# Recursive Reasoning or Statistical Extrapolation? In-Context Learning in Multi-Agent Interdependent Decision-Making

arXiv: https://arxiv.org/abs/2609.18591 · HTML: https://mlsanity.com/paper/2609.18591/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 3 of its 29 references that are in the map.
- First posted on arXiv 16 Sep 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 / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)

## Builds on (most cited first, 3 of 3)

- [In-Context Learning Is Provably Bayesian Inference: A Generalization Theory for Meta-Learning](https://mlsanity.com/paper/2510.10981/) (2025)
- [Corrupted by Reasoning: Reasoning Language Models Become Free-Riders in Public Goods Games](https://mlsanity.com/paper/2506.23276/) (2025)
- [Understanding LLM Agent Behaviours via Game Theory: Strategy Recognition, Biases and Multi-Agent Dynamics](https://mlsanity.com/paper/2512.07462/) (2025)

## Abstract (arXiv)

In-context learning (ICL) enables large language model (LLM) agents to improve decisions using interaction history, yet it remains unclear whether such improvement reflects refined internal reasoning or mere extrapolation of statistical patterns. To disentangle these mechanisms, we study LLM agents in multi-agent incomplete-information games that require recursive belief reasoning. By constructing a public goods game and manipulating the statistical structure of historical feedback, we evaluate decision quality against a history-independent rational expectations equilibrium (REE) benchmark. Our experiments reveal that when historical statistical patterns are disrupted, the benefits of longer context largely vanish, degrading decision quality to the no-context baseline in a way sharply amplified by stronger strategic interdependence. These results suggest that, in such strategic environments, ICL behavior is more consistent with statistical extrapolation than with strategic reasoning. Our work extends the mechanistic study of ICL to strategic multi-agent settings, introduces REE as a diagnostic tool for distinguishing reasoning from extrapolation, and provides a reusable framework for probing the boundaries of LLM reasoning in recursive belief tasks.