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As the performance of larger, newer Large Language Models continues to improve for strategic Theory of Mind (ToM) tasks, the demand for these state-of-the-art models increases commensurately. However, their deployment is costly both in terms of processing power and time. In this paper, we investigate the feasibility of creating smaller, highly-performing specialized algorithms by way of fine-tuning. To do this, we first present a large pre-trained model with 20 unique scenarios that combine different social contexts with games of varying social dilemmas, record its answers, and use them for Q&A fine-tuning on a smaller model of the same family. Our focus is on in-context game-theoretic decision-making, the same domain within which human interaction occurs and that requires both a theory of mind (or a semblance thereof) and an understanding of social dynamics. The smaller model is therefore trained not just on the answers provided, but also on the motivations provided by the larger model, which should contain advice and guidelines to navigate both strategic dilemmas and social cues. We find that the fine-tuned smaller language model consistently bridged the gap in performance between the smaller pre-trained version of the model and its larger relative and that its improvements extended in areas and contexts beyond the ones provided in the training examples, including on out-of-sample scenarios that include completely different game structures. On average for all games, through fine-tuning, the smaller model showed a 46% improvement measured as alignment towards the behavior of the larger model, with 100% representing indistinguishable behavior. When presented with out-of-sample social contexts and games, the fine-tuned model still displays remarkable levels of alignment, reaching an improvement of 18% and 28% respectively., Comment: 18 pages, 6 figures

This paper investigates the strategic decision-making capabilities of three Large Language Models (LLMs): GPT-3.5, GPT-4, and LLaMa-2, within the framework of game theory. Utilizing four canonical two-player games -- Prisoner's Dilemma, Stag Hunt, Snowdrift, and Prisoner's Delight -- we explore how these models navigate social dilemmas, situations where players can either cooperate for a collective benefit or defect for individual gain. Crucially, we extend our analysis to examine the role of contextual framing, such as diplomatic relations or casual friendships, in shaping the models' decisions. Our findings reveal a complex landscape: while GPT-3.5 is highly sensitive to contextual framing, it shows limited ability to engage in abstract strategic reasoning. Both GPT-4 and LLaMa-2 adjust their strategies based on game structure and context, but LLaMa-2 exhibits a more nuanced understanding of the games' underlying mechanics. These results highlight the current limitations and varied proficiencies of LLMs in strategic decision-making, cautioning against their unqualified use in tasks requiring complex strategic reasoning., Comment: 25 pages, 12 figures