PSN Game: Game-theoretic Prediction and Planning via a Player Selection Network

TL;DR

This work tackles the computational bottleneck of game-theoretic multi-agent planning with many agents by introducing PSN Game, which learns a Player Selection Network (PSN) to prune the planning problem to a small, influential subset of agents. A Goal Inference Network (GIN) enables operation under incomplete information by estimating others’ goals, feeding inferred objectives to a differentiable masked Nash solver in a receding-horizon framework. Empirical results show substantial runtime reductions (50–75%), while achieving state-of-the-art prediction accuracy and planning safety across simulations and real pedestrian datasets, and demonstrating robust generalization to unseen agent counts and incomplete information. The approach is flexible, requiring only past trajectory data at runtime and integrating seamlessly with existing multi-agent planning pipelines, making it practical for real-time, large-scale systems.

Abstract

While game-theoretic planning frameworks are effective at modeling multi-agent interactions, they require solving large optimization problems where the number of variables increases with the number of agents, resulting in long computation times that limit their use in large-scale, real-time systems. To address this issue, we propose 1) PSN Game: a learning-based, game-theoretic prediction and planning framework that reduces runtime by learning a Player Selection Network (PSN); and 2) a Goal Inference Network (GIN) that makes it possible to use the PSN in incomplete information games where agents' intentions are unknown. A PSN outputs a player selection mask that distinguishes influential players from less relevant ones, enabling the ego player to solve a smaller, masked game involving only selected players. By reducing the number of players in the game, and therefore reducing the number of variables in the corresponding optimization problem, PSN directly lowers computation time. The PSN Game framework is more flexible than existing player selection methods as it 1) relies solely on observations of players' past trajectories, without requiring full state, action, or other game-specific information; and 2) requires no online parameter tuning. Experiments in both simulated scenarios and human trajectory datasets demonstrate that PSNs outperform baseline selection methods in 1) prediction accuracy; and 2) planning safety. PSNs also generalize effectively to real-world scenarios in which agents' objectives are unknown without fine-tuning. By selecting only the most relevant players for decision-making, PSN Game offers a general mechanism for reducing planning complexity that can be seamlessly integrated into existing multi-agent planning frameworks.

Figures (3)

• Figure 1: Overview of our game-theoretic prediction and planning framework via the Player Selection Network (PSN) and the Goal Inference Network (GIN). At each timestep, the ego player (blue) observes other agents' past trajectories and inputs them to PSN. The network selects important players (red) and excludes less relevant ones (green). The ego player then solves a masked game over the selected subset to obtain the Nash strategy $u_{k|k}^{i*}$ and updates its state using \ref{['eqn:nashdynamics']}.
• Figure 2: Computation time using CLeARoboticsLab vs. the number of players in the game given in Section \ref{['subsec:game_structure']}. Time consumption grows cubically as player number increases.
• Figure 3: Trajectory visualization for PSN-Full-Rank (Top), PSN-Full-Threshold (Middle), and All (Bottom) in a 4 agent scenario. The ego agent (blue) iteratively solves the masked game that includes selected players (red) from the PSN and excludes irrelevant players (gray) for the equilibrium strategy.

Theorems & Definitions (3)

• Definition 1: Player Selection Mask
• Definition 2: Masked Nash Game
• Remark 1