While large language models (LLMs) have demonstrated remarkable success across various natural language processing tasks, their ability to reason and act strategically has limitations. Recent research suggests that game theory offers a promising framework for enhancing LLMs’ strategic capabilities in negotiation. By formalizing negotiations as games, exploring different strategies, and solving the games for equilibrium strategies using algorithmic game-theoretic solvers, the LLM can be given an understanding of the theoretically optimal solution. This thesis investigates whether the incorporation of revision of beliefs can further improve LLM performance— an idea that emerged from Harsanyi’s solution of games of incomplete information. Specifically, it examines to what extent LLM reasoning can gain from revising beliefs about the opponent’s private information. The work formalized a negotiation as a game, integrated revision of beliefs into the existing framework, and solved the game for equilibrium strategies using the game-theoretic solver counterfactual regret minimization (CFR). Evaluation was conducted by examining whether the addition of revision of beliefs changed the outcome of negotiations, and whether the resulting CFR strategy satisfied the conditions of an evolutionarily stable strategy. Results show that incorporating revision of beliefs increased both the number of agreements reached and the number of beneficial trades for a player, given that beliefs were accurately updated. However, revision of beliefs did not further improve LLM performance when combined with CFR. These findings suggest that belief revision can enhance the strategic capabilities of LLMs, but also indicate that CFR alone is sufficient to produce evolutionarily stable strategies.
Madeleine Lindström (Wed,) studied this question.