# Agentic Hives: Equilibrium, Indeterminacy, and Endogenous Cycles in Self-Organizing Multi-Agent Systems

arXiv: https://arxiv.org/abs/2603.00130 · HTML: https://mlsanity.com/paper/2603.00130/

## Key facts

- No citing papers in the map yet (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 4 of its 36 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## 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, 4 of 4)

- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework](https://mlsanity.com/paper/2308.00352/) (2023)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [Large Language Model based Multi-Agents: A Survey of Progress and Challenges](https://mlsanity.com/paper/2402.01680/) (2024)

## Abstract (arXiv)

Current multi-agent AI systems operate with a fixed number of agents whose roles are specified at design time. No formal theory governs when agents should be created, destroyed, or re-specialized at runtime-let alone how the population structure responds to changes in resources or objectives. We introduce the Agentic Hive, a framework in which a variable population of autonomous micro-agents-each equipped with a sandboxed execution environment and access to a language model-undergoes demographic dynamics: birth, duplication, specialization, and death. Agent families play the role of production sectors, compute and memory play the role of factors of production, and an orchestrator plays the dual role of Walrasian auctioneer and Global Workspace. Drawing on the multi-sector growth theory developed for dynamic general equilibrium (Benhabib & Nishimura, 1985; Venditti, 2005; Garnier, Nishimura & Venditti, 2013), we prove seven analytical results: (i) existence of a Hive Equilibrium via Brouwer's fixed-point theorem; (ii) Pareto optimality of the equilibrium allocation; (iii) multiplicity of equilibria under strategic complementarities between agent families; (iv)-(v) Stolper-Samuelson and Rybczynski analogs that predict how the Hive restructures in response to preference and resource shocks; (vi) Hopf bifurcation generating endogenous demographic cycles; and (vii) a sufficient condition for local asymptotic stability. The resulting regime diagram partitions the parameter space into regions of unique equilibrium, indeterminacy, endogenous cycles, and instability. Together with the comparative-statics matrices, it provides a formal governance toolkit that enables operators to predict and steer the demographic evolution of self-organizing multi-agent systems.