Reasonably reasoning agents avoid game-theoretic failures in zero-shot, provably

AI agents are increasingly deployed in interactive environments characterized by repeated AI-AI interactions. Despite AI agents' advanced capabilities, empirical studies reveal that such interactions often fail to stably induce a strategic equilibrium, such as a Nash equilibrium. Post-training methods have been proposed to induce a strategic equilibrium; however, it remains impractical to uniformly apply a single alignment across diverse, independently developed AI models in strategic settings. In this paper, we provide theoretical and empirical evidence that off-the-shelf reasoning agents can achieve Nash-like play zero-shot, without explicit post-training. Specifically, we prove that `reasonably reasoning' agents, i.e., agents capable of forming beliefs about others' strategies from previous observation and learning to best respond to these beliefs, eventually behave along almost every realized play path in a way that is weakly close to a Nash equilibrium of the continuation game. We then empirically validate this by simulating three game scenarios. Our findings suggest that AI agents naturally exhibit such reasoning patterns and therefore attain stable equilibrium behaviors intrinsically, obviating the need for universal alignment procedures in many real-world strategic interactions.