Español – Home / Capital; an experiment
Simulating Pure Capitalism
(Under construction)
Manuel Muiños, Pablo R. Liboreiro, Esther Mañe Borras, Lucía Andrés Algaba, Ivan Aparicio Cabeza, Ashad Ayub Parween, Fatima Boumahdi, Elitsa Dianova Kostadinova, Mikael Faria Guerra, Berta Fernández Martínez, Doae Iallachen Ahmittach, Laia Lafuente Navarro, Rebecca Levy Sanchez, Alba Lozano Jurado, Miriam Martínez Rosales, Blanca Masalles Ráfales, Jacqueline Moral Pérez, Aleix Pagès Moya, Erik Pérez García, Andrea Rubio Auge, Alejandro Trasierra Rabanal, Mariami Tskhovrebadze Abramishvili, Aniol Vancells Rovira, Carlos Vidal Montesinos, Esther Zamora Onate.
The paper Simulating Pure Capitalism: Experimental Evidence with Human Agents was presented at the 32nd International Input-Output Association Conference, https://www.iioa.org/conferences/32nd , on June 26, 2026. This is a provisional text, and a longer version will be published.
The paper (in PDF or without a reader) are available.
Summary
(Subtitles allow access to the corresponding section.)Table of contents and acknowledgments.
We analyze three theories: Leontief input-output matrices, maximum growth or the Von Neumann (VN) model, and Maximum Benefit in the Long-term Perspective (MBLP). Input-output matrices are a special case of VN, and VN is a special case of MBLP. We analyze the relationship between MBLP-VN and general equilibrium theory. We also explain our vision of essential capitalism. We will see that our simulations resemble MBLP, and their long-term behavior resembles VN, but that there are also differences.
Description of our simulation.
We simulated capitalism in its purest and most essential form: agents who exchange and produce to maximize profit.
Each agent begins the simulation with a set of goods. First, they exchange with other agents; then they choose a production process, in which they consume the goods they have available and obtain new goods as products; and the procedure is repeated. The objective of each agent is to achieve the highest production at the end of the simulation.
Three simulations were carried out, 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 and comparison with the theory.
The behavior in the three simulations was similar, which suggests that capitalism behaves regularly and that laws describing its dynamics can be found.
Production: Total production followed patterns parallel to MBLP, and also to VN in the long run, but with some differences.
Prices: Delivery ratios were similar to MBLP values, and to VN values in the long run.
Inefficiency: There were imbalances and waste, and the production level was lower than MBLP; the long-run growth rate reached 20% compared to 25% for VN.
Instability: Decreasing oscillations of a cobweb-like nature developed, whereas MBLP and VN do not exhibit cycles.
Inequality: There was a high concentration of wealth, with a tendency towards monopoly.
Networks: Specialization in production and the formation of networks of regular customers were common.
Regulation: The operation of the agents acted as a real algorithm, achieving regulation of the economy, despite the uncertainty and complexity of the decisions.
A fundamental question arises: how does the market manage to resemble MBLP even in the first session and VN in the long term?
A theory can only be considered scientific if it is tested against empirical data and evidence. While the natural sciences use controlled experiments to verify their laws, in economics this process is much more difficult due to the complexity of economic systems and the lack of precise data.
We propose using simulations of artificial economies as a tool parallel to laboratory experiments, since they allow us to study the behavior of capitalism under controlled conditions and compare the results with theoretical predictions.
We focus on the theory of Maximum Benefit in the Long-term Perspective (MBLP) and the John von Neumann model (VN), trying to verify whether the simulations reproduce the dynamics predicted by these theories. Validation is based on verifying the similarity between different simulations, their agreement with theoretical predictions, and the prior relationship of these theories with phenomena observed in real economies. Finally, we argue that the artificiality of simulations does not invalidate their scientific utility, just as it does with experiments in other disciplines, and that they can be a valuable tool for studying certain aspects of capitalism.
Appendix A2: Optimal allocations.
An optimal allocation is one that maximizes an objective. We use tools such as linear programming and Lagrange multipliers, which can be interpreted as prices or values of resources. We also analyze the concept of duality, according to which the problem of allocating resources and the problem of valuing those resources are equivalent and closely related. We show that, when there are external exchanges, these values correspond to exchange rates or market prices.
The relationship between Long-Run Profit Maximization (MBLP) and General Equilibrium Theory (GET) is analyzed. MBLP can be interpreted as a special case of the General Economic Theory (GET), when the turnpike theorems apply or when competition favors those who maximize long-term outcomes. But also as an alternative theory to GET, because the Long-Term Production Theory (MBLP), like Von Neumann model (VN), is production for production's sake and not a consumption-oriented economy.
Furthermore, a distinction is made between two ideal forms of capitalism: PM1, in which agents pursue diverse objectives, and PM2, in which profit is the dominant objective of economic activity. The simulations performed correspond to this second case, as they aim to represent capitalism in its purest and most essential form.
Finally, the possibility is raised that competition favors the evolution from PM1 systems to PM2 systems, as well as the interest in studying this process experimentally in future research.
Appendix A4: Comparison with other experiments and simulations.
We compare our simulation with other classic economic experiments, such as those of Chamberlin, Smith, and Barceló. We emphasize that its main innovation is simulating a complete capitalist system with repeated production and exchanges and quantitatively comparing the results with economic theories such as MBLP and Von Neumann. Unlike traditional experiments, which focus on individual decisions or specific markets, our simulation studies the behavior of the economic system as a whole and in the long term. Furthermore, we compare simulations with human and computational agents, arguing that the former allow us to observe spontaneous behaviors and social relationships that are difficult to reproduce using computer models.
Appendix A5: Some final considerations.
Our capitalisms work: they manage to provide a solution to the extremely difficult allocation problem by acting as a real algorithm, something that some proposed alternative systems have failed to achieve.
But with fundamental problems: this solution exhibits inefficiency, instability, inequality, particularism, and dehumanization, among other difficulties.
References
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 slight alterations 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, November 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
Dorfman, Robert, Paul Anthony Samuelson, and Robert M. Solow
[1] Linear Programming and Economic Analysis, McGraw-Hill 1958, https://ia601400.us.archive.org/4/items/in.ernet.dli.2015.137776/2015.137776.Linear-Programming-And-Economic-Analysis.pdf
Hommes, Cars and Blake LeBaron
[1] (eds.) Handbook of Computational Economics 4, Heterogeneous Agent Modeling, North Holland 2018, https://dokumen.pub/handbook-of-computational-economics-heterogeneous-agent-modeling-volume-4-4-hardcovernbsped-0444641319-9780444641311.html
Kagel, John H., and Alvin E. Roth
[1] (eds.) The Handbook of Experimental Economics, Princeton Universit 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
Kantorovich, Leonid V.
[1] The Best Use of Economic Resources, Harvard University Press 1965, https://archive.org/details/bestuseofeconomi0000kant
[1b] La asignación óptima de los recursos económicos, Ariel 1968.
[1] Essays in Optimal Planning, IASP 1976, https://archive.org/details/lvkantorovichess0000kant
Leontief, Wassily W.
[1] Input-Output Economics, 2nd ed., Oxford University Press, 1986, https://archive.org/details/inputoutputecono0000leon
[2] “Theoretical Assumptions and Nonobserved Facts”, The American Economic Review, Vol. 61, No. 1 (Mar., 1971), https://www.jstor.org/stable/1910537
McKenzie, Lionel W.
[1] “Turnpikes”, The American Economic Review, Vol. 88, No. 2, 1998, https://www.jstor.org/stable/116884
Morgenstern, Oskar, and Gerald Thompson
[1] Mathematical Theory of Expanding and Contracting Economies, Lexington Books, 1976, https://archive.org/details/mathematicaltheo0000morg
Muiños, Manuel
[1] Notes on the structure and evolution of societies, Doctoral thesis, Complutense University of Madrid, 2011,
https://sites.google.com/view/manuelmuinhospaneng
[2] Computing Von Neumann, VIII Conference on Input-Output Analysis, 2019, https://sites.google.com/view/manuelmuinhospaneng/computing-von-neumann
Muiños, Manuel, Victor Creus Cuevas, Júlia Sagarra Silvestre, Èric Santos Martos, Adrián Teixidó Vera, Huishan Chen, Helena Claver García, Joel Fernández Ramón, Emma Filgaira Enri, Pol Gallego Sánchez, Rim Ingrachen Chkadri, Lucía Martínez Corrales, Natàlia Martínez Faura, Roser Massanes Talabante, Mariia Obukhova, Mohamed Oulad Fezari El Korchi, Mar Pérez Llorente, and Martí Profitós Perpinyà
[1] Capital; an experiment, 10th Conference on Input-Output Analysis, 2024 https://sites.google.com/view/manuelmuinhospaneng/capital-an-experiment
Neumann, John von
[1] “Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes”, Ergebnisse eines mathematischen kolloquiums (editado por Karl Menger), 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 Ecoomic Studies no 13, 1945, http://www.jstor.org/stable/2296111
[1c] “Un modelo de equilibrio económico general”, included in Barceló, Alfons (editor), 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, and Oskar Morgenstern
[1] Theory of Games and Economic Behavior, 3rd ed., Princeton University Press, 1953, https://vdoc.pub/documents/theory-of-games-and-economic-behavior-61h8p7eto6c0
Shapley, Lloyd S.
[1] “Stochastic Games”, Proceedings of the National Academy of Sciences, Vol. 39, No. 10, https://www.pnas.org/doi/10.1073/pnas.39.10.1095
Smith, Adam
[1] An Inquiry into the Nature and Causes of the Wealth of Nations, Oxford University Press 1976, https://files.libertyfund.org/files/220/0141-02_Bk.pdf
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, 3rd ed., 2018.
Sraffa, Piero
[1] Production of Commodities by Means of Commodities. Prelude to a critique of economic theory, Cambridge University Press, London 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, Barcelon 1966. https://es.scribd.com/document/375927835/Produccion-demercancias-por-medio-de-mercancias-Piero-Sraffa-pdf
Tesfatsion, Leigh, and Kenneth L. Judd
[1] (eds.) Handbook of Computational Economics 2. Agent-based Computational Economics, North Holland 2006, https://archive.org/details/handbookofcomput0002unse
Walras, Léon
[1] Éléments d’Économie Politique Pure, (édition définitive) 1926, https://gallica.bnf.fr/ark:/12148/bpt6k1181431v.texteImage