# GamePlan: Game-Theoretic Multi-Agent Planning with Human Drivers at Intersections, Roundabouts, and Merging

arXiv: https://arxiv.org/abs/2109.01896 · HTML: https://mlsanity.com/paper/2109.01896/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2021.

## Built on by (most cited first, 16 of 16)

- [Principles and Guidelines for Evaluating Social Robot Navigation Algorithms](https://mlsanity.com/paper/2306.16740/) (2023)
- [Game-Theoretic Planning for Autonomous Driving among Risk-Aware Human Drivers](https://mlsanity.com/paper/2205.00562/) (2022)
- [Connected and Automated Vehicles in Mixed-Traffic: Learning Human Driver Behavior for Effective On-Ramp Merging](https://mlsanity.com/paper/2304.00397/) (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)
- [SOCIALGYM 2.0: Simulator for Multi-Agent Social Robot Navigation in Shared Human Spaces](https://mlsanity.com/paper/2303.05584/) (2023)
- [Decentralized Social Navigation with Non-Cooperative Robots via Bi-Level Optimization](https://mlsanity.com/paper/2306.08815/) (2023)
- [IR-STP: Enhancing Autonomous Driving with Interaction Reasoning in Spatio-Temporal Planning](https://mlsanity.com/paper/2311.02850/) (2023)
- [Integrated Decision Making and Trajectory Planning for Autonomous Driving Under Multimodal Uncertainties: A Bayesian Game Approach](https://mlsanity.com/paper/2409.13993/) (2024)
- [Multi-Agent Reinforcement Learning in Intelligent Transportation Systems: A Comprehensive Survey](https://mlsanity.com/paper/2508.20315/) (2025)
- [Multi-Agent Chance-Constrained Stochastic Shortest Path with Application to Risk-Aware Intelligent Intersection](https://mlsanity.com/paper/2210.01766/) (2022)
- [Prompt-Driven Domain Adaptation for End-to-End Autonomous Driving via In-Context RL](https://mlsanity.com/paper/2511.12755/) (2025)
- [MTR-VP: Towards End-to-End Trajectory Planning through Context-Driven Image Encoding and Multiple Trajectory Prediction](https://mlsanity.com/paper/2511.22181/) (2025)
- [Markov Potential Game and Multi-Agent Reinforcement Learning for Autonomous Driving](https://mlsanity.com/paper/2603.19188/) (2026)
- [Optimizing Crowd-Aware Multi-Agent Path Finding through Local Communication with Graph Neural Networks](https://mlsanity.com/paper/2309.10275/) (2023)
- [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 new method for multi-agent planning involving human drivers and autonomous vehicles (AVs) in unsignaled intersections, roundabouts, and during merging. In multi-agent planning, the main challenge is to predict the actions of other agents, especially human drivers, as their intentions are hidden from other agents. Our algorithm uses game theory to develop a new auction, called GamePlan, that directly determines the optimal action for each agent based on their driving style (which is observable via commonly available sensors). GamePlan assigns a higher priority to more aggressive or impatient drivers and a lower priority to more conservative or patient drivers; we theoretically prove that such an approach is game-theoretically optimal prevents collisions and deadlocks. We compare our approach with prior state-of-the-art auction techniques including economic auctions, time-based auctions (first-in first-out), and random bidding and show that each of these methods result in collisions among agents when taking into account driver behavior. We compare with methods based on DRL, deep learning, and game theory and present our benefits over these approaches. Finally, we show that our approach can be implemented in the real-world with human drivers.