The behavior of Large Language Models (LLMs) as artificial social agents is largely unexplored, and we still lack extensive evidence of how these agents react to simple social stimuli. Testing the behavior of AI agents in classic Game Theory experiments provides a promising theoretical framework for evaluating the norms and values of these agents in archetypal social situations. In this work, we investigate the cooperative behavior of Llama2 when playing the Iterated Prisoner's Dilemma against random adversaries displaying various levels of hostility. We introduce a systematic methodology to evaluate an LLM's comprehension of the game's rules and its capability to parse historical gameplay logs for decision-making. We conducted simulations of games lasting for 100 rounds, and analyzed the LLM's decisions in terms of dimensions defined in behavioral economics literature. We find that Llama2 tends not to initiate defection but it adopts a cautious approach towards cooperation, sharply shifting towards a behavior that is both forgiving and non-retaliatory only when the opponent reduces its rate of defection below 30%. In comparison to prior research on human participants, Llama2 exhibits a greater inclination towards cooperative behavior. Our systematic approach to the study of LLMs in game theoretical scenarios is a step towards using these simulations to inform practices of LLM auditing and alignment.