# A General Equilibrium Theory of Orchestrated AI Agent Systems

arXiv: https://arxiv.org/abs/2602.21255 · HTML: https://mlsanity.com/paper/2602.21255/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Social simulation and multi-agent debate, one of 16 directions in LLM agents and tool use.
- Builds on 4 of its 33 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## Placed in

- LLM agents and tool use / [Social simulation and multi-agent debate](https://mlsanity.com/agents/social-simulation-and-multi-agent-debate/)

## Builds on (most cited first, 4 of 4)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains](https://mlsanity.com/paper/1509.02029/) (2015)

## Abstract (arXiv)

We establish a general equilibrium theory for systems of large language model (LLM) agents operating under centralized orchestration. The framework is a production economy in the sense of Arrow-Debreu (1954), extended to infinite-dimensional commodity spaces following Bewley (1972). Each LLM agent is modeled as a firm whose production set Y a subset H = L 2 ([0, T ], R R ) represents the feasible metric trajectories determined by its frozen model weights. The orchestrator is the consumer, choosing a routing policy over the agent DAG to maximize system welfare subject to a budget constraint evaluated at functional prices p ∈ H A . These prices-elements of the Hilbert dual of the commodity space-assign a shadow value to each metric of each agent at each instant. We prove, via Brouwer's theorem applied to a finitedimensional approximation V K subset H, that every such economy admits at least one general equilibrium (p * , y * , π * ). A functional Walras' law holds as a theorem: the value of functional excess demand is zero for all prices, as a consequence of the consumer's budget constraint-not by construction. We further establish Pareto optimality (First Welfare Theorem), decentralizability of Pareto optima (Second Welfare Theorem), and uniqueness with geometric convergence under a contraction condition (Banach). The orchestration dynamics constitute a Walrasian tatonnement that converges globally under the contraction condition, unlike classical tatonnement (Scarf, 1960). The framework admits a DSGE interpretation with SLO parameters as policy rates.