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

TL;DR

This paper introduces the Agentic Hive framework, modeling self-organizing multi-agent systems with endogenous population dynamics, equilibrium analysis, and stability conditions inspired by dynamic general equilibrium theory.

Contribution

It develops a formal theory for when agents should be created, destroyed, or re-specialized, including analytical results on equilibrium existence, optimality, and endogenous cycles.

Findings

Proves existence of Hive Equilibrium using Brouwer's fixed-point theorem.

Identifies conditions for Pareto optimality and multiple equilibria.

Derives endogenous demographic cycles via Hopf bifurcation.

Abstract

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.