Enhancing Decision-Making with Large Language Models through Multi-Agent Fictitious Play

2026-06-17

AI Summary

This work addresses the challenge of coordinating decisions among multiple real-world stakeholders whose entangled positions hinder effective collaboration through conventional multi-agent approaches. To tackle this, the paper introduces the Multi-Agent Fictitious Play (MAFP) framework, which, for the first time, integrates the fictitious play mechanism from game theory into large language model–based multi-agent systems. In MAFP, each stakeholder’s stance is modeled as an agent, and iterative best responses combined with mixed-strategy updates are performed based on the empirical distribution of historical decisions, steering the system toward equilibrium-oriented joint decision-making. Experimental results demonstrate that MAFP significantly outperforms both single-round and multi-round baseline methods in competitive strategic tasks, achieving superior performance in terms of tournament strength and robustness, thereby effectively managing the novel decision complexity arising from entangled positions.

Abstract

Large language model (LLM)-based multi-agent systems (MAS) have demonstrated great potential in solving tasks with execution complexity, by distributing subtasks across cooperative agents. However, this divide-and-conquer paradigm falls short on decision-making tasks that are also prevalent in the real world. These tasks require simultaneous reasoning from the stances of all involved stakeholders whose decisions are mutually dependent and thus cannot be solved in isolation. We characterize this challenge as stance entanglement, a form of decision complexity distinct from execution complexity. To address it, we propose Multi-Agent Fictitious Play (MAFP), a novel MAS paradigm that represents stakeholder stances as agents and formulates decision-making as an equilibrium-seeking process. Built on the game-theoretic principle of fictitious play, MAFP iteratively updates each agent's decision by best responding to the empirical mixture of other agents' past decisions. This enables agents to expose and address one another's weaknesses, progressively improving decision quality and robustness. We evaluate MAFP on challenging decision-making tasks that test the capability of deciding strategies for competitive scenarios prior to acting. MAFP outperforms both single-round and multi-round baselines on two complementary metrics, tournament strength and robustness, demonstrating its effectiveness in addressing stance entanglement.

Problem

• stance entanglement
• decision-making
• multi-agent systems
• mutual dependency
• large language models

Innovation

• Multi-Agent Fictitious Play
• stance entanglement
• large language models
• equilibrium-seeking
• decision-making