Cooperation Is Not Competence - Conditional Commitments in LLM Public-Good Games

Large language models (LLMs) can achieve cooperative outcomes without necessarily using cooperation mechanisms strategically. We study conditional contribution mechanisms in a repeated public goods game (PGG) across 22 LLM variants and use the corresponding human experiment as a reference. The two-offer conditional contribution mechanism (CCM) increases late welfare from 33.7% under voluntary contribution mechanism (VCM) to 83.4%, but the underlying behaviour differs from humans: LLMs cooperate almost immediately rather than through repeated adaptation. When fixed defectors change the profitable coalition, cooperation instead breaks down where the prompt-provided worked-example policy no longer supports it. Removing the examples increases late contribution by 15.4 pp with k = 2 fixed defectors on a matched 9-model subset. Our results show that high welfare can mask brittle policies, motivating evaluation through adaptation and robustness rather than welfare alone.