# ALGAMES: A Fast Solver for Constrained Dynamic Games

arXiv: https://arxiv.org/abs/1910.09713 · HTML: https://mlsanity.com/paper/1910.09713/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2019.

## Built on by (most cited first, 9 of 9)

- [UMBRELLA: Uncertainty-Aware Model-Based Offline Reinforcement Learning Leveraging Planning](https://mlsanity.com/paper/2111.11097/) (2021)
- [Blending Data-Driven Priors in Dynamic Games](https://mlsanity.com/paper/2402.14174/) (2024)
- [Multi-Agent Strategy Explanations for Human-Robot Collaboration](https://mlsanity.com/paper/2311.11955/) (2023)
- [Integrated Decision Making and Trajectory Planning for Autonomous Driving Under Multimodal Uncertainties: A Bayesian Game Approach](https://mlsanity.com/paper/2409.13993/) (2024)
- [Online Competitive Information Gathering for Partially Observable Trajectory Games](https://mlsanity.com/paper/2506.01927/) (2025)
- [Non-zero-sum Game Control for Multi-vehicle Driving via Reinforcement Learning](https://mlsanity.com/paper/2302.03958/) (2023)
- [NashFormer: Leveraging Local Nash Equilibria for Semantically Diverse Trajectory Prediction](https://mlsanity.com/paper/2305.17600/) (2023)
- [PIER-Flow: Physics-Informed Efficient Rectified Flow for Real-Time Mobile Robot Navigation](https://mlsanity.com/paper/2607.10288/) (2026)
- [Input-to-State Stability Framework for Fully Distributed Primal-Dual Dynamics for Quadratic GNEPs Without Multiplier Consensus](https://mlsanity.com/paper/2609.06983/) (2026)

## Abstract (arXiv)

Dynamic games are an effective paradigm for dealing with the control of multiple interacting actors. This paper introduces ALGAMES (Augmented Lagrangian GAME-theoretic Solver), a solver that handles trajectory optimization problems with multiple actors and general nonlinear state and input constraints. Its novelty resides in satisfying the first order optimality conditions with a quasi-Newton root-finding algorithm and rigorously enforcing constraints using an augmented Lagrangian formulation. We evaluate our solver in the context of autonomous driving on scenarios with a strong level of interactions between the vehicles. We assess the robustness of the solver using Monte Carlo simulations. It is able to reliably solve complex problems like ramp merging with three vehicles three times faster than a state-of-the-art DDP-based approach. A model predictive control (MPC) implementation of the algorithm demonstrates real-time performance on complex autonomous driving scenarios with an update frequency higher than 60 Hz.