# Learning to Play Trajectory Games Against Opponents with Unknown Objectives

arXiv: https://arxiv.org/abs/2211.13779 · HTML: https://mlsanity.com/paper/2211.13779/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2022.

## Built on by (most cited first, 11 of 11)

- [Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification](https://mlsanity.com/paper/2502.02133/) (2025)
- [Energy-based Potential Games for Joint Motion Forecasting and Control](https://mlsanity.com/paper/2312.01811/) (2023)
- [DRL-Based Trajectory Tracking for Motion-Related Modules in Autonomous Driving](https://mlsanity.com/paper/2308.15991/) (2023)
- [Blending Data-Driven Priors in Dynamic Games](https://mlsanity.com/paper/2402.14174/) (2024)
- [On a Connection between Differential Games, Optimal Control, and Energy-based Models for Multi-Agent Interactions](https://mlsanity.com/paper/2308.16539/) (2023)
- [Safety-Critical Traffic Simulation with Adversarial Transfer of Driving Intentions](https://mlsanity.com/paper/2503.05180/) (2025)
- [Auto-Encoding Bayesian Inverse Games](https://mlsanity.com/paper/2402.08902/) (2024)
- [Bayesian Inverse Games with High-Dimensional Multi-Modal Observations](https://mlsanity.com/paper/2601.00696/) (2026)
- [Generalized Information Gathering Under Dynamics Uncertainty](https://mlsanity.com/paper/2601.21988/) (2026)
- [Zero Shot Coordination for Sparse Reward Tasks with Diverse Reward Shapings](https://mlsanity.com/paper/2604.25076/) (2026)
- [AI Coaching for Accelerating Human Skill Development with Reinforcement Learning](https://mlsanity.com/paper/2606.25337/) (2026)

## Abstract (arXiv)

Many autonomous agents, such as intelligent vehicles, are inherently required to interact with one another. Game theory provides a natural mathematical tool for robot motion planning in such interactive settings. However, tractable algorithms for such problems usually rely on a strong assumption, namely that the objectives of all players in the scene are known. To make such tools applicable for ego-centric planning with only local information, we propose an adaptive model-predictive game solver, which jointly infers other players' objectives online and computes a corresponding generalized Nash equilibrium (GNE) strategy. The adaptivity of our approach is enabled by a differentiable trajectory game solver whose gradient signal is used for maximum likelihood estimation (MLE) of opponents' objectives. This differentiability of our pipeline facilitates direct integration with other differentiable elements, such as neural networks (NNs). Furthermore, in contrast to existing solvers for cost inference in games, our method handles not only partial state observations but also general inequality constraints. In two simulated traffic scenarios, we find superior performance of our approach over both existing game-theoretic methods and non-game-theoretic model-predictive control (MPC) approaches. We also demonstrate our approach's real-time planning capabilities and robustness in two hardware experiments.