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

While game-theoretic planning frameworks are effective at modeling multi-agent interactions, they require solving optimization problems with hundreds or thousands of variables, resulting in long computation times that limit their use in large-scale, real-time systems. To address this issue, we propose PSN Game: a novel game-theoretic planning framework that reduces runtime by learning a Player Selection Network (PSN). 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 variables in the optimization problem, PSN directly lowers computation time. The PSN Game framework is more flexible than existing player selection methods as it i) relies solely on observations of players' past trajectories, without requiring full state, control, or other game-specific information; and ii) requires no online parameter tuning. We train PSNs in an unsupervised manner using a differentiable dynamic game solver, with reference trajectories from full-player games guiding the learning. Experiments in both simulated scenarios and human trajectory datasets demonstrate that i) PSNs outperform baseline selection methods in trajectory smoothness and length, while maintaining comparable safety and achieving a 10x speedup in runtime; and ii) PSNs generalize effectively to real-world scenarios without fine-tuning. By selecting only the most relevant players for decision-making, PSNs offer a general mechanism for reducing planning complexity that can be seamlessly integrated into existing multi-agent planning frameworks.