Money as a Medium of Exchange in an Economy with Artificially Intelligent Agents

Replication of Marimon, McGrattan & Sargent (1990)¶

This project provides a modern MyST Markdown version of the paper and a Python replication of the classifier system simulations from:

Marimon, R., McGrattan, E., & Sargent, T. J. (1990). Money as a Medium of Exchange in an Economy with Artificially Intelligent Agents. Journal of Economic Dynamics and Control, 14(2), 329–373. DOI: 10.1016/0165-1889(90)90025-C

The paper studies how artificially intelligent agents using Holland’s classifier systems learn to use commodity money in a Kiyotaki-Wright economy. Agents are endowed with production technologies and must trade to obtain their desired consumption goods. Through a bucket brigade payment system and genetic algorithms, agents learn which goods to accept in trade — and commodity money emerges endogenously.

The Paper¶

The original PDF has been converted to a MyST Markdown version — a modern, web-native format with cross-references, proper equation numbering, and navigable structure. The conversion captures ~93% of the original content including all 17 equations, 66 tables, 10 figures, 17 footnotes, and 21 references.

The key ingredients of the paper are:

• Kiyotaki-Wright (1989) economy: Multiple agent types with different production technologies, indivisible goods, and random pairwise matching

• Holland classifier systems: Trinary-encoded rules (0, 1, #) that compete via an auction mechanism to make trade and consumption decisions

• Bucket brigade: A payment system (Equations 10–11) that propagates rewards backward through the chain of classifiers responsible for successful outcomes

• Genetic algorithm: Periodic evolution of classifier populations through crossover and mutation to discover better trading strategies

The paper simulates 8 economies with varying parameters and demonstrates convergence to Nash-Markov equilibria, including the emergence of fiat money in Economy C.

Read the full paper text → | PDF → MyST conversion notes → | Download PDF

Python Replication¶

The primary companion notebook replicates all 8 economies from the paper using Python (NumPy, Matplotlib):

Supporting documentation:

• Quality Assessment Report — Detailed fidelity assessment against the paper (latest)

• Quality Assessment Report (2026-02-16) — Previous assessment

• Comparison with DeepSeek Implementation — How our replication compares to an alternative implementation

• Changelog — History of changes to the companion notebook

Experiments¶

• AlphaGo Implementations Comparison — Detailed comparison of two AlphaGo-style implementations