Game-theoretic LLM: Agent Workflow for Negotiation Games (2411.05990v2)

Abstract: This paper investigates the rationality of LLMs in strategic decision-making contexts, specifically within the framework of game theory. We evaluate several state-of-the-art LLMs across a spectrum of complete-information and incomplete-information games. Our findings reveal that LLMs frequently deviate from rational strategies, particularly as the complexity of the game increases with larger payoff matrices or deeper sequential trees. To address these limitations, we design multiple game-theoretic workflows that guide the reasoning and decision-making processes of LLMs. These workflows aim to enhance the models' ability to compute Nash Equilibria and make rational choices, even under conditions of uncertainty and incomplete information. Experimental results demonstrate that the adoption of these workflows significantly improves the rationality and robustness of LLMs in game-theoretic tasks. Specifically, with the workflow, LLMs exhibit marked improvements in identifying optimal strategies, achieving near-optimal allocations in negotiation scenarios, and reducing susceptibility to exploitation during negotiations. Furthermore, we explore the meta-strategic considerations of whether it is rational for agents to adopt such workflows, recognizing that the decision to use or forgo the workflow constitutes a game-theoretic issue in itself. Our research contributes to a deeper understanding of LLMs' decision-making capabilities in strategic contexts and provides insights into enhancing their rationality through structured workflows. The findings have implications for the development of more robust and strategically sound AI agents capable of navigating complex interactive environments. Code and data supporting this study are available at \url{https://github.com/Wenyueh/game_theory}.

Game-Theoretic LLM: Agent Workflow for Negotiation Games

The paper "Game-theoretic LLM: Agent Workflow for Negotiation Games" presents a comprehensive exploration of the decision-making capabilities of LLMs in strategic game-theoretic contexts. This paper targets the rational decision-making processes of LLMs when faced with games that require strategic thinking, evaluating these models both in complete-information and incomplete-information scenarios. The authors not only assess the current capacities of LLMs like Claude-3.5 Sonnet, Claude-3 Opus, GPT-4o, and o1 in game-theoretic tasks, but also propose structured workflows designed to enhance these models' reasoning and decision-making capabilities.

Complete-Information Games

In complete-information games, where all players have full knowledge of the game's structure, the LLMs tend to deviate from rational strategies as game complexity increases. The paper assesses LLM performance across various game types, including the Prisoner’s Dilemma, Stag Hunt, and Battle of the Sexes. The authors find that, without structured workflows, LLMs often fail to consistently select rational strategies, particularly when multiple equilibria exist.

The introduction of game-theoretic workflows, however, marks a significant improvement in performance. These workflows guide LLMs using principles such as Dominant Strategy Search and Backward Induction, helping models compute Nash Equilibria more effectively and choose optimal strategies in both simultaneous and sequential games. Yet, certain limitations persist, such as in the Escalation Game, where numerical insensitivity impairs performance. The integration of negotiation rounds further complicates outcomes, sometimes leading agents away from Nash Equilibria in pursuit of perceived pareto optimal solutions when workflows are not utilized.

Incomplete-Information Games

The paper transitions to incomplete-information games, particularly focusing on scenarios requiring resource allocation under uncertainty, exemplified by the "Deal or No Deal" negotiation dataset. Here, the authors propose a novel algorithm incorporating Bayesian updates to efficiently guide LLM-based agents towards envy free and pareto optimal allocations. This approach aligns agent decisions with optimal utility, considering both self-interest and fairness.

The results reveal a significant enhancement in LLM performance with the workflow, achieving near-optimal allocations while maintaining high levels of agreement and fairness. Agents leveraging the workflow exhibit increased robustness and stability, even across varying temperature settings, suggesting that structured workflows can counteract the inherent stochastic variability of LLM outputs.

Meta-Strategic Considerations and Future Implications

A pertinent assertion of this paper is the consideration of whether adopting such workflows is a strategic choice in itself. Notably, the decision to utilize the workflow varies based on the individual characteristics of the LLMs, highlighting the need for meta-strategies to navigate strategic interactions effectively. The paper proposes that future work should focus on developing meta-strategies that allow LLMs to dynamically choose when to apply specific workflows, balancing between strategic depth and vulnerability to exploitation.

Conclusion

This paper contributes significantly to understanding and improving the strategic decision-making capabilities of LLMs in game-theoretic contexts. It opens several avenues for further research, including exploring workflow vulnerabilities, advancing multi-stage game strategies, and developing metacognitive strategies for adaptive decision-making. The alignment of LLMs with personalized stances and interests also emerges as a crucial area of focus, suggesting a trajectory toward more nuanced and contextually aware AI agents capable of navigating complex interactive environments with rationality and strategic insight. This research not only clarifies current limitations but also sets a foundational path for future advancements in AI strategic reasoning and negotiation capabilities.