Effective Game-Theoretic Motion Planning via Nested Search

2025-11-11

AI Summary

Existing game-theoretic motion planning methods suffer from oversimplified dynamics modeling, susceptibility to local optima, and poor computational scalability. Method: We propose a nested search framework for multi-agent dynamic interaction without explicit communication, enabling efficient Nash equilibrium computation under general robot dynamics. Contribution/Results: Our approach introduces a joint inner–outer search mechanism: the inner loop rapidly prunes non-equilibrium trajectories in a low-dimensional space, while the outer loop guides action optimization subject to Nash constraints. It supports user-defined objectives for equilibrium selection. By avoiding dynamics simplifications and local optima traps, our method computes high-quality solutions in seconds on commodity hardware—demonstrated in autonomous driving and racing simulations—achieving significant improvements in computational efficiency and generalizability across diverse robotic domains.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Multiagent Systems: Mechanism Design
• Intelligent Robots: Motion and Path Planning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

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.

Problem

• Computing Nash Equilibria in multi-agent motion planning without trajectory enumeration
• Overcoming local minima and scalability issues in game-theoretic robot decision-making
• Enabling equilibrium selection for realistic autonomous driving interactions

Innovation

• Game-Theoretic Nested Search for Nash Equilibrium computation
• Inner search over lower-dimensional space discards invalid trajectories
• User-specified global objective enables explicit equilibrium selection