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Paper
A first paper with 18 co-authors has already been presented at the 10th Conference on Input-Output Analysis, https://io10.shaio.es/ , in September 2024, as a hasty, provisional, and limited description of the research, and also as an invitation to repeat the experiments.
To facilitate the study and understanding of the data, an update (July 11, 2025) of the presentation has been added (in PDF or without a reader) including data from the third simulation performed subsequently.
Summary
(Subtitles provide access to the corresponding section.)One of the greatest difficulties facing economics is contrasting empirical laws and theories, inevitably simple, with realities as complex as capitalism.
In other branches of science, this problem is solved with experiments, where conditions are controlled and behaviors are simple enough for the laws governing the phenomena to emerge.
In economics, data are not usually "hard," and large-scale experiments cannot be conducted. However, we can use simulations, as experiments are used in other branches of science, to quantitatively contrast theories in order to improve them.
We analyze three theories: Leontief input-output matrices, the maximum growth or von Neumann model (VN), and maximum long-term benefit (MLTB). Input-output matrices are a particular case of VN, and VN of MLTB. We analyze the relationship between MLTB and VN and general equilibrium theory. We also explain our vision of essential capitalism. We will see that our simulations resemble MLTB, and their long-term behavior resembles VN, but that there are also differences.
We simulate capitalism in its purest and most essential form: agents who exchange and produce to maximize profit.
Each agent begins the simulation with some commodities. They first exchange with other agents; they then choose a production process, in which the commodities they have available are consumed and new commodities are obtained as output; and the procedure is repeated. Each agent's objective is to achieve the highest output at the end of the simulation.
Three simulations were run, one in each semester of the 2023-2024 academic year and another in the second semester of the 2024-2025 academic year, with 210 UAB students as agents.
Results (very provisional).
The behavior in the three simulations was similar, suggesting that capitalism behaves regularly and that laws can be found to describe its dynamics.
Production: Total output followed patterns parallel to the MLTB, and also to the long-term VN, but with differences.
Prices: Delivery ratios were similar to the MLTB and long-term VN values.
Regulation: The operation of agents acted like a real algorithm, regulating the economy.
Inefficiency: There were disproportions and waste, and the production level was lower than the MLTB; the long-term growth rate reached 20% compared to 25% for VN.
Instability: Cobweb like downward oscillations developed, whereas there are no cycles in MLTB and VN.
Inequality: There was a high concentration of wealth, with a tendency toward monopoly.
Networks: Specialization in production and the formation of networks of regular customers were common.
Some considerations based on our simulations.
Our capitalisms work: they manage to provide a solution to the extremely difficult allocation problem by acting like a real algorithm, something that some proposed alternative systems would not achieve.
But with fundamental problems: this solution exhibits inefficiency, instability, inequality, particularism, and dehumanization, among other difficulties.
How does the market manage to resemble MLTB in the first session (and VN in the long run)?
Appendices
Teaching tool (very provisional).
The simulations were very effective as a teaching tool, allowing an intuitive understanding of how capitalism works, the uncertainty of agents regarding the future, exchanges aimed at producing for profit, price setting through negotiation, the importance of economic calculation, efficiency, reliable customers, contracts, etc.
Comparison with other simulations and experiments (very provisional).
Our experiment was inspired by Professor Barceló's simulation game, but we modified it to allow for scientific use, and we also attempted to improve its use as a teaching tool. We also made a comparison with the experiments of Chamberlin and Vernon Smith, and with most economic experiments, which tend to be limited to "micro" or even psychological aspects, while ours covers the dynamics of the entire system.
Simulations and economic theories (very provisional).
We point out the relationship with Sraffa and Von Neumann, as well as with the main visions of value.
Reiterate and improve the experiment, compare with AI as agents, contrast with other theories, etc.
Bibliography
Barceló, Alfons
[1] “Juegos de simulación con modelos económicos reproductivos”, El Trimestre Económico, Vol. 56, No. 223(3) (julio-septiembre de 1989), pages 547-569. https://www.jstor.org/stable/23397517
[1b] Reproduced with minor retouching and a small appendix with theoretical solutions to the models in Filosofía de la economía. Leyes, teorías y modelos, FUHEM – Icaria, 1992, pages 159-192.
Chamberlin, Edward H.
[1] "An Experimental Imperfect Market”, Journal of Political Economy, Vol. 56, No. 2 (Apr. 1948), pages 95-108, https://www.jstor.org/stable/1826387
Collado, Juan Carlos, J. Pérez, and Jordi Sevilla
[1] "La economía a través de un juego", Albarà, Valencia, noviembre 1977, pages 60-71. https://www.dropbox.com/scl/fo/19s0neiik3ou3vtqu8hcv/AJsomiJJcs74CHRJsYyPEOE/Collado%2C%20P%C3%A9rez%20y%20Sevilla?e=1&preview=La+econom%C3%ADa+a+trav%C3%A9s+de+un+juego.pdf&rlkey=sr6sbl4npbn52gem2o7l8c8i7
Dantzig, George B.
[1] Linear Programming and Extensions, Princeton University Press, 1963, https://www.rand.org/pubs/reports/R366.html
Kagel, John H., and Alvin E. Roth
[1] (eds.) The Handbook of Experimental Economics, Princeton University Press, 1995, https://dokumen.pub/qdownload/the-handbook-of-experimental-economics-9780691213255.html
[2] (eds.) The Handbook of Experimental Economics, volume 2, Princeton University Press, 2015, https://dokumen.pub/qdownload/the-handbook-of-experimental-economics-volume-2-the-handbook-of-experimental-economics-9781400883172.html
Leontief, Wassily W.
[1] Input-Output Economics, 2ª ed., Oxford University Press, 1986, https://archive.org/details/inputoutputecono0000leon
Muiños, Manuel
[1] Apuntes sobre la estructura y la evolución de las sociedades, Doctoral thesis, Universidad Complutense de Madrid, 2011, https://hdl.handle.net/20.500.14352/47818
[2] Computando a Von Neumann, VIII Jornadas de Análisis Input-Output, 2019, https://ddd.uab.cat/record/287089
Neumann, John von
[1] “Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes”, Ergebnisse eines mathematischen kolloquiums (Karl Menger ed.), vol. 8, pages 73-83, Deuticke, Leipzig 1937, https://www.dropbox.com/sh/pes5eth6td20cyo/AABcGIewPGI07Lq0Fn2nl6Nfa/Neumann/%C3%9Cber%20ein%20%C3%B6konomisches%20Gleichungssystem%20und%20eine%20Verallgemeinerung%20des%20Brouwerschen%20Fixpunktsatzes.pdf?dl=0
[1b] “A Model of General Economic Equilibrium”, Review of Economic Studies nº 13, 1945, http://www.jstor.org/stable/2296111
[1c] “Un modelo de equilibrio económico general”, included in Barceló, Alfons (ed.), El modelo de Von Neumann, Departamento de Teoría Económica, Universidad de Valencia, 1975, https://www.dropbox.com/sh/pes5eth6td20cyo/AADBk1kROrF3UJ0jgpJSvrXua/Neumann?preview=El+modelo+de+Von+Neumann.pdf
Neumann, John von, y Oskar Morgenstern
[1] Theory of Games and Economic Behavior, 3ª ed., Princeton University Press, 1953, https://vdoc.pub/documents/theory-of-games-and-economic-behavior-61h8p7eto6c0
Smith, Vernon L.
[1] “An Experimental Study of Competitive Market Behavior”, Journal of Political Economy, 70.2 (1962): 111-137. https://digitalcommons.chapman.edu/cgi/viewcontent.cgi?article=1027&context=economics_articles
[2] “Experimental Economics”, The New Palgrave Dictionary of Economics, pages 4215-4233, 3ª ed., 2018.
Sraffa, Piero
[1] Production of Commodities by Means of Commodities. Prelude to a critique of economic theory, Cambridge University Press, Londres 1960, https://www.nuevatribuna.es/media/nuevatribuna/files/2013/04/15/production_of_commodities_by_means_of_commodities.pdf
[1b] Producción de mercancías por medio de mercancías, Oikos-Tau, Barcelona 1966. https://es.scribd.com/document/375927835/Produccion-demercancias-por-medio-de-mercancias-Piero-Sraffa-pdf