for 1-stage, 2-stage, and 3-stage interactions in Sioux Falls network
  • Figure 4: Average travel time ratios of all strategies for 1-stage, 2-stage, and 3-stage interactions in Sioux Falls network
  • Figure 5: Trust prediction error of ROSTER for 1-stage, 2-stage, and 3-stage interactions in Sioux Falls network
  • ...and 1 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof