🤖 AI Summary
This work addresses the lack of a theoretical framework in existing AI multi-agent systems capable of supporting runtime dynamics such as agent creation, destruction, or re-specialization, which limits adaptability to environmental changes. The authors propose the Agentic Hive framework, introducing micro-agents equipped with sandboxed execution environments and language model capabilities that, under the coordination of a central orchestrator, exhibit population-level dynamics including birth, replication, specialization, and death. For the first time, dynamic general equilibrium theory is integrated into multi-agent systems, leveraging Brouwer’s fixed-point theorem, multi-sector growth models, and bifurcation analysis to uncover phenomena such as equilibrium multiplicity, endogenous cycles, and instability. The study establishes seven theoretical results, mapping the parameter space into a regime diagram that delineates regions of unique equilibrium, indeterminacy, periodicity, and instability, thereby providing a predictable and controllable governance toolkit for agent population evolution.
📝 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.