# Driving is a Game: Combining Planning and Prediction with Bayesian Iterative Best Response arXiv: https://arxiv.org/abs/2512.03936 ยท HTML: https://mlsanity.com/paper/2512.03936/ ## Key facts - Cited by 1 papers in the map (data through 14 Oct 2026). - Placed in Imitation-learning end-to-end planners, one of 9 directions in End-to-end autonomous driving. - Builds on 32 of its 46 references that are in the map. - First posted on arXiv 3 Dec 2025. ## Placed in - End-to-end autonomous driving / [Imitation-learning end-to-end planners](https://mlsanity.com/driving/imitation-learning-end-to-end-planners/) ## Builds on (most cited first, 30 of 32) - [VectorNet: Encoding HD Maps and Agent Dynamics from Vectorized Representation](https://mlsanity.com/paper/2005.04259/) (2020) - [NuPlan: A closed-loop ML-based planning benchmark for autonomous vehicles](https://mlsanity.com/paper/2106.11810/) (2021) - [TransFuser: Imitation with Transformer-Based Sensor Fusion for Autonomous Driving](https://mlsanity.com/paper/2205.15997/) (2022) - [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021) - [Wayformer: Motion Forecasting via Simple & Efficient Attention Networks](https://mlsanity.com/paper/2207.05844/) (2022) - [Parting with Misconceptions about Learning-based Vehicle Motion Planning](https://mlsanity.com/paper/2306.07962/) (2023) - [MotionDiffuser: Controllable Multi-Agent Motion Prediction using Diffusion](https://mlsanity.com/paper/2306.03083/) (2023) - [Scene Transformer: A unified architecture for predicting multiple agent trajectories](https://mlsanity.com/paper/2106.08417/) (2021) - [GOHOME: Graph-Oriented Heatmap Output for future Motion Estimation](https://mlsanity.com/paper/2109.01827/) (2021) - [Diffusion-Based Planning for Autonomous Driving with Flexible Guidance](https://mlsanity.com/paper/2501.15564/) (2025) - [Urban Driver: Learning to Drive from Real-world Demonstrations Using Policy Gradients](https://mlsanity.com/paper/2109.13333/) (2021) - [Multimodal Trajectory Prediction Conditioned on Lane-Graph Traversals](https://mlsanity.com/paper/2106.15004/) (2021) - [PlanT: Explainable Planning Transformers via Object-Level Representations](https://mlsanity.com/paper/2210.14222/) (2022) - [LookOut: Diverse Multi-Future Prediction and Planning for Self-Driving](https://mlsanity.com/paper/2101.06547/) (2021) - [LaPred: Lane-Aware Prediction of Multi-Modal Future Trajectories of Dynamic Agents](https://mlsanity.com/paper/2104.00249/) (2021) - [LAformer: Trajectory Prediction for Autonomous Driving with Lane-Aware Scene Constraints](https://mlsanity.com/paper/2302.13933/) (2023) - [DTPP: Differentiable Joint Conditional Prediction and Cost Evaluation for Tree Policy Planning in Autonomous Driving](https://mlsanity.com/paper/2310.05885/) (2023) - [From Prediction to Planning With Goal Conditioned Lane Graph Traversals](https://mlsanity.com/paper/2302.07753/) (2023) - [JFP: Joint Future Prediction with Interactive Multi-Agent Modeling for Autonomous Driving](https://mlsanity.com/paper/2212.08710/) (2022) - [Can Vehicle Motion Planning Generalize to Realistic Long-tail Scenarios?](https://mlsanity.com/paper/2404.07569/) (2024) - [CaRL: Learning Scalable Planning Policies with Simple Rewards](https://mlsanity.com/paper/2504.17838/) (2025) - [Safe Real-World Autonomous Driving by Learning to Predict and Plan with a Mixture of Experts](https://mlsanity.com/paper/2211.02131/) (2022) - [The Integration of Prediction and Planning in Deep Learning Automated Driving Systems: A Review](https://mlsanity.com/paper/2308.05731/) (2023) - [Contingencies from Observations: Tractable Contingency Planning with Learned Behavior Models](https://mlsanity.com/paper/2104.10558/) (2021) - [StarNet: Joint Action-Space Prediction with Star Graphs and Implicit Global Frame Self-Attention](https://mlsanity.com/paper/2111.13566/) (2021) - [Game-Theoretic Modeling of Multi-Vehicle Interactions at Uncontrolled Intersections](https://mlsanity.com/paper/1904.05423/) (2019) - [MBAPPE: MCTS-Built-Around Prediction for Planning Explicitly](https://mlsanity.com/paper/2309.08452/) (2023) - [Bridging the Gap Between Multi-Step and One-Shot Trajectory Prediction via Self-Supervision](https://mlsanity.com/paper/2306.03367/) (2023) - [Conditional Unscented Autoencoders for Trajectory Prediction](https://mlsanity.com/paper/2310.19944/) (2023) - [When Planners Meet Reality: How Learned, Reactive Traffic Agents Shift nuPlan Benchmarks](https://mlsanity.com/paper/2510.14677/) (2025) ## Built on by (most cited first, 1 of 1) - [INTERACT: Interactive Planning for Autonomous Driving via Anchor-Conditioned Prediction and Trust-Region Refinement](https://mlsanity.com/paper/2609.31137/) (2026) ## Abstract (arXiv) Autonomous driving planning systems perform nearly perfectly in routine scenarios using lightweight, rule-based methods but still struggle in dense urban traffic, where lane changes and merges require anticipating and influencing other agents. Modern motion predictors offer highly accurate forecasts, yet their integration into planning is mostly rudimental: discarding unsafe plans. Similarly, end-to-end models offer a one-way integration that avoids the challenges of joint prediction and planning modeling under uncertainty. In contrast, game-theoretic formulations offer a principled alternative but have seen limited adoption in autonomous driving. We present Bayesian Iterative Best Response (BIBeR), a framework that unifies motion prediction and game-theoretic planning into a single interaction-aware process. BIBeR is the first to integrate a state-of-the-art predictor into an Iterative Best Response (IBR) loop, repeatedly refining the strategies of the ego vehicle and surrounding agents. This repeated best-response process approximates a Nash equilibrium, enabling bidirectional adaptation where the ego both reacts to and shapes the behavior of others. In addition, our proposed Bayesian confidence estimation quantifies prediction reliability and modulates update strength, more conservative under low confidence and more decisive under high confidence. BIBeR is compatible with modern predictors and planners, combining the transparency of structured planning with the flexibility of learned models. Experiments show that BIBeR achieves an 11% improvement over state-of-the-art planners on highly interactive interPlan lane-change scenarios, while also outperforming existing approaches on standard nuPlan benchmarks.