A Hybrid Adaptive Nash Equilibrium Solver for Distributed Multi-Agent Systems with Game-Theoretic Jump Triggering

TL;DR

This paper introduces a hybrid adaptive Nash equilibrium solver for multi-agent systems that improves scalability, convergence, and emergency response through game-theoretic jump mechanisms and hybrid system design.

Contribution

It proposes a novel hybrid adaptive Nash equilibrium solver with jump triggering for distributed multi-agent systems, enhancing scalability and stability.

Findings

Significant improvements in convergence time.

Enhanced computational efficiency and scalability.

Effective coordination of discrete mode transitions.

Abstract

This paper presents a hybrid adaptive Nash equilibrium solver for distributed multi-agent systems incorporating game-theoretic jump triggering mechanisms. The approach addresses fundamental scalability and computational challenges in multi-agent hybrid systems by integrating distributed game-theoretic optimization with systematic hybrid system design. A novel game-theoretic jump triggering mechanism coordinates discrete mode transitions across multiple agents while maintaining distributed autonomy. The Hybrid Adaptive Nash Equilibrium Solver (HANES) algorithm integrates these methodologies. Sufficient conditions establish exponential convergence to consensus under distributed information constraints. The framework provides rigorous stability guarantees through coupled Hamilton-Jacobi-Bellman equations while enabling rapid emergency response capabilities through coordinated jump dynamics. Simulation studies in pursuit-evasion and leader-follower consensus scenarios demonstrate significant improvements in convergence time, computational efficiency, and scalability compared to existing centralized and distributed approaches.