Can LLMs find optimal paths in multi-agent games?
Two-person positive shortest path games have Nash equlibria in pure stationary strategies.
October 15, 2024
https://arxiv.org/pdf/2410.09257This paper explores the existence of Nash Equilibria (stable states where no player benefits from changing their strategy alone) in shortest-path games. It proves that two-player games with positive costs always have a NE.
While not directly about LLMs, the key takeaway for multi-agent LLM systems is the guaranteed existence of stable solutions in specific game-like scenarios. This is relevant when designing multi-agent systems where agents compete to optimize individual goals, like in resource allocation or task delegation. This theoretical foundation can inform the design of robust and predictable multi-agent LLM applications.