# Learning Game-Theoretic Models of Multiagent Trajectories Using Implicit Layers

arXiv: https://arxiv.org/abs/2008.07303 · HTML: https://mlsanity.com/paper/2008.07303/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2020.

## Built on by (most cited first, 13 of 13)

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- [Targeted Reduction of Causal Models](https://mlsanity.com/paper/2311.18639/) (2023)
- [Energy-based Potential Games for Joint Motion Forecasting and Control](https://mlsanity.com/paper/2312.01811/) (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)
- [I Know You Can't See Me: Dynamic Occlusion-Aware Safety Validation of Strategic Planners for Autonomous Vehicles Using Hypergames](https://mlsanity.com/paper/2109.09807/) (2021)
- [Generalized dynamic cognitive hierarchy models for strategic driving behavior](https://mlsanity.com/paper/2109.09861/) (2021)
- [Auto-Encoding Bayesian Inverse Games](https://mlsanity.com/paper/2402.08902/) (2024)
- [Learning soft interventions in complex equilibrium systems](https://mlsanity.com/paper/2112.05729/) (2021)
- [Fail-Safe Adversarial Generative Imitation Learning](https://mlsanity.com/paper/2203.01696/) (2022)
- [A taxonomy of strategic human interactions in traffic conflicts](https://mlsanity.com/paper/2109.13367/) (2021)
- [NashFormer: Leveraging Local Nash Equilibria for Semantically Diverse Trajectory Prediction](https://mlsanity.com/paper/2305.17600/) (2023)
- [Bayesian Inverse Games with High-Dimensional Multi-Modal Observations](https://mlsanity.com/paper/2601.00696/) (2026)

## Abstract (arXiv)

For prediction of interacting agents' trajectories, we propose an end-to-end trainable architecture that hybridizes neural nets with game-theoretic reasoning, has interpretable intermediate representations, and transfers to downstream decision making. It uses a net that reveals preferences from the agents' past joint trajectory, and a differentiable implicit layer that maps these preferences to local Nash equilibria, forming the modes of the predicted future trajectory. Additionally, it learns an equilibrium refinement concept. For tractability, we introduce a new class of continuous potential games and an equilibrium-separating partition of the action space. We provide theoretical results for explicit gradients and soundness. In experiments, we evaluate our approach on two real-world data sets, where we predict highway driver merging trajectories, and on a simple decision-making transfer task.