Assessment Report: Companion Notebook 1

Date: 2026-02-16
Updated: 2026-02-18 — Items 1–8, 11, 13 addressed in PR #5
Subject: Fidelity assessment of website/replication/companion-notebook-1.ipynb relative to Marimon, McGrattan & Sargent (1990)
Paper: “Money as a Medium of Exchange in an Economy with Artificially Intelligent Agents,” Journal of Economic Dynamics and Control, 14, 329–373.

Executive Summary¶

The companion notebook provides a substantial Python replication of all eight economies (A1.1, A1.2, A2.1, A2.2, B.1, B.2, C, D) from the MMS 1990 paper. Core mechanics—the Kiyotaki-Wright matching framework, trinary classifier encoding, bucket brigade strength updates, and genetic algorithm—are implemented and produce qualitatively correct convergence behavior. However, several algorithmic gaps, missing outputs, and a runtime bug reduce replication fidelity. This report details the findings economy-by-economy and provides prioritized recommendations.

1. Algorithm Fidelity¶

1.1 Classifier System — What Matches the Paper¶

1.2 Classifier System — Discrepancies¶

1.3 Code Architecture Issues¶

2. Economy-by-Economy Comparison¶

2.1 Economy A1.1 (Complete Enumeration, Fundamental Equilibrium)¶

Parameters: All match the paper (Table 3). ✅

Qualitative Result: Paper shows rapid convergence to fundamental equilibrium (Good 1 as medium of exchange). Notebook produces same qualitative convergence. ✅

✅ Updated: Classifier strength tables now reported via print_classifier_strengths() for all 3 agent types.

2.2 Economy A1.2 (Random + GA, Fundamental Equilibrium)¶

Parameters: Match paper (Table 16). ✅

✅ Updated: Exchange frequency and winning actions now reported at both t=1000 and t=2000 via print_full_analysis(t_idx=999).
✅ Updated: Classifier strength tables (Tables 20–27) now reported at t=1000 and t=2000 via print_classifier_strengths().

2.3 Economy A2.1 (Complete Enumeration, High Utility)¶

Parameters: Match paper (Table 28). ✅

Qualitative Result: The paper finds convergence to fundamental equilibrium despite the unique theoretical equilibrium being speculative. This is attributed to overly general consumption classifiers in type I agents. The notebook reports this finding but does not display the consumption classifiers that explain the failure to support speculative equilibrium. The paper notes that “the classifier $c^1_{\#,0}$ was slowly gaining strength” which requires classifier-level inspection not currently available.

2.4 Economy A2.2 (Random + GA, High Utility)¶

Parameters: Match paper. ✅

The paper only provides a brief qualitative summary for A2.2 (“refer the reader to the working paper for tables”). The notebook reports holdings, exchange frequency, winning actions, and consumption frequency at t=2000. This level of detail exceeds the paper’s reported results — which is appropriate for a companion notebook.

2.5 Economy B.1 (Alternative Production, Complete Enumeration)¶

Parameters: Match paper (Table in Section 7.3). ✅
Note: bid_trade=(0.25, 0.25) — correctly 10× larger than other economies, matching the paper.

Key Finding in Paper: Economy B.1 shows speculative equilibrium at t=500 that transitions to fundamental by t=1000. This dynamic transition is the most interesting result for this economy. ✅ Updated: The notebook now reports full analysis at both t=500 and t=1000, including exchange frequency, winning actions, and consumption frequency.

2.6 Economy B.2 (Alternative Production, Random + GA)¶

Parameters: Match paper (Table in Section 7.3). ✅
Note: bid_trade=(0.025, 0.025) — correctly different from B.1.

2.7 Economy C (Fiat Money)¶

Parameters: All match paper. ✅

• Storage costs: ✅ [9, 14, 29, 0]

• Utility: ✅ 100

• Classifiers: ✅ E_a=150, C_a=20

• Bids: ✅ bid_trade=(0.025, 0.025), bid_consume=(0.025, 0.25)

• Fiat money: ✅ 48 units injected

• ~~GA params: ⚠️ pcross=0.01, pmutation=0.2 — appears inverted vs. standard values~~ ✅ Fixed: Now pcross=0.6, pmutation=0.01 matching MATLAB winitial.m

Economy C has the best table coverage among all economies.

2.8 Economy D (Five Goods, Five Types)¶

Parameters: Match paper. ✅

~~Runtime Bug:~~ ✅ Fixed. The IndexError in print_5good_exchange_freq(), print_5good_holdings(), and print_5good_winning_actions() for negative t_idx values has been resolved. Functions now convert negative indices to valid positive indices.

Extra content: The notebook extends the paper by running Economy D for 3000 periods (paper only reports to t=1750) and includes a trading pattern analysis that checks whether agent strategies follow fundamental equilibrium logic. This is a valuable addition.

3. Summary: Table Coverage¶

Legend: ✅ = matches paper, ⚠️ = partial/incomplete, ❌ = missing

4. Prioritized Recommendations¶

Priority 1 — Bug Fixes (Blocking)¶

1. ~~Fix Economy D results cell (Cell 51):~~ ✅ Done. Negative index handling added to print_5good_holdings(), print_5good_exchange_freq(), and print_5good_winning_actions().

Priority 2 — Algorithm Improvements (High Impact)¶

2. ~~Implement specialization operator:~~ ✅ Done. apply_specialization() implemented with $f_s(t) = 1/(2\sqrt{t})$ and integrated into all three simulation classes.

3. ~~Activate diversification:~~ ✅ Done. apply_diversification() now called in get_trade_decision() and get_consume_decision() for all three agent classes.

4. ~~Investigate Economy C GA parameters:~~ ✅ Done. Confirmed as a bug by reading original MATLAB code (class003.m calls winitial with no overrides; winitial.m sets pcrosst=0.6, pmutationt=0.01 universally). Fixed to ga_pcross=0.6, ga_pmutation=0.01.

5. ~~Refine GA parameter mapping:~~ ✅ Done. GA rewritten to replicate ga3.m from MATLAB: two-stage parent selection (usage-weighted pre-selection p₂=0.7, then fitness-proportional roulette wheel), single-point crossover (not two-point), ternary cyclic mutation, crowding-based replacement via cankill set. EconomyConfig extended with all GA parameters. N_pairs now computed from round(propselect * n_classifiers * 0.5), giving 7 trade pairs and 1 consume pair for 72/12 classifiers.

Priority 3 — Missing Outputs (Medium Impact)¶

6. ~~Add intermediate-time reporting for A1.2, A2.1, B.1, B.2:~~ ✅ Done. All economies now use print_full_analysis(t_idx=...) for both time snapshots. Economy B.1 consumption frequency corrected to t=500.

7. ~~Add classifier strength tables for A1.1:~~ ✅ Done. print_classifier_strengths() function implemented and called for all 3 agent types in Economy A1.1.

8. ~~Add classifier strength tables for A1.2:~~ ✅ Done. print_classifier_strengths() now called for all 3 agent types at both t=1000 and t=2000, replicating paper Tables 20–27.

Priority 4 — Code Quality (Maintenance)¶

9. Unify agent and simulation classes: Refactor ClassifierAgent, FiatMoneyAgent, and FiveGoodAgent into a single parameterized agent class. Similarly unify the three simulation classes. This eliminates the risk of divergent bug fixes and reduces notebook length by ~40%.

10. Extend EconomyConfig to cover C and D: Add fields for n_fiat (fiat money count), n_bits (encoding width), and ga_params dictionary. This enables a single summary function that can compare all 8 economies from their configs.

11. ~~Populate classifier count constraint:~~ ✅ Done. create_classifier_replacing_weakest() replaces most redundant (or weakest) classifier when no match found, matching MATLAB create.m. Population size is now constant across all agent classes.

Priority 5 — Enhanced Analysis (Low Priority, High Value)¶

12. Add convergence diagnostics: The paper discusses convergence criteria in Section 5. Implement a convergence metric (e.g., rolling window standard deviation of holdings distribution) and report whether each economy has converged by its final period.

13. ~~Add Wicksell triangle visualization for all 3-good economies:~~ ✅ Done. Data-driven plot_wicksell_triangle() function reads actual exchange counts from simulation history and draws arrows with thickness proportional to exchange frequency. Called for all 8 economies (A1.1, A1.2, A2.1, A2.2, B.1, B.2, C, D) with appropriate layout (triangle for 3-type, pentagon for 5-type).

14. Add side-by-side comparison with paper values: For each table output, display the paper’s values alongside the notebook’s simulation values. This would make discrepancies immediately visible. Since the simulations are stochastic, exact matches are not expected, but qualitative patterns should align.

15. Explore bid-based vs strength-based auction: The paper’s informal text describes “highest bidder” winning the auction, while the formal equation uses highest strength. For complete enumeration (uniform specificity), these are equivalent. For random classifiers (varying specificity), bid-based selection would favor more specific rules. Consider adding a parameter to toggle between the two modes.

5. Numerical Reproducibility Note¶

The notebook uses fixed random seeds (seed=42 for most economies), which ensures deterministic results within a single execution environment. However, the paper’s results come from different random seeds and (presumably) FORTRAN code. Exact numerical matches with the paper are not expected. The assessment criterion should be:

1. Qualitative convergence: Does the simulated economy converge to the same type of equilibrium (fundamental vs. speculative) as the paper reports?

2. Pattern consistency: Do holdings distributions, exchange frequencies, and winning actions show the same structural patterns (which goods are held, which trades occur)?

3. Dynamic behavior: Does the economy exhibit the same time-evolution characteristics (e.g., Economy B.1’s transition from speculative to fundamental)?

Qualitative convergence appears correct for economies A1.1, A1.2, B.1, B.2, C, and D. Economy A2.1 should converge to fundamental (matching paper), but verification requires the classifier-level analysis described above. Economy A2.2 is inherently ambiguous (paper reports inconclusive results).

Appendix: Paper-to-Notebook Table Number Mapping¶

The paper uses continuous numbering for all tables and figures. Below is the mapping: