[Paper Review] Game-theoretic Modeling of Traffic in Unsignalized Intersection Network for Autonomous Vehicle Control Verification and Validation

Ran Tian, Nan Li+3 more|arXiv (Cornell University)|Oct 16, 2019

Traffic control and managementEngineering46 references19 citations

TL;DR

This paper proposes a game-theoretic framework using level-k modeling, receding-horizon optimization, and imitation learning to simulate heterogeneous, interactive vehicle behavior at unsignalized urban intersections. The method enables computationally efficient virtual testing of autonomous vehicle (AV) control systems, with results showing optimal AV performance when collision avoidance parameters are tuned to balance aggression and caution across varying traffic models.

ABSTRACT

For a foreseeable future, autonomous vehicles (AVs) will operate in traffic together with human-driven vehicles. Their planning and control systems need extensive testing, including early-stage testing in simulations where the interactions among autonomous/human-driven vehicles are represented. Motivated by the need for such simulation tools, we propose a game-theoretic approach to modeling vehicle interactions, in particular, for urban traffic environments with unsignalized intersections. We develop traffic models with heterogeneous (in terms of their driving styles) and interactive vehicles based on our proposed approach, and use them for virtual testing, evaluation, and calibration of AV control systems. For illustration, we consider two AV control approaches, analyze their characteristics and performance based on the simulation results with our developed traffic models, and optimize the parameters of one of them.

Motivation & Objective

• To develop a computationally efficient simulation framework for virtual testing of autonomous vehicle (AV) control systems in urban traffic with unsignalized intersections.
• To model heterogeneous, interactive vehicle behaviors—especially human-driven and AV interactions—using a game-theoretic approach that captures realistic driving styles.
• To enable early-stage verification and validation of AV control systems by integrating the traffic model into simulation environments with realistic interaction dynamics.
• To optimize AV control parameters using a performance index that penalizes collisions and deadlocks while rewarding high average speed.
• To demonstrate the framework’s utility through case studies on rule-based and adaptive AV control strategies in varying traffic models.

Proposed method

• The framework models vehicle decision-making as a dynamic game using level-k game theory, where vehicles predict others’ behaviors up to a finite level of reasoning.
• A hybrid algorithm integrates level-k modeling, receding-horizon optimization for real-time decision-making, and imitation learning to infer driving policies from observed behavior.
• Vehicle kinematics are modeled using standard dynamics, while interaction rules are derived from game-theoretic equilibrium concepts under uncertainty.
• The control policy is learned via imitation learning using expert demonstrations, with optimization performed over a finite horizon to ensure safety and efficiency.
• A performance index function combines penalties for collisions and deadlocks and rewards high average speed, with adjustable weighting factors.
• The model is validated in a simulation environment with 15 vehicles at an unsignalized intersection, using varying traffic models (level-1 to level-3) to represent different driving styles.

Experimental results

Research questions

• RQ1 How can a computationally efficient game-theoretic model simulate heterogeneous, interactive vehicle behavior at unsignalized urban intersections?
• RQ2 What is the impact of varying driving styles (aggressive to conservative) on AV control system performance in mixed-traffic scenarios?
• RQ3 How does the integration of receding-horizon optimization and imitation learning improve the scalability and realism of AV simulation?
• RQ4 What parameter settings in a rule-based AV control strategy yield optimal performance across diverse traffic models?
• RQ5 Can a unified simulation framework effectively support the verification and validation of AV control systems in complex urban traffic environments?

Key findings

• The optimal value of the collision avoidance radius $ R_c $ for the rule-based control approach lies in the range [11.5, 13] meters, where performance is consistently good and robust across different traffic models.
• Performance degrades significantly when $ R_c $ is in the range [7.5, 11] meters due to conflicting behaviors between moderately aggressive and conservative vehicles.
• Very small $ R_c $ values (6–7.5 m) yield good results only in conservative traffic models (level-1), as aggressive AV behavior is safely accommodated by yielding vehicles.
• Large $ R_c $ values lead to excessive caution, causing frequent deadlocks as the AV fails to enter intersections despite safe conditions.
• The performance index function effectively balances safety (collision and deadlock avoidance) and efficiency (average speed), with optimal tuning achievable via simulation.
• The proposed framework enables scalable, realistic simulation of AV interactions at unsignalized intersections, supporting effective V&V of control systems.