# Multimodal Maximum Entropy Dynamic Games

arXiv: https://arxiv.org/abs/2201.12925 · HTML: https://mlsanity.com/paper/2201.12925/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2022.

## Built on by (most cited first, 3 of 3)

- [Mixed Strategy Nash Equilibrium for Crowd Navigation](https://mlsanity.com/paper/2403.01537/) (2024)
- [NashFormer: Leveraging Local Nash Equilibria for Semantically Diverse Trajectory Prediction](https://mlsanity.com/paper/2305.17600/) (2023)
- [Feint Behaviors and Strategies: Formalization, Implementation and Evaluation](https://mlsanity.com/paper/2403.07932/) (2024)

## Abstract (arXiv)

Environments with multi-agent interactions often result a rich set of modalities of behavior between agents due to the inherent suboptimality of decision making processes when agents settle for satisfactory decisions. However, existing algorithms for solving these dynamic games are strictly unimodal and fail to capture the intricate multimodal behaviors of the agents. In this paper, we propose MMELQGames (Multimodal Maximum-Entropy Linear Quadratic Games), a novel constrained multimodal maximum entropy formulation of the Differential Dynamic Programming algorithm for solving generalized Nash equilibria. By formulating the problem as a certain dynamic game with incomplete and asymmetric information where agents are uncertain about the cost and dynamics of the game itself, the proposed method is able to reason about multiple local generalized Nash equilibria, enforce constraints with the Augmented Lagrangian framework and also perform Bayesian inference on the latent mode from past observations. We assess the efficacy of the proposed algorithm on two illustrative examples: multi-agent collision avoidance and autonomous racing. In particular, we show that only MMELQGames is able to effectively block a rear vehicle when given a speed disadvantage and the rear vehicle can overtake from multiple positions.