# MultiNash-PF: A Particle Filtering Approach for Computing Multiple Local Generalized Nash Equilibria in Trajectory Games

arXiv: https://arxiv.org/abs/2410.05554 · HTML: https://mlsanity.com/paper/2410.05554/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2024.

## Built on by (most cited first, 1 of 1)

- [MIMIC-D: Multi-modal Imitation for MultI-agent Coordination with Decentralized Diffusion Policies](https://mlsanity.com/paper/2509.14159/) (2025)

## Abstract (arXiv)

Modern robotic systems frequently engage in complex multi-agent interactions, many of which are inherently multi-modal, i.e., they can lead to multiple distinct outcomes. To interact effectively, robots must recognize the possible interaction modes and adapt to the one preferred by other agents. In this work, we propose MultiNash-PF, an efficient algorithm for capturing the multimodality in multi-agent interactions. We model interaction outcomes as equilibria of a game-theoretic planner, where each equilibrium corresponds to a distinct interaction mode. Our framework formulates interactive planning as Constrained Potential Trajectory Games (CPTGs), in which local Generalized Nash Equilibria (GNEs) represent plausible interaction outcomes. We propose to integrate the potential game approach with implicit particle filtering, a sample-efficient method for non-convex trajectory optimization. We utilize implicit particle filtering to identify the coarse estimates of multiple local minimizers of the game's potential function. MultiNash-PF then refines these estimates with optimization solvers, obtaining different local GNEs. We show through numerical simulations that MultiNash-PF reduces computation time by up to 50% compared to a baseline. We further demonstrate the effectiveness of our algorithm in real-world human-robot interaction scenarios, where it successfully accounts for the multi-modal nature of interactions and resolves potential conflicts in real-time.