Comparison Report: Companion Notebook 1 vs. DeepSeek Notebook

Date: 2026-02-16
Subject: Comparison of website/replication/companion-notebook-1.ipynb with Tom’s DeepSeek implementation tom/MMS_deepseek.ipynb
Paper: “Money as a Medium of Exchange in an Economy with Artificially Intelligent Agents,” Journal of Economic Dynamics and Control, 14, 329–373.

1. Faithfulness to the Paper¶

Our notebook closely follows the paper’s actual mechanisms:

• Trinary encoding with proper 2-bit numeric representation ([1,0], [0,1], [0,0]) and # (represented as -1) wildcards, matching Table 1 in the paper

• Bucket brigade strength updates using the paper’s equations (10–11): cumulative average with inter-classifier payments between exchange and consumption systems

• Genetic algorithm with two-point crossover, generalization operators, and frequency $f(t) = 1/\sqrt{t}$ as specified in the paper

• Complete enumeration (72 trade + 12 consume classifiers) for Economies A1/A2/B, random initialization for A1.2 and C — matching the paper’s two approaches

• Reproduces all eight economies: A1.1, A1.2, A2.1, A2.2, B.1, B.2, C, and D

DeepSeek’s notebook takes significant shortcuts:

• Uses string-based encoding ("10#01#") rather than proper numeric arrays — functional but less faithful

• Strength updates are ad hoc: winner.strength = old_strength - bid_amount + reward instead of the paper’s cumulative-average bucket brigade (eqs. 10–13)

• The GA is a rough approximation — creates variations with random probability rather than the paper’s structured crossover/mutation/generalization operators

• Initializes strengths with “rational” priors (10.0 for correct actions, 1.0 otherwise) — the paper explicitly starts all strengths at 0 and lets agents learn from scratch

• Only simulates Economies A1 and A2 (100 periods each), missing B and C entirely

2. Scale and Results¶

Our notebook uses 50 agents per type and 1,000–2,000 periods as in the paper. DeepSeek uses only 10 agents and 100 periods, which is too short for meaningful convergence.

3. Architecture Decision: Shared vs. Individual Classifiers¶

Our notebook: All agents of the same type share one classifier system (as the paper specifies — “to economize on computation,” Section 5). This means 3 classifier systems total for 150 agents.

DeepSeek: Each of the 30 individual agents gets its own classifier system. This is 30× more classifier systems but doesn’t match the paper’s design. With only 10 agents per type and 100 periods, individual classifiers get too few learning episodes to converge.

4. Key Mechanism Differences¶

Bucket Brigade (strength updates)¶

• Ours: Implements the paper’s interconnected payment chain — the consumption classifier pays the exchange classifier, which pays the previous consumption classifier. Strengths are cumulative averages (eqs. 12–13), which is crucial for convergence via stochastic approximation.

• DeepSeek: Simple strength = old - bid + reward. No inter-system payments, no cumulative averaging. This fundamentally changes the learning dynamics.

Auction¶

• Ours: Highest-strength matching classifier wins (as in the paper — strength is the bid, modulated by specificity)

• DeepSeek: Same basic idea, but the bid function multiplies (b11 + b12 * specificity) * strength, which is closer to Holland’s original formulation than the paper’s modification

Genetic Algorithm¶

• Ours: Two-point crossover between strength-proportionate selected pairs, with separate generalization operator (replace specific bits with #) at rate $p_g$

• DeepSeek: Randomly modifies bits of the winning classifier with 10% probability per position — no crossover, no proper selection

5. Results Quality¶

Our notebook produces results matching the paper across all eight economies:

• A1.1: Type 1 holds 100% Good 2, Type 3 holds 100% Good 1 — matches Table 4

• A1.2: Fundamental equilibrium with GA-driven exploration — matches Section 5b

• A2.1: Fundamental equilibrium despite high $u$ — matches the paper’s key finding (Section 7.2)

• A2.2: Speculative equilibrium emerges with GA — matches Table 1

• B.1/B.2: Model B production structure — matches Sections 6a–6b

• Economy C: Agents learn to accept fiat money — matches Section 7

• Economy D: Five goods, five agent types — the paper’s most complex economy (Section 8)

DeepSeek acknowledges its own limitations: “Average absolute difference” is reported but with only 100 periods and 10 agents, the results are noisy and don’t clearly demonstrate convergence.

6. Presentation and Exposition¶

DeepSeek does well in:¶

• Clean separation of economy setup, classifier system, and simulation engine into distinct classes

• Explicit comparison tables against theoretical predictions (the analyze_results function)

• The examine_classifier_strengths function is nicely structured

Our notebook does well in:¶

• Rich mathematical exposition connecting code to the paper’s equations

• Holdings distribution plots over time (replicating the paper’s Figures 5–8)

• Exchange pattern triangle diagram (replicating Figure 2)

• Classifier inspection with human-readable decoding (G1, G2, G3, ¬G1, etc.)

• Strength distribution histograms

• Economy C fiat money simulation with emergence of money as medium of exchange

7. What We Could Learn from DeepSeek¶

• The analyze_results function with explicit theoretical vs. empirical comparison tables is a nice pedagogical touch we could add

• The structured print discussion/conclusions format is readable

Summary¶

Our notebook is a substantially more faithful and complete replication covering all eight economies from the paper (A1.1, A1.2, A2.1, A2.2, B.1, B.2, C, D), including the five-good Economy D which is the paper’s most complex demonstration. DeepSeek’s version is more of a sketch — it captures the general idea but takes shortcuts on every core mechanism (strength updates, GA, scale, shared classifiers) that materially affect whether the results actually replicate the paper’s findings.

The 10-agent, 100-period setup with pre-seeded “rational” initial strengths means the DeepSeek simulation is largely running on its initial conditions rather than demonstrating emergent learning, which is the entire point of the paper.