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 abilities remain largely unexplored. Game theory provides a good framework for assessing the decision-making abilities of LLMs in interactions with other agents. Although prior studies have shown that LLMs can solve these tasks with carefully curated prompts, they fail when the problem setting or prompt changes. In this work we investigate LLMs' behaviour in strategic games, Stag Hunt and Prisoner Dilemma, analyzing performance variations under different settings and prompts. Our results show that the tested state-of-the-art LLMs exhibit at least one of the following systematic biases: (1) positional bias, (2) payoff bias, or (3) behavioural bias. Subsequently, we observed that the LLMs' performance drops when the game configuration is misaligned with the affecting biases. Performance is assessed based on the selection of the correct action, one which agrees with the prompted preferred behaviours of both players. Alignment refers to whether the LLM's bias aligns with the correct action. For example, GPT-4o's average performance drops by 34% when misaligned. Additionally, the current trend of "bigger and newer is better" does not hold for the above, where GPT-4o (the current best-performing LLM) suffers the most substantial performance drop. Lastly, we note that while chain-of-thought prompting does reduce the effect of the biases on most models, it is far from solving the problem at the fundamental level.