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The Emergence of Firms in a Population of Agents


  • Robert Axtell


A model in which heterogeneous agents form firms is described and empirically tested. Each agent has preferences for both income and leisure and provides a variable input ('effort') to production. There are increasing returns to cooperation, and agents self-organize into productive teams. Within each group the output is divided into equal shares. Each agent periodically adjusts its effort level to maximize its welfare non-cooperatively. Agents are permitted to join other firms or start up new firms when it is welfare maximizing to do so. As a firm becomes large, agents have little incentive to supply effort, since each agentÕs share is relatively insensitive to its effort level. This gives rise to free riders. As free riding becomes commonplace in a large firm, agents migrate to other firms and the large firm declines. It is demonstrated analytically that there exist Nash equilibrium effort levels within any group, but these are (1) Pareto-dominated by effort configurations that fail to be individually rational, and (2) dynamically unstable for sufficiently large group size. The out-of-equilibrium dynamics are studied by an agent-based computational model. Individual firms grow and perish, there is perpetual adaptation and change at the micro-level, and the composition of each firm at any instant is path-dependent. However, at the aggregate-level stationary firm size, growth rate and lifetime distributions emerge. These are compared to data on U.S. firms. In particular, the power law character of empirical firm size distributions is reproduced by the model. Log growth rates are distributed as a double exponential distribution, while the standard deviation in growth rates scales (decreases) with firm size, both in agreement with recent empirical analyses. Constant returns obtain at the aggregate level, in contrast to the increasing returns of the micro-level. A portrait of this agents-within-firms economy is developed by analyzing typical firm life cycles, typical agent careers, and through cross-sectional analysis. The model parameterization is systematically investigated. Right-skewed size distributions are robust to a variety of alternative specifications of preferences, compensation, interaction structure, and bounded rationality. The role of residual claimants within firms is briefly explored. Finally, it is argued any theory of the firm based on microeconomic equilibrium is unlikely to explain the empirical data on firm sizes, growth rates, and related aggregate regularities.

Suggested Citation

  • Robert Axtell, 1999. "The Emergence of Firms in a Population of Agents," Working Papers 99-03-019, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:99-03-019

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    Cited by:

    1. Chang, Myong-Hun & Harrington, Joseph Jr., 2006. "Agent-Based Models of Organizations," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 26, pages 1273-1337, Elsevier.
    2. Wright, Ian, 2005. "The social architecture of capitalism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(3), pages 589-620.
    3. Ying Fan & Menghui Li & Zengru Di, 2004. "Increasing Returns to Scale, Dynamics of Industrial Structure and Size Distribution of Firms," Papers cond-mat/0407383,
    4. Bill Gibson, 2008. "Keynesian And Neoclassical Closures In An Agent-Based Context," UMASS Amherst Economics Working Papers 2008-03, University of Massachusetts Amherst, Department of Economics.
    5. Buldyrev, Sergey V. & Salinger, Michael A. & Stanley, H. Eugene, 2016. "A statistical physics implementation of Coase׳s theory of the firm," Research in Economics, Elsevier, vol. 70(4), pages 536-557.
    6. Joshua M. Epstein, 2007. "Agent-Based Computational Models and Generative Social Science," Introductory Chapters, in: Generative Social Science Studies in Agent-Based Computational Modeling, Princeton University Press.
    7. Staffan Canback & Phillip Samouel & David Price, 2003. "Strategy and structure in interaction: What determines the boundaries of the firm?," Industrial Organization 0303003, University Library of Munich, Germany, revised 17 Mar 2003.
    8. U. Garibaldi & D. Costantini & S. Donadio & P. Viarengo, 2006. "Herding and Clustering in Economics: The Yule-Zipf-Simon Model," Computational Economics, Springer;Society for Computational Economics, vol. 27(1), pages 115-134, February.
    9. de Vany, Arthur & Kim, Cassey Lee Hong, 2003. "Stochastic Market Structure: Concentration Measures and Motion Picture Antitrust," Centre on Regulation and Competition (CRC) Working papers 30701, University of Manchester, Institute for Development Policy and Management (IDPM).
    10. Bill Gibson, 2007. "A Multi-Agent Systems Approach to Microeconomic Foundations of Macro," UMASS Amherst Economics Working Papers 2007-10, University of Massachusetts Amherst, Department of Economics.
    11. Francesco Pasimeni & Tommaso Ciarli, 2018. "Diffusion of Shared Goods in Consumer Coalitions. An Agent-Based Model," SPRU Working Paper Series 2018-24, SPRU - Science Policy Research Unit, University of Sussex Business School.
    12. Ge, Jiaqi, 2014. "Stepping into new territory: Three essays on agent-based computational economics and environmental economics," ISU General Staff Papers 201401010800004899, Iowa State University, Department of Economics.
    13. Robert L. Axtell, 2000. "Effect of Interaction Topology and Activation Regime in Several Multi-Agent Systems," Working Papers 00-07-039, Santa Fe Institute.
    14. Jacques Laye & Charis Lina & Herve Tanguy, 2006. "E-consumers' search and emerging structure of B-to-C coalitions," Computing in Economics and Finance 2006 374, Society for Computational Economics.
    15. Growiec, Jakub, 2010. "Knife-edge conditions in the modeling of long-run growth regularities," Journal of Macroeconomics, Elsevier, vol. 32(4), pages 1143-1154, December.
    16. Gatti, Domenico Delli & Guilmi, Corrado Di & Gaffeo, Edoardo & Giulioni, Gianfranco & Gallegati, Mauro & Palestrini, Antonio, 2005. "A new approach to business fluctuations: heterogeneous interacting agents, scaling laws and financial fragility," Journal of Economic Behavior & Organization, Elsevier, vol. 56(4), pages 489-512, April.
    17. Smith, David M.D. & Johnson, Neil F., 2006. "Pair formation within multi-agent populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(1), pages 151-158.
    18. Peter Marko & Petr Svarc, 2008. "Firms formation and growth in the model with heterogeneous agents and monitoring," Working Papers IES 2008/31, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Nov 2008.
    19. Veetil, Vipin P. & Wagner, Richard E., 2018. "Nominal GDP stabilization: Chasing a mirage," The Quarterly Review of Economics and Finance, Elsevier, vol. 67(C), pages 227-236.
    20. Tomas Klos, 1999. "Governance and Matching," Computing in Economics and Finance 1999 341, Society for Computational Economics.
    21. Edoardo Mollona, 2008. "Computer simulation in social sciences," Journal of Management & Governance, Springer;Accademia Italiana di Economia Aziendale (AIDEA), vol. 12(2), pages 205-211, May.
    22. Staffan Canback, 1998. "Managerial diseconomies of scale: Literature survey and hypotheses anchored in transaction cost economics," Industrial Organization 9810001, University Library of Munich, Germany, revised 04 Oct 2002.
    23. Mark Setterfield & Bill Gibson, 2013. "Real and financial crises: A multi-agent approach," Working Papers 1309, Trinity College, Department of Economics, revised Jul 2014.
    24. Myong-Hun Chang, 2009. "Industry dynamics with knowledge-based competition: a computational study of entry and exit patterns," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 4(1), pages 73-114, June.
    25. Edoardo Mollona & David Hales, 2006. "Knowledge-Based Jobs and the Boundaries of Firms Agent-based Simulation of Firms Learning and Workforce Skill Set Dynamics," Computational Economics, Springer;Society for Computational Economics, vol. 27(1), pages 35-62, February.


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