# Game-Theoretic Planning for Autonomous Driving among Risk-Aware Human Drivers

arXiv: https://arxiv.org/abs/2205.00562 · HTML: https://mlsanity.com/paper/2205.00562/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Cooperative and V2X driving, one of 9 directions in End-to-end autonomous driving.
- Builds on 15 of its 55 references that are in the map.
- First posted on arXiv 1 May 2022.

## Placed in

- End-to-end autonomous driving / [Cooperative and V2X driving](https://mlsanity.com/driving/cooperative-and-v2x-driving/)

## Builds on (most cited first, 15 of 15)

- [Machine Theory of Mind](https://mlsanity.com/paper/1802.07740/) (2018)
- [Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach](https://mlsanity.com/paper/1506.02188/) (2015)
- [Social Attention for Autonomous Decision-Making in Dense Traffic](https://mlsanity.com/paper/1911.12250/) (2019)
- [When Humans Aren't Optimal: Robots that Collaborate with Risk-Aware Humans](https://mlsanity.com/paper/2001.04377/) (2020)
- [CMetric: A Driving Behavior Measure Using Centrality Functions](https://mlsanity.com/paper/2003.04424/) (2020)
- [GamePlan: Game-Theoretic Multi-Agent Planning with Human Drivers at Intersections, Roundabouts, and Merging](https://mlsanity.com/paper/2109.01896/) (2021)
- [A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems](https://mlsanity.com/paper/1902.11277/) (2019)
- [Risk-Aware Planning and Assignment for Ground Vehicles using Uncertain Perception from Aerial Vehicles](https://mlsanity.com/paper/2003.11675/) (2020)
- [Using Graph-Theoretic Machine Learning to Predict Human Driver Behavior](https://mlsanity.com/paper/2111.02964/) (2021)
- [GraphRQI: Classifying Driver Behaviors Using Graph Spectrums](https://mlsanity.com/paper/1910.00049/) (2019)
- [Safety-Aware Optimal Control of Stochastic Systems Using Conditional Value-at-Risk](https://mlsanity.com/paper/1802.07903/) (2018)
- [GAMEOPT: Optimal Real-time Multi-Agent Planning and Control for Dynamic Intersections](https://mlsanity.com/paper/2202.11572/) (2022)
- [CVaR-based Flight Energy Risk Assessment for Multirotor UAVs using a Deep Energy Model](https://mlsanity.com/paper/2105.15189/) (2021)
- [A Framework for Time-Consistent, Risk-Averse Model Predictive Control: Theory and Algorithms](https://mlsanity.com/paper/1511.06981/) (2015)
- [Risk-Aware Path Planning for Ground Vehicles using Occluded Aerial Images](https://mlsanity.com/paper/2104.11709/) (2021)

## Built on by (most cited first, 7 of 7)

- [Principles and Guidelines for Evaluating Social Robot Navigation Algorithms](https://mlsanity.com/paper/2306.16740/) (2023)
- [SOCIALMAPF: Optimal and Efficient Multi-Agent Path Finding with Strategic Agents for Social Navigation](https://mlsanity.com/paper/2210.08390/) (2022)
- [Multi-Agent Inverse Reinforcement Learning in Real World Unstructured Pedestrian Crowds](https://mlsanity.com/paper/2405.16439/) (2024)
- [Decentralized Social Navigation with Non-Cooperative Robots via Bi-Level Optimization](https://mlsanity.com/paper/2306.08815/) (2023)
- [Prompt-Driven Domain Adaptation for End-to-End Autonomous Driving via In-Context RL](https://mlsanity.com/paper/2511.12755/) (2025)
- [Robust Planning for Autonomous Driving via Mixed Adversarial Diffusion Predictions](https://mlsanity.com/paper/2505.12327/) (2025)
- [Are LLMs The Way Forward? A Case Study on LLM-Guided Reinforcement Learning for Decentralized Autonomous Driving](https://mlsanity.com/paper/2511.12751/) (2025)

## Abstract (arXiv)

We present a novel approach for risk-aware planning with human agents in multi-agent traffic scenarios. Our approach takes into account the wide range of human driver behaviors on the road, from aggressive maneuvers like speeding and overtaking, to conservative traits like driving slowly and conforming to the right-most lane. In our approach, we learn a mapping from a data-driven human driver behavior model called the CMetric to a driver's entropic risk preference. We then use the derived risk preference within a game-theoretic risk-sensitive planner to model risk-aware interactions among human drivers and an autonomous vehicle in various traffic scenarios. We demonstrate our method in a merging scenario, where our results show that the final trajectories obtained from the risk-aware planner generate desirable emergent behaviors. Particularly, our planner recognizes aggressive human drivers and yields to them while maintaining a greater distance from them. In a user study, participants were able to distinguish between aggressive and conservative simulated drivers based on trajectories generated from our risk-sensitive planner. We also observe that aggressive human driving results in more frequent lane-changing in the planner. Finally, we compare the performance of our modified risk-aware planner with existing methods and show that modeling human driver behavior leads to safer navigation.