Changelog: Companion Notebook 1

Subject: Change history for website/replication/companion-notebook-1.ipynb
Paper: “Money as a Medium of Exchange in an Economy with Artificially Intelligent Agents,” Journal of Economic Dynamics and Control, 14, 329–373.

2026-02-18¶

Bug Fixes¶

• Economy C GA parameters: Fixed ga_pcross=0.01, ga_pmutation=0.2 → ga_pcross=0.6, ga_pmutation=0.01. Confirmed as a bug by reading the original MATLAB code: class003.m calls winitial with no overrides, and winitial.m sets pcrosst=0.6, pmutationt=0.01 universally for all economies.

Algorithm Improvements¶

• GA rewritten to replicate ga3.m: Complete rewrite of apply_genetic_algorithm() to faithfully replicate the MATLAB ga3.m algorithm:

  • Two-stage parent selection: usage-weighted pre-selection ($p_2 = 0.7$), then fitness-proportional roulette wheel

  • Single-point crossover (was two-point) matching MATLAB

  • Ternary cyclic mutation (was random choice) matching MATLAB

  • Crowding-based replacement via cankill filtering (was weakest replacement) matching MATLAB crowdin3.m

  • N_pairs now computed from round(propselect * n_classifiers * 0.5) (7 trade pairs, 1 consume pair for 72/12 classifiers)

• Creation operator fixed: New create_classifier_replacing_weakest() replaces the most redundant or weakest classifier (matching MATLAB create.m), maintaining constant population size. Previously, classifiers were appended, growing the population unboundedly.

• EconomyConfig extended: Added GA parameters: ga_propselect ($p_1=0.2$), ga_propused ($p_2=0.7$), ga_crowdfactor_trade (8), ga_crowdfactor_consume (4), ga_crowdsubpop (0.5), ga_uratio (0.0, 0.2)

• GA parameters propagated: KiyotakiWrightSimulation, FiatMoneySimulation, and FiveGoodSimulation now pass all GA parameters through to apply_genetic_algorithm()

New Features¶

• A1.2 classifier strength tables: Added print_classifier_strengths() calls for all 3 agent types at both t=1000 and t=2000, replicating paper Tables 20–27

• Data-driven Wicksell triangles: New plot_wicksell_triangle() function reads actual exchange counts from simulation history and draws exchange pattern diagrams with arrow thickness proportional to exchange frequency. Called for all 8 economies with appropriate layout (triangle for 3-type, pentagon for 5-type).

2026-02-17¶

Bug Fixes¶

• Economy D IndexError: Fixed crash in print_5good_exchange_freq(), print_5good_holdings(), and print_5good_winning_actions() when called with negative t_idx — negative indices now correctly converted to positive before slicing

New Features¶

• Time-indexed analysis: print_exchange_frequency() and print_consumption_frequency() now accept a t_idx parameter for querying exchange/consumption frequencies at any historical time point, not just the final period

• Classifier strength tables: Added print_classifier_strengths() function showing top-N classifiers with condition strings, actions, strengths, usage counts, and specificity — replicating paper Tables 10–15

• Enhanced print_full_analysis(): Now accepts t_idx for time-specific full-analysis snapshots; uses historical holdings distributions when querying past time points

• Intermediate reporting standardized: Economies A1.2, A2.1, A2.2, B.1, and B.2 now report full analysis (holdings, exchange freq, consumption freq, winning actions) at intermediate time points using print_full_analysis() with t_idx, replacing ad-hoc manual holdings-only reporting

Algorithm Improvements¶

• Diversification operator activated: apply_diversification() now called in get_trade_decision() and get_consume_decision() for all three agent classes (ClassifierAgent, FiatMoneyAgent, FiveGoodAgent). Paper Section 6 specifies diversification is “used each time the classifier system is called upon” to ensure both actions are represented among matching classifiers

• Specialization operator implemented: Added apply_specialization() implementing the paper’s Section 6 specialization operator — probabilistically converts # wildcards to specific bit values with frequency $f_s(t) = 1/(2\sqrt{t})$. Integrated into all three simulation loops (KiyotakiWrightSimulation, FiatMoneySimulation, FiveGoodSimulation)

Documentation¶

• Economy C GA parameters: Added investigative comment noting that ga_pcross=0.01, ga_pmutation=0.2 appear swapped vs the standard pcross=0.6, pmutation=0.01 used in other economies — flagged for verification against the original MATLAB code

2026-02-16¶

Bug Fixes¶

• Classifier strength update denominators (Eqs 10–11): Exchange classifier now uses $\tau_e$ (n_used before increment); consumption classifier uses $\tau_c - 1$ (n_used before increment) — matching the paper’s exact formulation

• Consumption of wrong goods (Eq 12): Agents can now attempt consumption of any held good, receiving $u_i(k) = 0$ for $k \neq i$, rather than being blocked from consuming

• Economy B.2 bid parameters: Corrected bid_trade from (0.25, 0.25) to (0.025, 0.025) to match paper Table 2

• Economy C and D: Applied the same strength-update and consumption fixes to FiatMoneyAgent/FiatMoneySimulation and FiveGoodAgent/FiveGoodSimulation

New Features¶

• Frequency tracking: All three simulation classes (KW, FiatMoney, FiveGood) now track exchange and consumption frequency per period

• Analysis functions: Added print_exchange_frequency(), print_consumption_frequency(), print_winning_classifier_actions(), and print_full_analysis() for detailed result inspection

• Intermediate reporting: Results now reported at time points matching the paper’s tables (e.g., $t = 500, 1000$ for A1.1; $t = 1000, 2000$ for A1.2)

• Economy-specific analysis: Custom analysis functions for FiatMoney (4-good) and FiveGood (5-good) economies

Housekeeping¶

• Fixed section numbering to be sequential (1–15)

2026-02-10¶

companion-notebook-1.ipynb¶

Added three missing economies to achieve complete coverage of all eight economies from the paper’s master table (Table 1):

• Economy A2.2 (Section 5b): High utility ($u_i = 500$) with random initial classifiers and the genetic algorithm. Tests whether the GA’s increased experimentation enables agents to escape the myopic lock-in that prevented the speculative equilibrium from emerging in A2.1. The paper’s master table lists this economy with equilibrium type “S” (speculative).

• Economy B.2 (Section 6b): Model B production structure with random initial classifiers and the genetic algorithm. The paper reported this economy “had not converged after 2000 periods” but was “moving towards the fundamental equilibrium.”

• Economy D (Section 8): Five agent types, five goods, 250 total agents — the most complex economy in the paper and its key “triumph.” Includes:

  • FiveGoodAgent class with 3-bit encoding for 5 goods

  • FiveGoodSimulation class with the full production structure (Type I→Good 3, II→Good 4, III→Good 5, IV→Good 1, V→Good 2)

  • Holdings distribution table and time-series plots

  • Trading pattern analysis verifying the discovered fundamental-like Nash equilibrium

  • Production structure and exchange pattern diagrams (replicating paper Figures 10–11)

  • Discussion of why this economy matters: classifier systems discovered a Nash equilibrium the authors had not analytically derived

Updated existing sections:

• Summary table (Section 9): Now includes all 8 economies (A1.1, A1.2, A2.1, A2.2, B.1, B.2, C, D) with paper equilibrium type and simulation results

• Conclusions (Section 14): Expanded to reflect complete coverage, highlighting Economy D as the paper’s most compelling demonstration of classifier systems as equilibrium-discovery tools