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

As autonomous AI agents increasingly mediate online platform markets, a fundamental question emerges: do these markets generate stable strategic outcomes? In repeated strategic environments, the Nash equilibrium provides a natural benchmark for this stability. However, empirical evidence on off-the-shelf LLM agents is mixed, leaving it unclear whether independently deployed agents can converge to equilibrium behavior without explicit strategic post-training. In this paper, we provide an affirmative answer. Extending the Bayesian learning literature in theoretical economics, we prove that AI agents, acting as Bayesian posterior samplers rather than expected utility maximizers, are guaranteed to eventually become weakly close to a Nash equilibrium in infinitely repeated games. We further extend this analysis to settings in which stage payoffs are unknown ex ante, and agents observe only their privately realized stochastic payoffs, and obtain the same convergence guarantees. Finally, we empirically evaluate these theoretical implications across five repeated-game environments, ranging from the Prisoner's Dilemma to marketing promotion games. Taken together, our findings suggest that strategic stability in AI-mediated markets can emerge from the intrinsic reasoning and learning properties of modern AI agents, without the need for unrealistic universal fine-tuning.