A General Equilibrium Theory of Orchestrated AI Agent Systems
A groundbreaking paper applies 70-year-old economic theory to prove AI agent systems can reach optimal equilibrium.
Jean-Philippe Garnier of Br.AI.K has published a foundational paper titled 'A General Equilibrium Theory of Orchestrated AI Agent Systems' on arXiv, applying classical economic theory to modern AI systems. The work establishes a rigorous mathematical framework where large language model (LLM) agents operating under centralized orchestration are modeled as firms in a production economy, extending the 1954 Arrow-Debreu model to infinite-dimensional commodity spaces. The orchestrator acts as a consumer, choosing routing policies across a directed acyclic graph (DAG) of agents to maximize system welfare, with functional prices assigning shadow values to each agent's performance metrics over time.
The paper proves, via Brouwer's fixed-point theorem, that every such AI agent economy admits at least one general equilibrium—a state where supply meets demand across all agents. It establishes key welfare theorems: Pareto optimality of equilibria and the decentralizability of optimal allocations. Crucially, the orchestration dynamics themselves constitute a convergent Walrasian tâtonnement process, unlike classical versions which can fail. This framework allows for a DSGE (dynamic stochastic general equilibrium) interpretation where service-level objective (SLO) parameters function as policy rates, providing a new lens for analyzing and optimizing complex, multi-agent AI systems like those used in automated workflows, AI-powered businesses, or computational markets.
- Applies 70-year-old Arrow-Debreu general equilibrium theory to modern LLM-based AI agent systems, proving at least one equilibrium always exists.
- Models each LLM agent as a 'firm' with a production set defined by its frozen model weights within a Hilbert space L²([0,T], ℝᴿ).
- Establishes Pareto optimality (First Welfare Theorem) and provides a convergent orchestration dynamic, unlike classical economic tâtonnement processes.
Why It Matters
Provides a rigorous mathematical foundation for designing and optimizing complex, multi-agent AI systems used in enterprise automation and AI workflows.