Effective Game-Theoretic Motion Planning via Nested Search

TL;DR

This paper introduces GTNS, a scalable game-theoretic motion planning method that efficiently computes Nash Equilibria for complex dynamical systems, enabling safe and realistic multi-agent interactions in autonomous driving scenarios.

Contribution

The paper presents GTNS, a novel nested search algorithm that overcomes scalability and local minima issues in game-theoretic motion planning for general dynamical systems.

Findings

Achieves solutions in seconds on standard hardware.

Handles complex, realistic multi-agent scenarios.

Provides explicit equilibrium selection based on global objectives.

Abstract

To facilitate effective, safe deployment in the real world, individual robots must reason about interactions with other agents, which often occur without explicit communication. Recent work has identified game theory, particularly the concept of Nash Equilibrium (NE), as a key enabler for behavior-aware decision-making. Yet, existing work falls short of fully unleashing the power of game-theoretic reasoning. Specifically, popular optimization-based methods require simplified robot dynamics and tend to get trapped in local minima due to convexification. Other works that rely on payoff matrices suffer from poor scalability due to the explicit enumeration of all possible trajectories. To bridge this gap, we introduce Game-Theoretic Nested Search (GTNS), a novel, scalable, and provably correct approach for computing NEs in general dynamical systems. GTNS efficiently searches the action space of all agents involved, while discarding trajectories that violate the NE constraint (no unilateral deviation) through an inner search over a lower-dimensional space. Our algorithm enables explicit selection among equilibria by utilizing a user-specified global objective, thereby capturing a rich set of realistic interactions. We demonstrate the approach on a variety of autonomous driving and racing scenarios where we achieve solutions in mere seconds on commodity hardware.