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

2025-11-11

AI Summary

This paper investigates the interaction dynamics of multi-agent language models under objective conflict: when two LLM-based agents reciprocally regulate each other via in-context iterative gradient updates, the system converges to a biased equilibrium where neither agent achieves its objective. We propose the “prompt geometry” framework—a theoretical characterization of how objective deviation and prompt-space structure govern convergence bias—and derive conditions for asymmetric convergence. Furthermore, we design a first-order adversarial algorithm with provable unilateral success. Our methodology integrates in-context learning, differentiable prompt optimization, and rigorous theoretical analysis, validated empirically on both Transformer-based architectures and GPT-5 via linear regression tasks. Results confirm the theoretically predicted systematic convergence bias and, for the first time, enable quantitative control over stability, bias direction, and robustness in multi-agent LLM interactions.

Technology Category

• Multiagent Systems: Adversarial Agents
• Game Theory and Economic Paradigms: Adversarial Learning
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

We develop a theoretical framework for agent-to-agent interactions in multi-agent scenarios. We consider the setup in which two language model based agents perform iterative gradient updates toward their respective objectives in-context, using the output of the other agent as input. We characterize the generation dynamics associated with the interaction when the agents have misaligned objectives, and show that this results in a biased equilibrium where neither agent reaches its target - with the residual errors predictable from the objective gap and the geometry induced by the prompt of each agent. We establish the conditions for asymmetric convergence and provide an algorithm that provably achieves an adversarial result, producing one-sided success. Experiments with trained transformer models as well as GPT$5$ for the task of in-context linear regression validate the theory. Our framework presents a setup to study, predict, and defend multi-agent systems; explicitly linking prompt design and interaction setup to stability, bias, and robustness.

Problem

• Analyzing convergence dynamics when AI agents have conflicting objectives
• Predicting biased equilibrium from objective gaps and prompt geometry
• Establishing conditions for asymmetric convergence in multi-agent systems

Innovation

• Theoretical framework for multi-agent gradient interactions
• Characterizes biased equilibrium from misaligned objectives
• Algorithm achieves asymmetric convergence with one-sided success