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

arXiv: https://arxiv.org/abs/2603.18563 · HTML: https://mlsanity.com/paper/2603.18563/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 31 of its 71 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [Financial trading and forecasting agents](https://mlsanity.com/agents/financial-trading-and-forecasting-agents/)

## Builds on (most cited first, 30 of 31)

- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Large Language Model based Multi-Agents: A Survey of Progress and Challenges](https://mlsanity.com/paper/2402.01680/) (2024)
- [From Decoding to Meta-Generation: Inference-time Algorithms for Large Language Models](https://mlsanity.com/paper/2406.16838/) (2024)
- [GTBench: Uncovering the Strategic Reasoning Limitations of LLMs via Game-Theoretic Evaluations](https://mlsanity.com/paper/2402.12348/) (2024)
- [What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalization](https://mlsanity.com/paper/2305.19420/) (2023)
- [How Well Can LLMs Negotiate? NegotiationArena Platform and Analysis](https://mlsanity.com/paper/2402.05863/) (2024)
- [Can Large Language Models Serve as Rational Players in Game Theory? A Systematic Analysis](https://mlsanity.com/paper/2312.05488/) (2023)
- [Embodied LLM Agents Learn to Cooperate in Organized Teams](https://mlsanity.com/paper/2403.12482/) (2024)
- [How FaR Are Large Language Models From Agents with Theory-of-Mind?](https://mlsanity.com/paper/2310.03051/) (2023)
- [LLMs Are Few-Shot In-Context Low-Resource Language Learners](https://mlsanity.com/paper/2403.16512/) (2024)
- [How Far Are We on the Decision-Making of LLMs? Evaluating LLMs' Gaming Ability in Multi-Agent Environments](https://mlsanity.com/paper/2403.11807/) (2024)
- [Nicer Than Humans: How do Large Language Models Behave in the Prisoner's Dilemma?](https://mlsanity.com/paper/2406.13605/) (2024)
- [Algorithmic Collusion by Large Language Models](https://mlsanity.com/paper/2404.00806/) (2024)
- [Is In-Context Learning in Large Language Models Bayesian? A Martingale Perspective](https://mlsanity.com/paper/2406.00793/) (2024)
- [Game-theoretic LLM: Agent Workflow for Negotiation Games](https://mlsanity.com/paper/2411.05990/) (2024)
- [ALYMPICS: LLM Agents Meet Game Theory -- Exploring Strategic Decision-Making with AI Agents](https://mlsanity.com/paper/2311.03220/) (2023)
- [Position: Theory of Mind Benchmarks are Broken for Large Language Models](https://mlsanity.com/paper/2412.19726/) (2024)
- [Will Systems of LLM Agents Cooperate: An Investigation into a Social Dilemma](https://mlsanity.com/paper/2501.16173/) (2025)
- [In-Context Learning Is Provably Bayesian Inference: A Generalization Theory for Meta-Learning](https://mlsanity.com/paper/2510.10981/) (2025)
- [The Coming Crisis of Multi-Agent Misalignment: AI Alignment Must Be a Dynamic and Social Process](https://mlsanity.com/paper/2506.01080/) (2025)
- [Magentic Marketplace: An Open-Source Environment for Studying Agentic Markets](https://mlsanity.com/paper/2510.25779/) (2025)
- [LLM Strategic Reasoning: Agentic Study through Behavioral Game Theory](https://mlsanity.com/paper/2502.20432/) (2025)
- [Toward Efficient Exploration by Large Language Model Agents](https://mlsanity.com/paper/2504.20997/) (2025)
- [Game Theory Meets Large Language Models: A Systematic Survey with Taxonomy and New Frontiers](https://mlsanity.com/paper/2502.09053/) (2025)
- [The Automated but Risky Game: Modeling and Benchmarking Agent-to-Agent Negotiations and Transactions in Consumer Markets](https://mlsanity.com/paper/2506.00073/) (2025)
- [FAIRGAME: a Framework for AI Agents Bias Recognition using Game Theory](https://mlsanity.com/paper/2504.14325/) (2025)
- [Evaluating LLM Agent Collusion in Double Auctions](https://mlsanity.com/paper/2507.01413/) (2025)
- [When Agents Say One Thing and Do Another: Validating Elicited Beliefs from LLMs](https://mlsanity.com/paper/2602.06286/) (2026)
- [Active Exploration via Autoregressive Generation of Missing Data](https://mlsanity.com/paper/2405.19466/) (2024)
- [The Agentic Economy](https://mlsanity.com/paper/2505.15799/) (2025)

## Built on by (most cited first, 1 of 1)

- [Competition and Cooperation of LLM Agents in Games](https://mlsanity.com/paper/2604.00487/) (2026)

## Abstract (arXiv)

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.