The Prisoner’s Dilemma is a well-established game theory scenario that enables the analysis of cooperation dynamics within social groups. By far, researchers have proposed numerous theoretical frameworks to capture human behavior patterns in the Prisoner’s Dilemma. These theories have varying degrees of success in explaining real individuals’ choices in laboratory settings. In this study, we investigate how large language models (LLMs)—artificial intelligence algorithms based on neural networks trained on vast corpora of textual data—behave in an iterated Prisoner’s Dilemma game. We compare the behavior of LLMs with some theoretical equilibria: the Nash equilibrium, the Nash equilibrium in Markov strategies, and the quantal response equilibrium in Markov strategies. Besides this, we investigate if cooperation rates of LLMs change following a socialization procedure, and if these rates differ from those observed for real participants.