arXiv:2508.15510v1 Announce Type: new Abstract: With the prospect of autonomous artificial intelligence (AI) agents, studying their tendency for cooperative behavior becomes an increasingly relevant topic. This study is inspired by the super-additive cooperation theory, where the combined effects of repeated interactions and inter-group rivalry have been argued to be the cause for cooperative tendencies found in humans. We devised a virtual tournament where language model agents, grouped into teams, face each other in a Prisoner's Dilemma game. By simulating both internal team dynamics and external competition, we discovered that this blend substantially boosts both overall and initial, one-shot cooperation levels (the tendency to cooperate in one-off interactions). This research provides a novel framework for large language models to strategize and act in complex social scenarios and offers evidence for how intergroup competition can, counter-intuitively, result in more cooperative behavior. These insights are crucial for designing future multi-agent AI systems that can effectively work together and better align with human values. Source code is available at https://github.com/pippot/Superadditive-cooperation-LLMs.