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Game-Theoretic Lens on LLM-based Multi-Agent Systems

Jianing Hao, Han Ding, Yuanjian Xu, Tianze Sun, Ran Chen, Wanbo Zhang, Guang Zhang, Siguang Li

TL;DR

The paper addresses the need for a unified theoretical foundation for LLM-based multi-agent systems. It proposes a four-element game-theoretic framework—players, strategies, payoffs, and information—and maps MAS to traditional game-theoretic environments to enable systematic analysis. Through a comprehensive review, it examines cooperative, competitive, and mixed-motive settings, and discusses mechanisms such as mechanism design, reward shaping, and penalty-based regulation under full and partial observability. It identifies key gaps in equilibrium selection and incentive compatibility and proposes forward-looking directions, including hierarchical superagent orchestration, agentic evolution, and rigorous theoretical formalization, to bridge classical game theory with LLM-driven MAS. This work provides a foundation for designing reliable, autonomous, and socially intelligent multi-agent systems that leverage language-based coordination and strategic interaction.

Abstract

Large language models (LLMs) have demonstrated strong reasoning, planning, and communication abilities, enabling them to operate as autonomous agents in open environments. While single-agent systems remain limited in adaptability and coordination, recent progress has shifted attention toward multi-agent systems (MAS) composed of interacting LLMs that pursue cooperative, competitive, or mixed objectives. This emerging paradigm provides a powerful testbed for studying social dynamics and strategic behaviors among intelligent agents. However, current research remains fragmented and lacks a unifying theoretical foundation. To address this gap, we present a comprehensive survey of LLM-based multi-agent systems through a game-theoretic lens. By organizing existing studies around the four key elements of game theory: players, strategies, payoffs, and information, we establish a systematic framework for understanding, comparing, and guiding future research on the design and analysis of LLM-based MAS.

Game-Theoretic Lens on LLM-based Multi-Agent Systems

TL;DR

The paper addresses the need for a unified theoretical foundation for LLM-based multi-agent systems. It proposes a four-element game-theoretic framework—players, strategies, payoffs, and information—and maps MAS to traditional game-theoretic environments to enable systematic analysis. Through a comprehensive review, it examines cooperative, competitive, and mixed-motive settings, and discusses mechanisms such as mechanism design, reward shaping, and penalty-based regulation under full and partial observability. It identifies key gaps in equilibrium selection and incentive compatibility and proposes forward-looking directions, including hierarchical superagent orchestration, agentic evolution, and rigorous theoretical formalization, to bridge classical game theory with LLM-driven MAS. This work provides a foundation for designing reliable, autonomous, and socially intelligent multi-agent systems that leverage language-based coordination and strategic interaction.

Abstract

Large language models (LLMs) have demonstrated strong reasoning, planning, and communication abilities, enabling them to operate as autonomous agents in open environments. While single-agent systems remain limited in adaptability and coordination, recent progress has shifted attention toward multi-agent systems (MAS) composed of interacting LLMs that pursue cooperative, competitive, or mixed objectives. This emerging paradigm provides a powerful testbed for studying social dynamics and strategic behaviors among intelligent agents. However, current research remains fragmented and lacks a unifying theoretical foundation. To address this gap, we present a comprehensive survey of LLM-based multi-agent systems through a game-theoretic lens. By organizing existing studies around the four key elements of game theory: players, strategies, payoffs, and information, we establish a systematic framework for understanding, comparing, and guiding future research on the design and analysis of LLM-based MAS.
Paper Structure (28 sections, 12 equations, 5 figures, 1 table)

This paper contains 28 sections, 12 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background and Taxonomy
  3. Foundations of Game Theory
  4. Multi-Agent Systems as Game-Theoretic Environments
  5. Taxonomy based on Game-Theoretic Elements
  6. Game-Theoretic Elements in MAS
  7. Players
  8. Cooperative Systems.
  9. Competitive Systems.
  10. Mixed-Motive Systems.
  11. Strategies and Equilibrium
  12. Payoffs
  13. Mechanism Design.
  14. Reward Shaping.
  15. Penalty and Regulation Mechanisms.
  16. ...and 13 more sections

Figures (5)

  • Figure 1: A game-theoretic framework for LLM-based multi-agent systems illustrates the dynamic interplay between the four core elements of a game: Players, Strategies, Payoffs, and Information.
  • Figure 2: Illustration of three interaction structures among LLM-based players.
  • Figure 3: Illustration of information structures among LLM-based players.
  • Figure 4: Framework and performance of SWE-Debate. (Left) The workflow incorporates a multi-agent debate mechanism to iteratively refine modification plans. (Right) This competitive architecture achieves a SOTA 41.4% Pass@1 (DeepSeek-V3), significantly outperforming non-competitive baselines and validating the efficacy of adversarial interactions.
  • Figure 5: Reward shaping in the FinCon framework. (Left) A decentralized multi-agent financial system coordinated by a manager agent, where agent behaviors are guided through shaped rewards derived from heterogeneous financial observations. (Right) Empirical comparison illustrating how reward shaping and regulatory penalties influence agent performance across assets and backbone models.