  The remarkable progress in Large Language Models (LLMs) opens up new avenues
for addressing planning and decision-making problems in Multi-Agent Systems
(MAS). However, as the number of agents increases, the issues of hallucination
in LLMs and coordination in MAS have become increasingly prominent.
Additionally, the efficient utilization of tokens emerges as a critical
consideration when employing LLMs to facilitate the interactions among a
substantial number of agents. In this paper, we develop a modular framework
called LLaMAC to mitigate these challenges. LLaMAC implements a value
distribution encoding similar to that found in the human brain, utilizing
internal and external feedback mechanisms to facilitate collaboration and
iterative reasoning among its modules. Through evaluations involving system
resource allocation and robot grid transportation, we demonstrate the
considerable advantages afforded by our proposed approach.
