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Human-Like Decision Making for Autonomous Driving: A Noncooperative Game Theoretic Approach

Peng Hang, Chen Lv, Yang Xing, Chao Huang, Zhongxu Hu

arXiv:2005.11064v2cs.ROeess.SY

TL;DR

With human-driven and autonomous vehicles expected to share roads, this paper addresses how AVs can interact in human-like ways and accommodate differing driving preferences. It models driving styles and social interaction through noncooperative Nash and Stackelberg games, finding both produce reasonable decisions and Stackelberg performs better than Nash across safety, comfort, and efficiency.

  • Problem

    With human-driven and autonomous vehicles expected to share roads, the paper addresses how AVs can interact in human-like ways and accommodate differing preferences for safety, comfort, and travel efficiency.

    Source: B. Human-like Decision Making for… · p. 2

  • Method

    The framework identifies three driving styles from real-world data, embeds their social-interaction characteristics in decision models, and applies Nash and Stackelberg noncooperative games.

    Source: C. Contribution · p. 2

  • Results

    Both game-theoretic approaches generated reasonable AV decisions, while Stackelberg performed better than Nash in driving safety, ride comfort, and travel efficiency.

    Source: C. Discussion of the Testing Results · p. 10

  • Takeaways & Limitations

    The findings support using noncooperative game-theoretic approaches to simulate human-driver interaction and produce reasonable AV decisions in the tested scenarios.

    Source: C. Discussion of the Testing Results · p. 10

    The framework has limitations in varied complex traffic scenarios, where changing conditions require different decision models and greater system complexity increases computational demands.

    Source: C. Discussion of the Testing Results · p. 10

Abstract

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Considering that human-driven vehicles and autonomous vehicles (AVs) will coexist on roads in the future for a long time, how to merge AVs into human drivers traffic ecology and minimize the effect of AVs and their misfit with human drivers, are issues worthy of consideration. Moreover, different passengers have different needs for AVs, thus, how to provide personalized choices for different passengers is another issue for AVs. Therefore, a human-like decision making framework is designed for AVs in this paper. Different driving styles and social interaction characteristics are formulated for AVs regarding driving safety, ride comfort and travel efficiency, which are considered in the modeling process of decision making. Then, Nash equilibrium and Stackelberg game theory are applied to the noncooperative decision making. In addition, potential field method and model predictive control (MPC) are combined to deal with the motion prediction and planning for AVs, which provides predicted motion information for the decision-making module. Finally, two typical testing scenarios of lane change, i.e., merging and overtaking, are carried out to evaluate the feasibility and effectiveness of the proposed decision-making framework considering different human-like behaviors. Testing results indicate that both the two game theoretic approaches can provide reasonable human-like decision making for AVs. Compared with the Nash equilibrium approach, under the normal driving style, the cost value of decision making using the Stackelberg game theoretic approach is reduced by over 20%.

I. INTRODUCTION … C. Contribution

The paper proposes human-like AV decision making that models driving styles and social interactions through noncooperative games, with MPC and potential fields supporting motion prediction and path generation. It motivates this design by the expected coexistence of human-driven and autonomous vehicles and passengers’ differing preferences for safety, comfort, and efficiency.

I. INTRODUCTION

  • Decision making links AV environment perception to motion control and affects driving safety, ride comfort, travel efficiency, and energy consumption.The paper describes the decision-making module as the AV’s “brain.”Source: §I · p. 1

A. Decision Making for AVs

  • Prior probabilistic approaches model decision uncertainty,,,,, while MCDM and MADM address complex urban environments,.The review notes that some probabilistic approaches have difficulty handling complex, dynamic decision missions.Source: A. Decision Making for AVs · p. 1
  • Learning-based methods include KELM, SVM, DNNs, and reinforcement learning,,, but dataset quality, data demands, or learning efficiency remain limitations.The review also describes rule-based expert systems and fuzzy logic as interpretable approaches that struggle with scenario variety and increasing system complexity.Source: A. Decision Making for AVs · pp. 1–2

B. Human-like Decision Making for Autonomous Driving

  • Human-like AV behavior could make vehicles more predictable to human drivers and improve interaction in mixed traffic, but game-theoretic studies rarely considered different driving styles, [26],.Prior work also explored human-like lane-change, multi-point-turn, and risk-handling decisions,,, as well as hybrid potential maps.Source: B. Human-like Decision Making for… · p. 2
  • Passengers may prioritize safety and comfort or travel efficiency differently, so human-like AV decision making should offer personalized driving-style options.The paper contrasts comfort and safety needs for pregnant women, elderly people, and children with efficiency needs for commuters or passengers rushing to flights.Source: B. Human-like Decision Making for… · p. 2

C. Contribution

  • The paper extracts three driving styles from real-world data and embeds their characteristics and social interactions in AV decision-making models.It formulates decisions and interactions using Nash equilibrium and Stackelberg noncooperative games.Source: C. Contribution · p. 2
  • Both Nash equilibrium and Stackelberg games generate reasonable AV decisions, with Stackelberg advantageous in resultant decision-making performance.The paper tests and validates the algorithms through simulation in various scenarios.Source: C. Contribution · p. 2, B. Human-like Decision Making for… · p. 2
  • Algorithms combining MPC with potential fields realize high-accuracy motion prediction and collision-free path generation for AVs.Source: C. Contribution · p. 2

D. Paper Organization … A. Characteristic Analysis of Different Driving Styles

The paper develops a human-like decision-making framework for AVs and uses NGSIM freeway data to characterize aggressive, normal, and conservative driving styles for modeling. These extracted characteristics inform AV decision-making and motion planning.

D. Paper Organization

  • The paper proceeds from the decision-making framework and integrated driver-vehicle model to game-theoretic decisions, MPC and potential-field planning, tests, and conclusions.Source: D. Paper Organization · pp. 2–3

A. System Framework for Human-like Decision Making

  • The framework combines style-aware modeling, noncooperative game decision-making, and potential-field-assisted MPC motion prediction and planning for lane changes.It uses surrounding vehicles’ motion states and positions to support decision-making and planning, including collision-avoidance paths.Source: A. System Framework for Human-like… · p. 3, Figure 1 · p. 3

B. Human-like Decision Making Modeling

  • Aggressive drivers prioritize dynamic performance and efficiency, conservative drivers prioritize safety and comfort, and normal drivers trade off all three.The paper associates driving styles with human factors and environmental conditions, and models them through driver and vehicle-road integration.Source: B. Human-like Decision Making Modeling · p. 3

C. Human-like Decision Making Methodology

  • The Nash approach treats AVs as equal independent players minimizing their own costs, whereas Stackelberg makes the ego car a leader accounting for surrounding cars’ behavior.Source: C. Human-like Decision Making… · p. 3

III. MODELING FOR HUMAN-LIKE DRIVING

  • The integrated human-like driving model combines extracted driver-style characteristics with the vehicle-road model for AV decision-making and motion planning.Source: §III · p. 3

A. Characteristic Analysis of Different Driving Styles

  • NGSIM analysis found aggressive drivers had higher velocity and acceleration but smaller time headway; conservative drivers showed the opposite, while normal drivers fell between them.Velocity represents travel efficiency, acceleration ride comfort, and time headway safety; the extracted patterns can inform AV cost-function design.Source: Figure 2 · p. 3, A. Characteristic Analysis of… · pp. 3–4

B. Driver Model · C. Vehicle-Road Model

The framework uses a preview-based driver model to predict AV motion and represent driving styles, then couples it with a simplified bicycle vehicle-road model. The integrated model supports vehicle motion prediction and control.

B. Driver Model

  • The driver model predicts a future vehicle point and steers to minimize its distance from the eye-defined preview point, whose sequence forms the planned path.Front-wheel steering realizes this objective.Source: B. Driver Model · p. 4
  • Driving style is reflected in driver delay, predicted time, and steering gain; conservative drivers have larger physical delay than aggressive drivers.Conservative drivers require more time for mental signal processing and muscular activation.Source: B. Driver Model · p. 4

C. Vehicle-Road Model

  • To simplify controller design, the four-wheel vehicle is represented by a two-wheel bicycle model.The paper uses this model as its vehicle-road representation.Source: C. Vehicle-Road Model · p. 4
  • Assuming a small front-wheel steering angle, the vehicle dynamics describe longitudinal and lateral velocity and yaw-rate changes from tire forces.The equations use front and rear longitudinal and lateral tire forces.Source: C. Vehicle-Road Model · p. 4
  • The bicycle model characterizes vehicle dynamics using lateral velocity, yaw rate, tire forces, wheelbases, mass, yaw inertia, cornering stiffness, and tire slip angles.The passage defines the tire forces and geometric and inertial parameters used in the model.Source: C. Vehicle-Road Model · p. 4
  • Combining the driver and vehicle-road models yields an integrated model with vehicle motion and steering states and the preview-point lateral position as its control input.The state includes longitudinal and lateral velocities, yaw rate, yaw angle, global position, steering angle, and steering rate.Source: C. Vehicle-Road Model · pp. 4–5

IV. DECISION MAKING BASED ON NONCOOPERATIVE GAME THEORY · A. Cost Function for Lane-change Decision Making

The section formulates lane-change decisions using weighted safety, ride-comfort, and travel-efficiency costs, then applies Nash equilibrium and Stackelberg game theory to noncooperative decisions. Different driving styles are represented through different cost weights.

IV. DECISION MAKING BASED ON NONCOOPERATIVE GAME THEORY

  • Nash equilibrium and Stackelberg game theory are applied to noncooperative lane-change decisions, with obstacle vehicles modeled only as accelerating or decelerating.Source: §IV · p. 5

A. Cost Function for Lane-change Decision Making

B. Noncooperative Decision Making Based on Nash Equilibrium

The section formulates lane changes as a noncooperative Nash game between an ego car (EC) and an autonomous car (AC), with a corresponding extension for ACs on both adjacent lanes.

B. Noncooperative Decision Making Based on Nash Equilibrium

  • The Nash formulation treats the EC and AC as two players, optimizing their longitudinal accelerations and the EC’s lane-change behavior subject to acceleration and velocity bounds.The section describes the accelerations as optimal choices and identifies the lane-change behavior as the EC’s decision variable.Source: B. Noncooperative Decision Making… · p. 6
  • With ACs in both the left and right lanes, the Nash formulation is rewritten using the two cost functions J1 and J2.The section points to Fig. 5 for this scenario and gives the rewritten objective as an optimization over the decision set.Source: B. Noncooperative Decision Making… · p. 6

C. Noncooperative Decision Making Based on Stackelberg Equilibrium

The section applies Stackelberg equilibrium to lane-change decisions, with EC as leader and AC as follower, so AC behavior affects EC’s decision. It contrasts this with Nash equilibrium’s equal, independent players and notes a reformulation for two ACs in adjacent lanes.

C. Noncooperative Decision Making Based on Stackelberg Equilibrium

V. MOTION PREDICTION AND PLANNING BASED ON THE POTENTIAL FIELD MODEL METHOD AND MPC

The section combines the potential field method with MPC to provide motion prediction and collision-avoidance planning for the decision-making framework.

V. MOTION PREDICTION AND PLANNING BASED ON THE POTENTIAL FIELD MODEL METHOD AND MPC

  • The potential field method models dynamic obstacles and roads, while its combination with MPC predicts motion states and collision-avoidance paths.The combined approach supports motion planning for the decision-making framework.Source: §V · p. 6

A. Potential Field Method for Collision Avoidance · B. Motion Prediction Based on MPC

The collision-avoidance potential field combines obstacle-vehicle and road fields. MPC predicts and plans ego-vehicle motion using a discretized time-varying model, weighted objectives, and constrained control optimization.

A. Potential Field Method for Collision Avoidance

  • The integrated collision-avoidance field combines obstacle-car and road potentials; obstacle cars include lead vehicles and adjacent cars.The road potential uses distance to a lane line, a safety threshold, and obstacle-car width.Source: A. Potential Field Method for… · pp. 6–7
  • The obstacle-car potential is defined by its center-of-gravity position, maximum value, convergence coefficients, heading, longitudinal velocity, and shape coefficient.Source: A. Potential Field Method for… · pp. 6–7

B. Motion Prediction Based on MPC

VI. TESTING RESULTS AND PERFORMANCE EVALUATION

The paper evaluates its human-like AV decision-making framework in two lane-change testing scenarios. In Scenario A, results distinguish driving-style tradeoffs and show lower decision-cost values for Stackelberg than Nash under normal driving.

VI. TESTING RESULTS AND PERFORMANCE EVALUATION

  • The framework was evaluated in two testing scenarios on MATLAB-Simulink; Scenario A models a highway merge where EC must change lanes as its lane ends, accounting for AC’s reaction.Initial EC and AC longitudinal velocities were 20 m/s and 15 m/s, respectively, with EC 2 m ahead of AC.Source: §VI · p. 7, Figure 6 · p. 7
  • Aggressive merging prioritized travel efficiency over safety, conservative driving prioritized safety, and normal driving balanced safety, comfort, and efficiency.Aggressive EC accelerated suddenly to increase the gap, while normal EC accelerated progressively and changed lanes only when the gap was large enough; conservative behavior was opposite to aggressive behavior.Source: §VI · pp. 7–8, Figure 7 · p. 8, Figure 8 · p. 8
  • In Scenario A, SE took longer than NE to decide on merging, producing a larger merging velocity and EC–AC gap.In SE, EC was the lead player and incorporated AC’s follower behavior into its decision, whereas in NE the vehicles were equal, independent players minimizing their own costs.Source: Table IV · p. 8, §VI · p. 8
  • Under normal driving, SE reduced EC’s driving-safety, ride-comfort, and travel-efficiency cost values by 22%, 20%, and 22%, respectively, versus NE.The reported cost values are RMS values.Source: Table V · p. 8, §VI · p. 8

B. Scenario B

In Scenario B, the overtaking decision varies with EC’s driving style, while SE yields lower costs than NE across driving performances. In the normal style, SE reduces safety, comfort, and travel-efficiency costs relative to NE.

B. Scenario B

  • Scenario B tests EC’s overtaking choice on a three-lane curved highway, where it must decide whether to follow slow LC or pass on either side amid AC1 and AC2.Initial speeds for LC, EC, AC1, and AC2 are 15, 20, 15, and 13 m/s, respectively.Source: B. Scenario B · pp. 8–9
  • Aggressive and normal EC choose a left lane change, whereas conservative EC keeps its lane because lane changing costs more than lane keeping.Aggressive EC accelerates more and completes overtaking sooner than normal EC; conservative EC decelerates to maintain a larger safe distance. The styles also differ in their preferred driving-performance costs: aggressive favors travel efficiency, while conservative favors safety and comfort.Source: Figure 11 · p. 9, Figure 12 · p. 9, Figure 13 · p. 9
  • For EC in Scenario B, SE has smaller cost values than NE for driving safety, ride comfort, and travel efficiency; in normal style, reductions are 31%, 34%, and 27%, respectively.Source: Table VII · p. 9, B. Scenario B · p. 9

C. Discussion of the Testing Results · VII. CONCLUSIONS AND FUTURE WORKS

The testing discussion finds that driving styles produce distinct trade-offs and that Stackelberg game decision-making performs better than Nash equilibrium across safety, comfort, and efficiency. The conclusion presents a human-like, personalized AV decision framework and identifies scenario adaptability, computation efficiency, and real-time validation as future work.

C. Discussion of the Testing Results

VII. CONCLUSIONS AND FUTURE WORKS

  • Greater system complexity requires more computation resources, so improving algorithmic efficiency is a future direction.Source: C. Discussion of the Testing Results · p. 10, §VII · p. 10
  • The framework combines style- and interaction-aware Nash and Stackelberg decision-making with potential-field and MPC planning for collision avoidance and motion prediction.Source: §VII · p. 10
  • Tests in two scenarios indicate the framework makes reasonable human-like decisions under different driving styles and offers personalized choices for passengers.Source: §VII · p. 10
  • Future work will use hardware-in-the-loop experiments to validate the algorithms’ real-time performance.Source: §VII · p. 10

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