Are Large Language Models Strategic Decision Makers? A Study of Performance and Bias in Two-Player Non-Zero-Sum Games

Large Language Models (LLMs) have been increasingly used in real-world settings, yet their strategic decision-making abilities remain largely unexplored. To fully benefit from the potential of LLMs, it's essential to understand their ability to function in complex social scenarios. Game theory, which is already used to understand real-world interactions, provides a good framework for assessing these abilities. This work investigates the performance and merits of LLMs in canonical game-theoretic two-player non-zero-sum games, Stag Hunt and Prisoner Dilemma. Our structured evaluation of GPT-3.5, GPT-4-Turbo, GPT-4o, and Llama-3-8B shows that these models, when making decisions in these games, are affected by at least one of the following systematic biases: positional bias, payoff bias, or behavioural bias. This indicates that LLMs do not fully rely on logical reasoning when making these strategic decisions. As a result, it was found that the LLMs' performance drops when the game configuration is misaligned with the affecting biases. When misaligned, GPT-3.5, GPT-4-Turbo, GPT-4o, and Llama-3-8B show an average performance drop of 32\%, 25\%, 34\%, and 29\% respectively in Stag Hunt, and 28\%, 16\%, 34\%, and 24\% respectively in Prisoner's Dilemma. Surprisingly, GPT-4o (a top-performing LLM across standard benchmarks) suffers the most substantial performance drop, suggesting that newer models are not addressing these issues. Interestingly, we found that a commonly used method of improving the reasoning capabilities of LLMs, chain-of-thought (CoT) prompting, reduces the biases in GPT-3.5, GPT-4o, and Llama-3-8B but increases the effect of the bias in GPT-4-Turbo, indicating that CoT alone cannot fully serve as a robust solution to this problem. We perform several additional experiments, which provide further insight into these observed behaviours.