  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.
