# Convergence dynamics of Agent-to-Agent Interactions with Misaligned objectives

arXiv: https://arxiv.org/abs/2511.08710 · HTML: https://mlsanity.com/paper/2511.08710/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 28 of its 30 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 28 of 28)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [The Rise and Potential of Large Language Model Based Agents: A Survey](https://mlsanity.com/paper/2309.07864/) (2023)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [What learning algorithm is in-context learning? Investigations with linear models](https://mlsanity.com/paper/2211.15661/) (2022)
- [Why Do Multi-Agent LLM Systems Fail?](https://mlsanity.com/paper/2503.13657/) (2025)
- [ReConcile: Round-Table Conference Improves Reasoning via Consensus among Diverse LLMs](https://mlsanity.com/paper/2309.13007/) (2023)
- [Why Can GPT Learn In-Context? Language Models Implicitly Perform Gradient Descent as Meta-Optimizers](https://mlsanity.com/paper/2212.10559/) (2022)
- [Rethinking the Bounds of LLM Reasoning: Are Multi-Agent Discussions the Key?](https://mlsanity.com/paper/2402.18272/) (2024)
- [Evaluation and Benchmarking of LLM Agents: A Survey](https://mlsanity.com/paper/2507.21504/) (2025)
- [Cut the Crap: An Economical Communication Pipeline for LLM-based Multi-Agent Systems](https://mlsanity.com/paper/2410.02506/) (2024)
- [Prompt Infection: LLM-to-LLM Prompt Injection within Multi-Agent Systems](https://mlsanity.com/paper/2410.07283/) (2024)
- [Red-Teaming LLM Multi-Agent Systems via Communication Attacks](https://mlsanity.com/paper/2502.14847/) (2025)
- [Linear attention is (maybe) all you need (to understand transformer optimization)](https://mlsanity.com/paper/2310.01082/) (2023)
- [Effective Prompt Extraction from Language Models](https://mlsanity.com/paper/2307.06865/) (2023)
- [Talk Isn't Always Cheap: Understanding Failure Modes in Multi-Agent Debate](https://mlsanity.com/paper/2509.05396/) (2025)
- [Prompt Stealing Attacks Against Large Language Models](https://mlsanity.com/paper/2402.12959/) (2024)
- [Flow: Modularized Agentic Workflow Automation](https://mlsanity.com/paper/2501.07834/) (2025)
- [Transformers Learn to Implement Multi-step Gradient Descent with Chain of Thought](https://mlsanity.com/paper/2502.21212/) (2025)
- [Aegis: Automated Error Generation and Attribution for Multi-Agent Systems](https://mlsanity.com/paper/2509.14295/) (2025)
- [MAEBE: Multi-Agent Emergent Behavior Framework](https://mlsanity.com/paper/2506.03053/) (2025)
- [System Prompt Extraction Attacks and Defenses in Large Language Models](https://mlsanity.com/paper/2505.23817/) (2025)
- [Emergence in Multi-Agent Systems: A Safety Perspective](https://mlsanity.com/paper/2408.04514/) (2024)
- [Exploring the Adversarial Capabilities of Large Language Models](https://mlsanity.com/paper/2402.09132/) (2024)

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

- [SoK: When Safe Agents Fail Together: The Security of Multi Agent LLM Systems](https://mlsanity.com/paper/2609.00595/) (2026)

## Abstract (arXiv)

We develop and analyze a theoretical framework for agent-to-agent interactions in a simplified in-context linear regression setting. In our model, each agent is instantiated as a single-layer transformer with linear self-attention (LSA) trained to implement gradient-descent-like updates on a quadratic regression objective from in-context examples. We then study the coupled dynamics when two such LSA agents alternately update from each other's outputs under potentially misaligned fixed objectives. Within this framework, we characterize the generation dynamics and show that misalignment leads to a biased equilibrium where neither agent reaches its target, with residual errors predictable from the objective gap and the prompt-induced geometry. We also characterize an adversarial regime where asymmetric convergence is possible: one agent reaches its objective exactly while inducing persistent bias in the other. We further contrast this fixed objective regime with an adaptive multi-agent setting, wherein a helper agent updates a turn-based objective to implement a Newton-like step for the main agent, eliminating the plateau and accelerating its convergence. Experiments with trained LSA agents, as well as black-box GPT-5-mini runs on in-context linear regression tasks, are consistent with our theoretical predictions within this simplified setting. We view our framework as a mechanistic framework that links prompt geometry and objective misalignment to stability, bias, and robustness, and as a stepping stone toward analyzing more realistic multi-agent LLM systems.